# Standard Big Bang model vs Inflationary model

• B

## Main Question or Discussion Point

Hello.

I have some questions concerning the Standard Hot Big Bang model versus the Inflationary model.

I've read that the Standard model cannot solve the Horizon and Flatness problems but Inflationary cosmology can.

Firstly, is this so?
Any replies that are pitched at my basic level of understanding would be appreciated.

Secondly, it's my understanding that within the discipline of science a model or theory of greater explanatory power will supersede one of lesser power. Am I on the right track here?

Thirdly, I've read that in the Standard model there was no viable mechanism to solve the Horizon and Flatness problems. Is that so?

Lastly, assuming that the Standard model does suffer from these weaknesses and the Inflationary model doesn't is there any viable case for continued support of the Standard model over the Inflationary one?

Thank you,

Cerenkov.

Orodruin
Staff Emeritus
Homework Helper
Gold Member
The standard hot Big Bang model is generally not believed to be extendable back to the ”singularity” for several reasons. In that spirit, inflation is not so much a replacement of the BB as a (possible) extension of it designed to explain some things that otherwise would seem peculiar.

The question is therefore not so much if BB is able to resolve the horizon problem etc, but what happened before the onset of the standard hot Big Bang. One alternative for this, that offers a resolution of some issues is inflation. Inflationary models (or other cosmological models) necessarily need to include a standard BB after inflation ends or they would violate observations.

From what you say it seems that I've misinterpreted this graphic?

https://www.researchgate.net/figure/How-the-Concordance-Model-of-Cosmology-was-developed-Theories-and-observations-motivated_fig2_308806912

I suppose that this is a hierarchy, with each level building upon it's predecessor?

If so, then to rephrase one of my questions and split it into two parts.

Is there a case for maintaining that the second level (Hot Big Bang Theory, FRW) is a fully workable and adequate cosmological model?

While ignoring the CDM and Inflation levels?

Thank you,

Cerenkov.

kimbyd
Gold Member
To add a little bit more to this, these questions are still debated within cosmology. It's unfortunately a bit of a confusing topic.

The super short version of it is:
Certainly on the surface, inflation appears to solve the horizon, flatness, and singularity problems. However, when you look in more detail it's a lot more complicated. My personal take-away is that what we really need is data. If we could get a successor to the Planck satellite which was designed to measure polarization to a high degree of accuracy (such as the COrE mission proposal that wasn't picked up), then we'd have a chance of determining it.

From a purely theoretical standpoint, inflation is probably better. It's definitely superior in that it predicts a nearly scale-invariant power spectrum, which is what is observed (the classical big bang theory doesn't predict any power spectrum at all). But the horizon and flatness problem issues are really complex.

The justification for both problems is easy to state.

Horizon problem:
Locations on the CMB sky separated by more than about 1 degree could never have communicated with one another at any time, as their past light cones never intersect in the hot big bang model. So how did those regions end up at almost the same temperature without any causal connection?

Flatness problem:
In order for the universe to be, say, flat to 1% today, it had to be flat to around 0.001% when the CMB was emitted. Go back to the time of nucleosynthesis, and it had to be flat to better accuracy than a billionth of a percent. How could the early universe have become so incredibly flat?

Inflation attempts to solve both of the above problems in two ways:
1) By modifying the past expansion history, it ensures that every location within our observable universe was causally connected. In fact, inflation predicts a set of quantum fluctuations which would have formed the seeds of early structure formation, and the statistics we observe match the statistics we would expect from that.
2) Inflation asymptotically pushes the universe towards flatness, so that it becomes difficult to have an inflation model with any measurable spatial curvature at all.

However, it doesn't entirely solve the horizon issue because inflation has its own horizon problem: in order for inflation to happen at all, you need to have a small, nearly-uniform region dominated by a certain type of quantum field (dubbed the inflaton). That makes for its own horizon problem, but many theorists feel it's less of a problem because it's over a much, much smaller volume of space (much smaller than a proton). But from a theoretical standpoint it's not always clear that is a solution.

And on the side of flatness, the above argument for flatness implicitly assumes a certain kind of initial condition for the big bang model, one in which curvature is a free parameter whose natural range at the "start" is between -1 and 1 in some natural units, which would make values around one part in a hundred billion seem really, really odd. But what if that's the wrong way to look at things? It's possible that by being a bit more careful about reasonable values for the curvature at the start, the problem might go away. And indeed, some have come up with models where it's entirely natural for the curvature to be pretty much zero, even without invoking inflation.

For even more fun, inflation also doesn't solve the singularity problem: it has its own past singularity to deal with. This is largely interpreted as a statement that inflation had to start via some physical process, and that we can't just extrapolate backward in time to determine that process.

kimbyd wrote...

To add a little bit more to this, these questions are still debated within cosmology. It's unfortunately a bit of a confusing topic.

The super short version of it is:
Certainly on the surface, inflation appears to solve the horizon, flatness, and singularity problems. However, when you look in more detail it's a lot more complicated. My personal take-away is that what we really need is data. If we could get a successor to the Planck satellite which was designed to measure polarization to a high degree of accuracy (such as the COrE mission proposal that wasn't picked up), then we'd have a chance of determining it.

What about LiteBird? http://litebird.jp/eng/ Would that mission have a chance of collecting the data in question?

From a purely theoretical standpoint, inflation is probably better. It's definitely superior in that it predicts a nearly scale-invariant power spectrum, which is what is observed (the classical big bang theory doesn't predict any power spectrum at all). But the horizon and flatness problem issues are really complex.

I didn't know that, kimbyd.
About the failure of the Standard Big Bang model to predict anything about the (CMB?) power spectrum. Is this related to the near-perfect agreement between prediction and observation of the CMB blackbody radiation curve?

And surely, if the Standard Model says nothing about the power spectrum, that's another strike against it?
Making the tally three things that Inflation does say something about, but the Standard Model doesn't - the Horizon, Flatness and Power Spectrum problems?

The justification for both problems is easy to state.

Horizon problem:
Locations on the CMB sky separated by more than about 1 degree could never have communicated with one another at any time, as their past light cones never intersect in the hot big bang model. So how did those regions end up at almost the same temperature without any causal connection?

Flatness problem:
In order for the universe to be, say, flat to 1% today, it had to be flat to around 0.001% when the CMB was emitted. Go back to the time of nucleosynthesis, and it had to be flat to better accuracy than a billionth of a percent. How could the early universe have become so incredibly flat?

Inflation attempts to solve both of the above problems in two ways:
1) By modifying the past expansion history, it ensures that every location within our observable universe was causally connected. In fact, inflation predicts a set of quantum fluctuations which would have formed the seeds of early structure formation, and the statistics we observe match the statistics we would expect from that.
2) Inflation asymptotically pushes the universe towards flatness, so that it becomes difficult to have an inflation model with any measurable spatial curvature at all.

However, it doesn't entirely solve the horizon issue because inflation