Christina, when you're ready.
Yeah. Okay.
Our pleasure to have Sarunas here from Chicago.
Aguas…
particularly hoping I was going to talk about gravitational waves, abroad, but the…
in the reheating time that the…
with the emulation that you did with Marco Studios. No, it's all there. Yeah, perfect! Yeah, so, gonna be here what I want. So, yeah, so we're gonna talk about sectors in the early universe.
And you have to gravitational wave there. Yeah, yeah, because it's actually mostly about gravitational waves, but I put a generic title so that I can talk about anything I want, but it's actually going to be about radiation waves. So thank you, Nico, for the introduction. I'm very happy to visit Rodgers, and yeah, you seem to have a very vibrant department.
And I'm really enjoying my time here. So, today I'll be talking about spectator scalar fields. So these are the fields that are present during inflation, but might not necessarily drive inflation, and I'll give all the definitions and introduce everything in a moment. And I'll primarily be interested in the gravitational waves, and what kind of signals or constraints we can expect from having these spectator fields in the early universe,
Um, original idea was to actually, um, look for new ways to probe, maybe,
the super heavy, whimsilla-like dark matter scenario, but unfortunately, it didn't work out. But we did manage to put some stronger constraints, and I'll show all the summary in the bots in a moment.
So, moving on to the outline, I'll first start by talking about inflation and spectator scalar fields. I'll give a couple of definitions and just simple, um, introduction of inflation.
Uh, of course, most of it might be… well, most people might be familiar with that, but I still want to summarize some key points.
Then I'll just briefly discuss curvature and isocurvature and their existing constraints. Primarily, I'll show that just by adding the spectator scalar field, and it could be any… it doesn't even have to be a scalar field, as long as it's a boson.
But I'll primarily be talking about the simplest possibilities. I'll show that it typically leads to the… it will generate blue-tilted isocurvature, which will then source the scalar perturbations and lead to gravitational waves.
And after that, that was summarized by showing some gravitia wave signals, what we can expect, what kind of constraint we can put by having this, uh, these additional gravitational waives coming from spectator scalar.
So, firstly, I'll just begin with a very simple summary, why we need inflation, and how it solves some big problems in hot big bank cosmology.
So the first very simple explanation is that the first problem is the horizon problem, is that how do you explain that two causally disconnected patches in space are sharing their almost the same temperature and look homogeneous and isotropic?
So, inflation, if you add some additional expansion of the universe in the earlier… in the early… in the very early universe,
You can actually show that some of these patches that seem to be causally disconnected were actually in contact at some very, very early time.
The second point that I want to mention is the usual flatness problem, is how do we explain that our universe appears so flat?
And we know that from the observations, but if you go back in time and start a little bit with your usual hotbic fan conditions, it means that
we had to have some very fine-tuned, extremely flat universe at the beginning of Hot Big Bang, and how do we naturally explain why our universe appears so flat? And inflation actually provides the solution for the flatness problem. And the third point, which is maybe even most important point these days, it wasn't that important back in the day when inflation was proposed in the 80s,
Right now, we're talking about the origin and structure of the universe, and inflation actually provides these primordial seeds that it could explain how our structure of the general… like, a general structure, for example, like galaxies, clusters, or voids actually form.
And the additional problem… and I put it in gray, but this is, like, additional expl…
Motivation for inflation, if you like Grand Unified Theories, or if you believe it, that we…
broke some higher-dimensional symmetry in the early universe, you would have some… you would have produced some topological defects or magnetic monopoles,
And because we're not observing them in the present… in our current universe, we need to explain somehow, if we believe in grand unified theories, why are we not seeing these magnetic models?
And inflation actually explains that if we broke that symmetry in the early universe, these topological defects, which get inflated away, and we would not actually observe.
So, cosmic inflation solved these very important problems, and in general, applying data will provide some constraints on inflation, and of course, we need some cosmological models that we will agree with the experiment.
So now we live in the near of precision cosmology, and the amount of data that we have is truly astounding, and it keeps coming and coming. It's very interesting to start connecting the data to our theories and models, and what we're seeing these days is truly
So, here I'm showing the blank CMB map, which, of course, many people have seen millions of times before, and on the right side on the bottom, it's showing the DESI 3-dimensional galaxy map.
And the key point is that inflation, it actually explained both of these pictures or phenomena, in a very nice way. So initially, inflation will see some primordial fluctuations, and they will stretch these quantum perturbations into astrophysical and cosmological scales, which will eventually exit the horizon,
After they're expanding, and then eventually, at some later times, they will re-enter the horizon and will lead to… it will lead to some interesting features, like CMBI isotropies.
Or, if they re-enter it a log later, they will give some gravitational perturbations, which will eventually grow into cosmic structure that we're seeing here with this three-dimensional galaxy.
So, this map just basically shows the cosmic web, which is primarily seeded by these
Uh, modes rendering the horizon at some wave time.
So this is a very general summary of cosmology timeline. Of course, I'm not including all the relevant details like BBN and, like, a recombination and so on, but I just want to emphasize the key points from the cosmological timeline, is that initially we have some inflation, which is just a rapid expansion in
This also… this epoch leads to quantum fluctuations.
Then, at the end of inflation, we're left with a universe which is just dominated by the energy density of the infliction, but somehow we need to reheat the universe because we have many particles, we have radiation, and something has to happen, so we need to heat the universe.
So typically, we assume that the simflaton will decay into some radiation, and you will have a very big energy dump of particles and usually some radiation. Of course, this is a very model-dependent statement, but I'll just treat reheating temperature as, like, uh, that's a variable.
Uh, for my gravitational wave signals.
So, the other two points that I just mentioned before is the cosmic microwave background, which corresponds to the light released when the universe was approximately 380,000 years old.
And then finally, again, I showed the DESI three-dimensional Galaxy cluster map, that modes that reenter the very late, they will lead to galaxies, cluster, and various structure of the universe that we
But what I wanted to emphasize is that the same framework of physics, primarily these perturbations that we see in the CMB and the structure formation, could also lead to the stochastic gravitational wave background, and if we have some additional fields during inflation, this will lead to some interesting signals, which are also primarily feeded by subcurvature.
Um, and some other perturbations that I'll show in a moment. The advisor would be very sad that you don't put BDN there.
Oh, did you hear? Yeah, because that…
Well, that sounds very pretty. We know that… No, no, I actually, I deliberately simplified so that you know, like, I didn't want to put the whole, like, uh, all, all things, because that would be confusing. So, like you said, it's missing a lot, you know, like…
face transitions and, like… How about VD is something that we know this too, right?
Well, yeah, yeah, I'm too, maybe lithium problem, but we knew already, you know, how to address it these days. But yeah, um, but then I, again, I did input it so that… I didn't want to talk too much about, yeah,
Um, so getting back to a very simple summary of inflation, this is just something, again, if you've seen this millions of times, too, I apologize. But then I just want to summarize the background dynamics and how actually the infliction evolves.
So I'm introducing a simple scalar field, which I call the inflictm phi, and then I'm assuming that it evolves using, uh, just following the usual Klein-Gordon equation, and here I have the additional Hubble friction, which is basically coming here because of the expansion of the universe,
Where Hubble is defined as a change in the scale factor as a function of time divided by the scale factor, so this is the usual definition of the Hubble parameter. For inflation to persist, we need the accelerated expansion so that the A double dot is greater than zero.
And then I'm also introducing the definitions of number of e-folds. So, one e-folds correspond to the scale factor growth by an exponential factor, and then the e-faults remaining after the mode exits the horizon will be given by this end start quantity, which
is typically, at least back in the day, it was known as, like, 50 to 60 folds, but if we actually introduced reheating and all the other variables, it's… it's…
Typically something like 45 to maybe 57 eFolds, but it's a very model-dependent statement. But I'll… in general, I'll include these details in my competition.
So what we know from…
Okay, could I ask a question question from Zoom?
Yeah. Yep.
Could you be more precise about A sub I and a sub star
Um, sorry, they subbed, uh…
A sub i and
Oh, uh, yeah, yeah, so here's just some, uh, general definition that I have for my number of e-folds. So, this is the initial scale factor that I'm picking, and this is the evolution of the scale factor with respect to my initial condition.
And here, uh, I'm actually specifying my A star is the moment when the CMB scale leaves the horizon.
So this is the usual 55E folds.
Uh, and this is the end of inflation.
But those are not free parameters, but arbitrary for the most part. Yes, that's right. They are arbitrary, but then I'll choose a model of inflation, and then I'll have… this will become more numerical, so it means that
I'm a… this… this is typically the number that, like, 45 to 55, or 50 to 60 folds before the end of inflation,
And this is the end of inflation with respect to when the CMB mostly at Horizon Scale.
Um, yeah, so what I wanted to emphasize now is that the observable CMBL large-scale structure modes only span approximately of 10 e-folds, and as I mentioned, inflation lasts a lot longer.
Uh, but before moving on to the actual picture of what we can measure and how to constrain inflation, I'll just briefly reintroduce the CMB observables and the slow roll parameters.
So inflation condition is given by this epsilon value, which is equal to minus H dot over H squared, and inflation lasts until it satisfies this constraint, so until epsilon is less than 1.
And then we can introduce the potential slow roll parameters, the usual epsilon and native parameters here, which actually depend only on the shape of the potential. If you look at some simple simplified single-field models,
So this is, in a way, like a… it only depends on the model of inflation.
But in a way, you can pick some inflationary potential B, and you'll get different, uh, slow roll parameters.
And then we can actually connect it to observable inflationary parameters, which is the spectral tilt of the curvature power spectrum.
And then the ratio of the denser bar spectrum to scalar bar spectrum.
So these are the quantities that are constrained by the CMB, and I'll show some plots for particular models, because I'll get to the point where my discussion, um, it cannot be general, because I have many, like, important non-linear effects, so I'll have to pick a model of inflation.
But this is the general picture of, uh, inflation. So I have the cosmic inflation, I have the plateau-like region,
And what I'm emphasizing here, that only this small part is actually appropriate by the experiment, which corresponds to approximately 10 keyfolds of inflation.
But if we expect to have 45 to 55, it means that we have a lot of dynamics that we're not constraining yet, and we actually don't know what's happening in this region.
So, here I'm just showing how the inflatown lake slowly rolls towards the minimum, and then starts oscillating, and then eventually reheats the universe and decays into some particles.
But we still don't know what kind of model inflation we can have, how many fields it contains, and we only see this very simplified picture there.
So we can also have multi-field inflation, and only this small part is actually brought by the experiment, but if we're considering multi-field models of inflation, that means that we'd have some interesting twists and turns and bends,
And this could still have some… something… some interesting features or enhancement of the curvature perturbations that were not constraining or observing yet.
So this is what we know right now. This is the matter-power spectrum. This is a three-dimensional linear matter spectrum at the present day, and this combines the blank data, dark energy survey data, SDSS, and EBOSS Lyman alpha data, and if you look at the wave number, which typically goes from 10 to the minus 4 to 1,
Uh, in the inverse megapar6, so that corresponds to this range of co-moving scales.
And if I translate it into defaults, that only corresponds to 10 defaults.
So, as I mentioned, for a more complete model of inflation, I can expect to have something between 45 to 60 eFolds, so it means that, in a way, I'm only constraining this very small part, and I could…
something interesting could happen if I'm considering a more complete model, but I need more data, I need more experiments,
to actually constrain or probe this, uh, whole range of inflation.
So this is, uh…
These are the proposed tip… it constraints and projections for primordial power spectrum, and the part that we are constraining now, that they know that the curvature power spectrum is almost scale invariant,
is given by Planck and Liman alpha data.
And here, I'm simply extrapolating the slide with a spectral dealer of 0.965, but like I mentioned before, we don't know what's happening for K values that are larger than the 1 inverse Mamba parsec, which corresponds to very small scale.
But we can have some very interesting features happening here. And I'll show that if you add some spectator scalar fields during inflation, you could actually enhance the curvature power spectrum, and eventually probe or constrain these models.
So this is, um, we only have the FIRS data for spectral distortions now. I still hope that Pixi or something else will get built to measure, actually, spectral distortions at, uh, yeah.
Where on this plot is constrained by the data? Here, so blank and Lyman Alpha, this is what we have right now. So it's just that little bit? Yes, and FYRUS is another one that we have. I wanted to put it in the, like, with dashed lines that are proposed missions, so I apologize for that. But we typically just have the…
limited amount of constraints now.
But I wanted to measure the… measure, no, like, and the other constraints, right? Because, like… Yeah. Right, so…
Uh, yes, but uh… but this… this would be actually the most interesting part that we could probe, because even if you have something interesting happening here, you would… that would lead to some spectral distortions and deviations from blackbody spectrum.
And I'm very disappointed that we're, you know, not building, like, Pixie or something else to measure, because… That's just…
For folks. Yeah, yeah, it was supposed to happen, but it keeps getting delayed. Yeah,
Yeah, it's been being too… since it continuously, but now they have more proposals, like some European proposals, but it's all, like…
paperwork. So, uh, I hope that this gets measured, because, like, so many things, like, just simple particle physics, uh, and cosmology, inflation could be measured, but just these spectral distortions.
And we have a very old, like, virus measurement, that's all what we have right now. So that's something that I'm a bit disappointed about in terms of the experiment, because it's…
Not an extremely expensive mission, and I don't know why we're not doing it faster.
As I understand this better. So, you're saying at higher skills…
higher Ks, higher K, shorter field. Yeah, small scale, yeah, small scale. Uh, yeah, there's no direct…
constraints. Yeah, that we don't have any. So, is there an issue with, um, connecting whatever data you do measure?
to the, um… I mean, yeah, to the primordial…
Spectrum is in unfolding all the nonlinearities that have been…
Um…
I'm not sure about that, because here, like, uh…
Um, if you would have an enhanced spirus spectrum… so, it's okay, so we're constraining it up to this point, and then we're basically… this is the only extrapolated line, so this is… we don't have any constraints.
So, I'm not sure about nonlinearity. So, um…
we get to some… the scales would become so small when you would definitely have to include that. So, yes, that we would need to… Or maybe you have my question's totally off base. I mean, I'm asking about, like, the non-linearities from structure, formation, like going to galaxies at or shorter scales.
you know, some payrolls and…
Yeah, that should actually matter.
Um… but, like, when you say, say, Lisa or something, can see stuff that 10 to the 12…
K, which is a super short scale. Yeah.
Um, oh, sorry, I'll just connect. So this is only through gravitational waves, because the enhanced curvature power spectrum will also lead to some enhanced, like, secondary induced gravitational waits, and then you can directly connect it to the gravitational wave constraint. Okay, so it's not, like, reprocessed by small-scale lanularity? So, so what would happen?
You would have… you would have this delta zeta squared piece, then this is going to source the gravitational waves, and you just take the laser constraints, and then if you're not seeing these gravitational waves, it means that it's not there.
So, in a way, these are, like, only gravitational weight constraints, and again, I'm emphasizing the point that this would be something different, like a spectral distortion measurement. So these are, like, a little bit different analyses. This is for gravitational waves, this is for spectral distortion, but still, like, with this combined analysis, we can
constrain the curvature power spectrum.
I think some people also do that with, like,
Now, linearities, but then I think those are very model of dependent. Model-dependent, yes. Atari, for example, of that, yeah.
Hmm. Yeah, I didn't want to… yeah, but that… you're absolutely right, but these are very model-dependent statements. I wanted to…
try to be as agnostic as possible, but then, of course, I'll get to the point where I'll have to pick a model and do something.
And then this is just, uh, another slide that, like, how do I translate the…
game modes into frequencies, but then, you know, this would correspond to picoertz frequencies. This is the usual nanohertz because it's this PTA and SKA, and then this course, Lisa and part of BBO would correspond to a millihertz frequencies.
But this is the whole summary of my discussion, is how can we actually approach these small scales? And scaling the Iranian power spectrum is consistent with the CMB and LSS.
So, this is, uh, this part that we know from the experiment.
Um, and do we also know from Planck measurements that applying pivot scale of 0.05 inverse mecoparsec, we have… we constrain the framework curvature of our spectrum to be of order 10 to the minus 9. So if you look at this plot, this is just here, this is the amplitude.
And then we also know that we have the upper limit for the premorial isocurvature power spectrum, and I'll also use this constraint from the CMB to see what kind of spectator scalar fields I could have.
So the key question now is, how could we probe the scales that are… well, small scales are k larger than 1 inverse mecoparsec, and that, as I showed in my picture, that this corresponds to inflationary dynamics towards the end of inflation. It could also show some interesting fecal
produce gravitational waves related to reheating dynamics. And finally, I'll discuss isocurvature and the properties of the scalar fields.
So this is a very general summary. Like, what if there are other scalar fields during, uh, inflation?
And I'll call them spectator-scaled fields, the ones that are present during inflation but are not driving inflation, and some examples could include the Higgs field,
that Betty Quinfield, if you like the Axiom Dark Matter, could be just a generic stable dark matter scalar or a vector, and something called, like, curvature online field, so these will be the fields that are there during inflation, but eventually they decay and just you get the centropy dump, and they leave some gravitational wave imprints.
Of course, there could be more, like, if you like theories of supersymmetry and supergravity, any
Others, fields in your… if you're doing, like, if you have super fields, you could also have signals coming from super fields.
But I, again, I didn't want to talk about supergravity.
Um, but we can expect to observe three key effects. So the first one is that we're… because of the curved background and how it's changing, non-adiabatically, we're going to have gravitational particle production.
Then, because of the presence of the spectator scalar fields, we're going to have isocurvature, power spectrum, and this is typically going to be blue tilted our spectrum. And this power spectrum is going to feed into secondary gravitational waves and produce some very interesting signals.
So this is just a quick summary. Gravitational waves are a direct probe of the early universe, and gravitational waves from spectator scalar fields will reveal more about inflation and reheating.
So, I get to the point where I need to pick a model of inflation. Um, I tried…
We tried to analyze it in the, like, as-modeled-independent way as possible. We tried different plateau-like models of inflation that still satisfy the current CMB constraints.
But while we were completing this project, like ACT and SPT data came out, so…
These models are not as great as they were when we only had planned data, but this would be a very, very different, uh,
dark seminar, because we don't actually, like, this is very interesting from the model-building perspective, that the scalar tilt is actually increasing, and then ACT data is showing that it's… it favors larger values.
Which, from, again, model-building perspective, it's actually not that easy to make models with such a small
deviation from one, or just, like, something that would favor, like,
uh, spectral tilt of 0.974, something would pack data shows.
So, but again, that would be a very different topic, and in general,
You would either need to do something more exotic, add additional fields, have very weird
constructions or potentials.
Um, you could still do it with some, you know, basic model building in supergravity. You would need to introduce some instabilities or some features, but in general, if we take some simplest models of inflation, like something like what's called T-model inflation,
Uh, proposed by Colossian Lind in 2013, which is just based on
The hyperbolic dam squared potential, or something that is just a generic, but do like inflation model,
Um, that is now getting a relatively low spectral tilt, and we would…
need to figure out a way how to increase it to favor the current data.
But this is, again, like, a completely different topic.
So, for our numerical runs, we picked the T-model of inflation, and when we started doing this project, it was perfectly fine.
Um, but then the key points that I want to emphasize is that that input on the realization scale is roughly over 10 to the minus 11,
Which I know from the primordial curvature Power Spectrum, and I'm taking the 55E folds of inflation, which is just a number. I could take something else,
Uh, but we also tried a little bit different plateau-like inflation models and slightly different NSTAR values,
And their results are not particularly sensitive to that. They're, like, maybe there's a factor of 3 or 5 difference, but in general, like, all the features are… they're still the same.
So, because we have the… because I'm taking this model, uh, the inflation scale is going to be of roughly 10 to the 13 GV,
and the N of inflation is given by this value.
And eventually, I'll compute the dimensionless power spectrum. I'll introduce some spectator scalar fields and see what kind of isocurvature power spectrum I can produce.
And I'll, again, I'll show all the definitions and summarize it to a couple of slides.
So, the first ingredient that we need is the gravitational particle production. During inflation and reheating, because we will be working with a curved spacetime, this will lead to the phenomenon of gravitational particle production, and because I'm introducing the spectator scalar field, I'll need to compute its abundance to figure out what kind of gravitational wave signals I could expect.
So first, um, this is just a very brief summary of simple quantization and curved spacetime. So, introducing my massive scalar field action and curved spacetime. So I have the inflaton,
Which is just driving my inflation, and my numerical runs my V, is going to be the hyperbolic tangent model.
And then I'm introducing the simplest spectator scalar field that I could have, so I'm just taking the quadratic potential here, like, which is 1 half m squared chi squared, and in some cases, I'll consider a direct interaction term between the spectator scalar field and the inflaton, and see what kind of signals I could expect.
But I'll primarily focus on this, like,
simple possibility of having, uh, spectator scalar field, which just has the simple quadratic potential.
Um, so now, if I have my spectator scalar field action, and I'm just dropping the infotain term here, in order to, uh, just have the conventional mode equation, I'll need to rescale my field in order to get rid of the Hubble friction,
And then I'll move to all four-year expand my field X.
And then just find this simple mode equation with the following mode frequency, so the things that I want to emphasize here is that M chi-squared is my bare mass,
term. When I turn on the interaction, it's gonna… I'm gonna have additional terms, sigma phi squared, but because I'm working in the curved background, it's always going to depend on my Ricci scalar, which is evolving during inflation and reheating. So this is the key point, the key ingredients that will lead to gravitational particle production. That's because my effective mass is changing non-adiabatically, and this reaches Ricci scalar is evolving from the usual
desiridisitor value, like, 12 each squared, and then it oscillates about the minimum, this will lead to the change in my effectiveness.
So this is a very simple, generalized picture of how I'm computing the co-moving number density.
So I have the spectrum here.
computed in the following way. So this is my case spectrum, and this is the usual K cubed over 2 by squared, and here I rewrote it in terms of the mode frequency.
Uh, and the field values in case space, or this is, if you're familiar with the Bugaluba rotation, this could also be rewritten in terms of the beta squared coefficient, which I'll show in a couple of slides.
Um, but here I'm just showing how my reaches scalar is evolving. So I start with some value here, where this is, like, quasi-disciplinary, then it evolving towards the minimum, and then it starts oscillating about this minimum, and the effective mass keeps changing.
And then if I compute the spectrum,
that's how it looks in general.
as the effective mass increases, I suppress my infrared modes, and then it becomes a Bluetoothilted, but I usually get an enhanced ultraviolet structure, and post-inflationary production.
So here, I'm showing the spectrum as a function of K modes, which are rescaled to the end of… with respect to the end of inflation. So it means that superhorizon modes correspond to K less than 1,
And then whatever happens after inflation, or post-inflationary particle production during reheating would correspond to K values that are larger than 1.
And then to, in order to compute the whole commuving number density of my produced spectator scalar fields, I would just integrate this spectrum.
Um, so now to get some intuition, uh, you don't have to do the numerics, and you can actually do it in, uh,
relatively simple way, just to know, like, the order of magnitude and what kind of number you can expect to have. So if I expect that at the end of inflation, or, like,
Well, okay, it should be HM, but something that
Um, that the energy density at the inflicon from a Friedman equation is just going to be 8 squared times n prime squared.
But then you can show using something known as, like, a stochastic formalism shown by Storabinski,
that, uh, if you compute the two-point correlation function of the spectator scalar field and multiply it by the mass squared, you can expect the order of magnitude to be approximately h to the fourth.
And then if you take the ratio of fro-chi, the energy density of the spectator scalar field over the infliction energy density, you can expect it to be H squared over N plane squared, and because my H is roughly over 10 to the 13 GB,
I can expect this ratio to be roughly of 10 to the minus 10.
So, of course, because when you do the full numerical spectrum, this will affect us, like,
There's going to be some prefactor, but I just want to emphasize that because of this,
uh, gravitational particle production effect and changing background, you're gonna have, uh, ROCI orofi at the end of inflation is going to be roughly of 10 to the minus 10.
Yeah, the reason you don't get…
production of the…
gluons and photons of the standard model is because of conformal invariance? Yes.
Because, uh, there's no Ricci scalar dependence. So, if it's massless, then it's conformally coupled, then, uh, then there's no reachescaler.
Alright, sweet. Yeah, so… But you would get it for DSU2K plus. I would, yeah, yeah.
Uh, for Higgs, for SCU, for, uh, many particles, yes.
Uh, it would just be a little bit different, in fact, because I'm primarily talking about scalars. So, because of polarization, I would need, like, transverts and longitudinal modes if I have supergravity, I would also have gravitinos.
So, yeah, we had a little bit different particle production, but I wanted to simplify this picture, and for particle production, Scalar is actually the simplest one. So, but, but…
you could have Vector or something else, yeah.
And it matters that they're boson slope.
Uh, yes. So, for fermions, because of Fermion direct distribution, you would be… you would get nothing.
Yeah, so I have to dig both out. So, like, scalars or vectors,
Um, vectors are… might even lead to stronger signals, so we might eventually do a paper on that, because…
Vectors don't have the isocurvature problem, so we could actually have larger particle production, which would enhance the gravitational…
Um, I'm sorry, gravitational wave background, but you… I don't know why we…
have not written a paper in that.
It's not a… it's not a difficult paper to write, like, because we have all the tools, we just change the equation of motion.
Uh, we should do that.
Yeah, but thank you for the question.
Um, so the UV particle production, because, uh, it's also very easy to understand this UV, uh, this post-inflationary particle production using this simple, uh, S-channel particle production with a graviton propagator.
So you can simply assume that you have the infotain condensate scattering through with a graviton propagator and producing some spectator fields X, and this particular part, because we can approximate that we have Minkowski background at the end of inflation, after a couple of e-folds,
We can actually compute the number, abundance, and part of the spectrum using the simple Feynman diagram. So this is a very straightforward and simple way to do it. But the only issue is that where we can capture the setter part, so we're missing this part of information,
But if it's a relatively larger mass, and if it doesn't lead to large exponential suppression, you could still use the Feynman diagram computation.
So the second part that I wanted to…
Yeah, go ahead.
Can I ask a question? Excuse me, I have some naive questions. Could you yeah in your in your formula for f sub chi. I mean, what presumably you're taking an expectation value of this thing in absolute square
Yeah. Yeah, I'm thinking…
In some state
I'm taking it to be zero.
Or at the minimum, basically.
If I would displace it, I would have, uh…
Wait, do you mean it
You mean in the ground state of that oscillator? I'm not quite sure what you're doing.
Yeah, so…
Okay.
What is the meaning of this? X sub k is a quantum field or a mode of a quantum field
Yeah, yeah.
Yeah. Yes.
So f sub chi is a scalar valued function of k and t. So what do you mean?
So I'm taking my, uh, expectation value of chi to be zero.
So it means that I'm not displacing my field, it's lying at the minimum.
Okay
Okay.
Um, if I would choose my field, that would lead to a very different phenomenon, and that has been computed. Then my classical would dominate, because my field would evolve during inflation,
And then my… I would get very different signals.
Okay, so that's the state in which you're calculating an expectation value, is that right?
That is correct, yes. Yes.
Okay, and then on the next slide
You had S over chi, I don't know what the S is. What is S over chi?
I'm sorry, at, uh…
The slide…
Yes, yes.
Oh, sorry, sorry, sorry, yes.
What is S divided by chi?
Yeah, yeah, sorry about that. This is just, like, a generic scalar, but then S or CHI, so this is just like a… I just wanted to denote the generic scalar, sorry about that.
Okay, got it.
Um, yeah, yeah, I should have clarified that, but yeah, but I just wanted to show that it's the same for some…
generic scaler. I think I took it from the paper where he had different channels, and he wanted to be the dark matter and the Higgs, so I think we just had a couple, like, it was like a sloppy notation, so I apologize.
Um, so this is just a scalar hour, uh, state.
Um, yeah, so now moving on to the blue tilted isopurvature part.
is that what I wanted to show,
Um, is that because of the presence of the spectator scalar fields, I'll have the element of isopurvature, and from the CMB constraints, I know that it has to be blue-tilted.
So, firstly, I'll just briefly remind the curvature perturbations and the isocurvature, uh, competition of the isocurvature. So, if I take the spacetime metric in the Newtonian gauge, I'll have some scalar perturbations, and the denser perturbations.
So, I'll show how these scalar perturbations could be eventually re-expressed in terms of the iso-curvature power spectrum, which will feed into the tensor perturbation at the second order. So, I'll get to that in a couple of slides.
But here's just the summary of, like, the definition of the uniform energy density curvature perturbation, which is the usual gauge invariant quantity, and then I'll just have some evolution of my inflodon, which I'm assuming that is fully converted into radiation. And I'll just take the usual Friedmann equations.
So, this is just a reminder of what is isopurvature. What is curvature and isocurvature. So curvature perturbations are some fluctuations of shape and geometry of space,
Leading to variations in local energy density, which eventually leads to the formation of galaxies, stars, clusters, and voids. So if I have two, uh, local spaces, like a space…
Um, local variables row here, and I turn on my curvature perturgations,
This is going to lead to some… but you cannot see this part, stuff like that.
Um… let me lower the zoom.
Yeah, how do I lower the bar?
including that. Yeah. So…
Now, if I made it better, because now you can see…
Uh… well…
the best I can do. Uh, so this is gonna lead to some over-dense region and under-dense region.
Um, oh.
Yeah. Yeah.
So, uh, in general, I can define it in terms of the gauge and varying curvature perturbation that I discussed before, and typically we talk about two-point correlation functions and compute the curvature power spectrum.
And then I'll… this is the usual dimensionless power spectrum that I was showing before, and uh… in general, you take some model of inflation, and you can compute the spectrum by computing your correlation function.
But now, because they have multi-fluid systems, so I'm adding additional component. So, because I have the spectator scalar field, this is going to lead to something that is known as isocurvature perturbations,
Which refers to some fluctuation between different components in the universe, could be, like, dark matter, or photons, or neutrinos.
And they could have an equal distributions, but overall curvature will stay the same.
So if I have two, um, uh, energy density distributions like these ones…
And then I turn on the isocurvature perturbations, you can see what one blue ball, which corresponds to a different fluid, went to this, like, different space.
So again, this is just, like, I turn on my curvature… isopurvature perturbation system and get something like this.
So, in terms of a more mathematical definition,
My supervature perturbation would be, uh, defined as the difference between the curvature power spectrum of the spectator scalar field minus the curvature power spectrum of the radiation.
And then I also complete the usual correlation function, and then I can also have the dimensionless isopurvature power spectrum.
So this is the numerical example, which was very, very difficult to compute, but we did manage to do it. So…
Here I'm showing, guys, so Hermitropower Spectrum is a function of K with respect to Kn.
Um, and then I'm showing different colors correspond to different masses. So, MCHI is varying from 0.5 to 0.9.
And in general, if I want to consider a…
gravitation-produced dark matter model. Because of these isocurvature constraints that are here,
I need… I expect my…
Um, dark matter candidate to be heavier than roughly 0.6 times the inflationary scale, so it means that, in general, we have a very narrow window for this scenario in terms of the masses.
It's roughly between 0.6 times the inflationary scale to maybe, like, 1.5, 1.7 times the inflationary scale, so the window of the gravitationally produced particles is quite narrow,
And we'll… I'll show later that we managed to put the lot stronger constraint from gravitational waves and narrow down this
to… like, a relatively narrow window for these freeze-in, uh, super heavy dark matter candidates.
So, all of a sudden…
The isopurvature.
field as the spectator field has become dark matter.
Not necessarily, but it doesn't have to be dark matter.
So I'm trying to do it in a general way,
Uh, but I'll show some plots where it's dark matter, and I'll have some plots when it's not dark matter.
Okay, because up till now, you didn't say the word stark matter. Yeah, that's right.
But this is just, like, a side point that I wanted to emphasize.
is because the iso curvature constraints they hold for the dark matter candidates. So I need… if I want to satisfy the plan constraints, and if it's my dark matter candidate, it has to be heavy.
But, uh, I can have any generic fields.
So, um…
But the tiles… hell…
specifically show dark matter and not dark matter.
doesn't have to be dark matter.
So I have a question. So if you, I mean, it looked to me like the iso curvature doesn't have a
A well-defined sign. It could be positive or negative. So, if you have many, many components, couldn't they cancel out?
Um…
You have zeta chi minus zeta R
Not sure what zeta R is. I thought it was from the
ZetaR would be… yeah, just let me show you the definition. So, uh, this is the definition. Zeta R would be the same perturbation, and then delta rho R over rho bar R prime.
So you would just put the radiation component here?
What do you think?
I see. Okay, so if you had many components, I mean, so if you go back to your isocurvature definition
Yeah.
Okay.
Okay, I don't see any reason why one should be… I mean, is there, it's a question. Is there no the previous slide, I think.
Um,
The definition. Yeah, there. Definition of curly s.
Yeah.
Is there some reason that Zeta Chi should be
much smaller or much larger than zeta R for all the components, because otherwise, if
Uh, no, not… no, not truly.
Well, if you have not one chi, but hundreds
Yeah.
And you can sum them up
You know, who knows? They could be cancellations, right?
Uh, yes, that's, uh, very, very interesting question. I have not thought about it, and…
I would need to think about it, like,
I don't know if they're… I don't see… No, because usually you talk about isocorture. Here is…
Yeah. Is the curvature in the density, you can also have in the different components, so you can always do that, but the apple, like, is…
Yeah, but that's what I'm thinking, but in general, if you're adding many, many fields and you have different distributions, on Facebook, you can have cancellation, right? So I'm not seeing any reason
Uh, while you couldn't have cancellation. So that's a very good point, that I could have clean solutions.
But, I mean, that…
I mean, unless you knew that the Zeta Chi's were always small compared to the Zeta R's or something
Sorry, can you repeat the question?
Unless you knew that the Zeta Chi's are always small compared to the zeta R's or vice versa.
I mean, but if you don't, they're comparable magnitude
Um… yeah, but we don't… we do… we do… we only have the upper limit for dark matter isocurvature.
But in general, I don't see… like, if you have multi-fluid system, and you have… you could have cancellation. Yeah, I don't know what would…
that what would happen?
Okay, thanks
Um, I also don't see a reason why you couldn't have that, but of course that would have to be, like, a coincidence, and…
Uh, but we don't know… I don't think that we have enough information to necessarily conclude that this cannot happen, so…
I think that this could happen, but maybe it's not as probable as
we could expect, but that does not mean that it's, uh…
It would be interesting if you had a model that enforced a cancellation.
Um, like, that generally comes to with…
I was thinking that this one. We can talk about it. I have some examples about this. That's a very, very interesting… yeah, I have never… yeah, thank you for bringing this up. I have not thought about it. This is a very interesting idea. Maybe that could be done more on the particle production part, that you basically write some equations of motion.
with some different, like, you know, reach scales and factors and see what kind of, like, effective mass cancellation you would have. Of course, if you're taking something more complicated, where eye curvature is generated later,
then, um… then that would be more complicated. But yeah, thank you for this, uh, very interesting question. I have not thought about it, and…
uh, you know, I'll definitely think about this cancellation aspect.
Yep.
Uh, but getting back to the isocurvature power spectrum, I'm just showing that if you have a directive direction between the spectator scalar field and the inflaton,
I would also suppress my curvature by just adding this interaction term, because my effective mass, as sigma increases, and if my infoton values of Planck value… phi is at the order of M Planck, then I can expect to have an effective mass which significantly suppresses my circurvature and makes it blue tilted.
So this is just, like, I'm showing two examples here.
Um, and this is just a generic slide that I wanted to show. I won't talk a lot about it, but we just managed to find, using, like,
for this, uh, well, quasi-decenter, this setter solutions and, uh, stochastic approach to find some very good analytical fits.
Which show that you don't necessarily need to do the full complicated simulations, and you can…
get relatively good analytics and still get gravitational wave signals that almost agree with the full numerical results.
Um, so this is the simulation that takes a ridiculous amount to produce, and it's a very complicated system.
Um, but in general, I'm just showing how this blue-tilla guy is super curvature is produced for the particular coupling of sigma over lambda of 10 to the minus 3 halves.
Um, and the key point that I wanted to show that
Uh, you start producing this blue-til that, uh, isocurvature during inflation,
then it keeps growing, growing, and then eventually, right after inflation, when you reach a scalar stops evolving, you kind of have this full blue-to-diso curvature, and the UV tail also is barely, like, always barely changing, but in general, you have this whole picture of isopurvature, which will then lead to gravitational waves.
So then the last part of the doc is the gravitational wave soars by the high super curvature in the field power spectrum, and this is the key point that I wanted to show and emphasize and show the signals.
So, getting back to the spacetime metric that I had before, I had some scalar perturbations that will eventually source the tensor perturbations at the second order.
And then, if I take this general equation of the second order, I will have some low frequency gravitational waves sourced by the isopurvature, but there's also another term, which will lead to high frequency gravitational waves, or field matter-power perturbations,
But I'm not exactly… I'm gonna show two, or maybe one slide on these gravitational waves, because I believe that it's going to be very, very difficult, if not… if probably, probably not even possible, to measure such high frequency gravitational.
Which, in this case, will be of, like, maybe gigahertz frequency or higher. So, I want to… I will primarily talk about the lower frequency gravitational loops.
Um, so now if I take this expression… Could you remember what it's not like a time derivator of the potential?
Oh, you already assumed something there. Sorry, where? In the blue.
like, it's only, like, gradients, right?
Uh, yeah, but they're at the higher order, so they're, like, I'm dropping that.
Okay. It is surprised. So there's one more term. In the usual literature, there are three terms.
Um, dropping that one because it's up the… if… I think it's at the cubic order, so it's… I'm taking the lowest order at the second order equation. There's one more term that I'm dropping.
Okay. So I'm just taking this, uh, simplified information. We could have an effect, but I… well, we don't know how to fully compute it, because when you're computing, the 2.
Before correlation functions.
You will have to, you know, take all these components, and then it's just… Oh yeah, they come down from the gate. You're basically dead.
Um, but this is the simplified picture. You can pick, uh, because you have the gauge freedom to do so, you can pick a simplified gauge. The gauge that simplifies these expressions.
So if I pick something known as the Uniform Density gauge, I have what's called co-moving gauge? That is correct, yeah.
Um, yeah, I don't know why we…
I don't know, more in modern books use a uniform. There's speech with you.
Um, so… Poisson equation now, it can be written in the following way, and if we move to k-space, and then solve it for H, we need to compute the two-point correlation function, and this is… of course, I'm dropping all the terms and I'm simplifying everything, because that's not the purpose of the talk.
But then I have to do the integral of this 4-point correlation function, which, as you can imagine, is pretty horrible.
Uh, we tried to simplify, we did manage to find ways how to…
do it almost, like, semi-analytically, but it took us…
I don't know, like, 3 months of just doing algebra.
Continue to have more than one field, the uniform?
It's not the same as the…
the uniform density gauge is not the same as the Komovic.
When you have several fields.
Um, because that's…
Oh, yeah, yeah, yeah, that's right, yeah, the commoding is for Tingle, inflate, like, inflation, same with you for, uh, uniform densities, uh, 2 or more. But yeah, but the end is, for one, it's the same. Yeah, yeah, totally, yeah, totally, I agree.
Uh, yeah, that four-point function is calculated in Minkowski space, or in Decido space. Uh, this one is in Minkowski. Minkowskowski. I…
Well, a visitor, that would be very complicated. But I did Minkowski, yeah, like, I wouldn't know. There was one more assumption, so I'll be very transparent and honest.
I did, like, a, you know, wig contraction, I split it into, like, two-point correlator functions, and then assumed that it's, like, Gaussian. In reality, these are some non-Gaussianities, and I would need to do an expansion, but that would usually lead to a stronger signal, actually. So I took the most conservative approximation, I assume everything's Gaussian, and then split it into two-point correlation functions,
This is the conservative estimate.
We are now trying to figure out how to do, like, with full-on-Gaussianities, but unfortunately, it's quite complicated.
And uh… we still haven't figured out how to do it, and the literature is not particularly helpful. It's helpful when you know exactly how to do, like, FNL expansion or something like that, when you can do, like, a nice perurative expansion, but if it's something more complicated, then we don't really know how to do it in a generic way and include the non-Gaussian.
hurt the non-Castian term's much smaller, though.
Um…
Not necessarily, actually.
Um…
this would… you're looking at the connected 4-point function, or…? Uh, we're looking at, uh…
Uh, let me see…
connect through disconnected.
We're looking at, uh, disconnected. Disconnected, yeah.
Um, so now I'm just focusing on this particular, uh, part of the HIJ, or sorry, of the source term, so I'm dropping the second term for high frequencies.
And then I'm just showing the… just including a couple of equations for gravitational wave density.
Uh, but this is the horrible integral that we have to solve. This is the… like, we really tried to simplify it.
Um, I…
Now, that's the best we can do, actually, so I'm… so this is, like,
3 months of work, actually, so…
It's… it looks pretty horrible, and we don't know how to simplify it. Eventually, we expect that this project to be a lot easier, but I think we got to that point where it's like, you know, like, sunk cost fallacy, we spend, like, half a year or a year. The original idea was…
We saw a very blue-tilted isocurvature. We wanted to find a new mechanism to produce primordial black holes.
But then we realized that it actually gets diluted, and then it doesn't work out. So then we switch to gravitational waves, and then I think we spend too much time, and we just had to finish it.
So it's… it's this project, but we're just being very stubborn. But basically, I get this quite a horrible integral, which
You could do a couple of rotations and tricks, and we… this is, like, super simplified, like, double integral, but what you do have here is a double isocurvature integral here for your power spectrum,
And you could… we still managed to do some semi-analytics and some fits, so it's not that horrible, it just took us a very long time to figure out this equation.
But these are, like, second-order effects, and that, unfortunately, physics gets very complicated.
So this is just the time.
I missed the I missed the definition of the the function in orange.
The delta squared sub S of P, what do you know about that function?
Oh, sorry, this is the Isaac curvature bios spectrum that I was showing. So, this is the…
Yeah
Uh… this was the spectrum.
Oh, I see. So you had to evaluate that numerical?
I see.
Yeah, yeah. But, but you… but we also know how to do the analytical, uh, fits, and we do have, like, a closed-form
Yeah, yeah, yeah. So this is the…
Oh, I see, there it is. Okay, it's an explicit function. Okay.
Yeah. So, again, this was solved in, like, quasi-visitor background, and then just to solve the mode equations, do some simplifications.
It's still a very complicated expression. Well, it doesn't look that bad, but it's…
It wasn't that easy, but it fits extremely well within the merits.
Okay.
Yeah, so the general summary is that…
You have some spectator skill that fields will generate isocurvature perturbations. These isocurvature perturbations will source the gravitational waves, and then these gravitational waves provide a new constraint or probe for inflation.
And now that's where I'm specifying the two main scenarios, so something that I call curv-yon-like scenarios, or, like, unstable fields that will decay.
The curve I don't like is maybe more like a historic relic. I could have just called them unstable fields, but I don't know, like…
I think I was inspired by older papers from the early 2000s.
Uh, and then the dark matter scenarios where my spectator scalar field is stable, uh, and that's going to lead to some very strong constraints for these particular dark matters.
Um, oh, just before continuing, I just want to emphasize the key point, that you will see some very red-tilted spectrum, and that's mostly coming from the P to the 7 and Q to the 7 piece in the denominator.
Um, so these are the gravitational wave probes, uh, so we have the Planck B mode constraint, the lightbird proposed mission, which we're still not sure if it's happening, because they keep…
They're not sure about the funding, like, uh, every month I hear different information. I hope that will happen.
Uh, we have the spectral distortion missions, the pixie that I showed before, which I still hope something will happen, because this is a very important regime for particle… well, particle physics and gravitational waves, and I'm really frustrated that we're not building it.
Oh, sorry, the CMBS4 should go away because it got canceled. That's another source of my depression.
Um, and then we… Oh, and resonant cavity should also be discarded, so… Okay, yeah, yeah. No, no, no, the high frequency, no, like, I introduced this, like, I keep forgetting to remove this part,
So, you know, I introduced… I got the… I had this bit, and then I gave the same, similar talk, and then the audience, they were, like, mostly, like, experimental people working with LIGO and so on. They were not happy.
So yeah, so sorry, so we did disregard the resonant cavity experiment because Iverted from, like, uh, 40-plus people that it's incorrect.
Even though that paper is very well cited and published and so on, that doesn't mean anything up here.
Can you elaborate on that, for those of us who are not in this field? Oh, yeah, safer, are you guys secretly referring to? Uh…
I don't know if I have the reference here, but I can show you after the dog, but basically they have this, like, resonant cavity proposal that converts gravitons into photons.
And then they expected to see it in the resonant cavity, but the problem is that the signal-to-noise ratio there, like, they're so optimistic that, like, the background would just, like, you would not see anything.
So, the whole paper, the whole idea, I think they're…
Many, many papers criticizing that particular paper, saying that the signal-to-noise ratio, that you would not see anything. So basically, that it's not that easy to convert gravitons into photons and have to get such a…
uh… great efficiency. So they're just, like, extremely overestimating how to do it.
Somebody got many citations.
Oh, that's, like, probably, like, a couple hundred now, or… but the critical papers are labeled telling them that… But it's, like, 50, but there's still, like, it was well-cited paper,
I maybe did not check it carefully, but in published version, it's not there, so at least I did that right, but you know, like, I thought it's well-cited, it's published at JCAP, it's a good paper, I didn't really look into that, because I just needed the parameter constraints, and then, you know, I started giving these talks, and I'll lie to people. What are you doing?
So, yeah, but basically forget about the high frequency part.
Um, so this is the perfection scenario, where I curvedon decays relatively late, so basically this ratio F chi… F chi is the ratio of rho chi and row radiation. When my matter-like field becomes almost… well, equals to the gig… uh…
When it's redshift, it keeps growing, and then when it becomes equal to 1.
Um, it decays. So this is, of course, it depends on when these, uh,
permit accounts decay. If I take this value to be a little bit smaller, then my signals get slightly lower, but it's not that sensitive to this particular ratio. It's the most sensitive… it's mostly sensitive to the reheating temperature.
So I'm varying the reheating temperature from 10 to the 13 to 10 to the 5 GV. If we have something below, let's say, 1TV in most cases, then you're not going to see anything. So, I just hope that, you know, we still have, like, roughly
Then, well, it was like 13 orders of magnitude if they were hitting temperatures relatively high, but if we get something closer to, like, TV scales, or below, or, like, maybe closer to GV or BBN scale,
then we're not going to really see anything. So, unfortunately, we don't know how to… we don't know enough about preheating, we don't know how to constrain it, we have too many orders of magnitude available, but as long as the reheating temperature is not crazy low, we should still see these gravitational wave signals.
But because of this red tilt that I'm showing, we can put some very nice constraints from ineffective bounds and non-observation of the B modes, and then eventually it's going to be probed by Lieberg mission.
So this is the particular scenario of MKI of 0.65, but I'll show a couple more examples.
Um, so here I'm turning on the, uh, direct interaction between the spectator field and the, uh, infotion, and I get very, very similar signals, and of course they large.
And I could put some strong constraints just from these, uh, uh, gravitational wave signals.
And this is a little bit more fine-tuning example.
Uh, that if you have, like, this particular range of .041 to .045, which is, again, this is, like I said, I'm telling you, it's a fine-tuning example, you would be able to see this multi-band, uh, you would be able to do this multi-frequency band test, and it would cross the light bird.
BMOT mission, and then, uh, nano, uh, nanohertz frequencies, and maybe, you know, LISA, BBU, or something else.
But this is… this is a little bit more model-dependent.
So now, I'm also emphasizing the dark matter scenario. The original idea was actually to look for new production mechanism for primordial black holes.
The second idea, which also didn't work out, was to maybe look for
how to probe this nightmare scenario, freeze in dark matter when you have some super heavy candidate. We expect… because when we saw the blue-tailed is a curvature, we expected that if blue till… if the iso curvature grows so much,
we should have… we should see some signals, but unfortunately, because of the threat till we can only put some stronger constraints.
Um, but that still leads to some interesting, uh, plots.
Where, in general, this was before only constrained by the isocurvature. I'm showing the mass.
Versus their reheating temperature. So again, as long as it's something above 10 to the 3 to, you know, 10 to the 13, so 10 orders of magnitude,
We can really constrain these dark matter models, but because of the ineffective bounds and non-observation of the Planck B modes, and if Lightbird will eventually happen, we'll have some even stronger constraints on these dark matter scenarios,
And we can impose this limit to be, like, maybe even greater than 0.8,
In terms of inflationary scale, which is, uh…
Now what we expected, but I would still think that maybe it's a very interesting result to at least start excluding some models, because, like, maybe these freeze-in models becoming
Well, super heavy dark matter models are becoming very limited, because you're only going to have very narrow range.
of masses, and it sounds very fine-tuned and special to actually occur in nature, and…
Like, if we get stronger signals, uh, or start stronger constraints, maybe, yeah, at least we could start excluding this particular, uh, dark matter model.
Um, this is just a quick summary that I showed before, that because of this particular presence of the spectator scalar field,
We will also enhance the curvature power spectrum, so that's the second throw that we could have, and that would cross us… that's why I emphasized the spectral distortion part, that if you have, like, pixie or something, if you're more optimistic, you could definitely see some features of the curvature power spectrum, and that could be… it doesn't have to be these particular models, it could be…
Many, many different models, just the presence of the spectator scalar field or something, like, even we know that the Higgs exists.
We know that it's unstable, there are some issues with what's happening within the early universe with the Higgs field, but in general, there are many models that could give this, uh,
enhancement in this particular range, and it would be very, very interesting to probe this specific, like, spectral distortion region.
And this is, like, of course, if I'm putting the direct interaction, I can enhance the curvature spectrum even more. But this is a more model-dependent statement, but at least if you have something
Uh, simple, and you do… you just have a spectator scalar field with relatively high reheating temperatures,
you could still have to… you could still expect to have these features.
And then this is my, uh…
The last slide, well, before the conclusions, but this is the high frequency part that I wanted to mention, which we, in a way, did for completion, because these high-frequency
high frequency graphic HOAs, I think, will be almost impossible if…
Uh, I don't know if they're gonna… how diff… they're probably… we're not gonna be able to probe them, uh, soon.
But I just did it for completion, because at least in this paper, we managed to, uh… before we get to this, like, strong back reaction regime, we did manage to do it fully analytically without doing the lattice study, so we did provide the full formalism how to do it with something like what is known as a heart-free Falk approximation, and just using the usual field theory.
So, it's an interesting result, but from
maybe more, um…
observational perspective, these high-frequency grad facial weights might not be that interesting.
So, here are my conclusions. Uh, that spectator scalar fields could, uh, are the new pro of inflation, and if we had any kind of spectator scalar field, and like I mentioned, it could be Higgs, it could be your superfield and supersymmetry or super gravity, it could be dark matter model, or it could be just some scalar that eventually decays,
It could lead to some very interesting gravitational wave signals, which is coming from the blue-tilated isocurvature,
These blue-tailored ISA curvature, um,
this blue toilet icy curvature Spectre will source these gravitational waves, which will span exceptionally broad frequency range, and then I'm
showing this, like, 10 to the minus 20 to 1Hz, which is a multiband test. And then we, of course, can start doing some interesting model building. You can consider direct interactions, we can add vectors, we can add something else.
And that will also lead to something very interesting, and in addition, it also leads to the broad resonance and high-frequency gravitational waves.
And then the joint gradation wave signals with the isocurvature bounce will lead to tighter bounds on dark matter, which is produced through ultraviolet freezing.
And, uh, here I'm putting this constraint of MCI greater than 0.7 times the inflationary scale, and this is a new probe of inflation.
Thank you.
Any more questions for our speaker?
I guess that you have, like, one dumb question. So, why you say that in the case when…
ROM equals to rhoR is just because you don't want to do the…
The equation state of the universe changed? Sorry, what do you mean? Would you say that your model indicates when the…
Probably, yeah, because you didn't want to do the…
Now, we actually did that in the paper, but I wanted to minimize the number of details in the talk, but in the paper, we included… we include that.
like our mother, eh, right? Yeah.
And then how you do it with an orientalities?
Uh, okay, with non-Gaussianities, we… No, we know linearities. Oh, non-linearities.
Um… or you just decay before the nonlinear… Yeah, we assume, yeah, yeah, that has to be okay before non-linear. But that's for sure, because that would just be, like, a completely separate project. Yeah, yeah, yeah. But we are still thinking about it, but we're so exhausted from this project that we just want to do something else.
Okay, if there are more questions, let's take the speaker, I'll get it.
way, way, way. Are you gonna be around for the internet? Yeah. Okay, so let me know if you want to go to dinner, and I will let you know which place are we going.
Thank you, Christina!
I can…
Oh, I'm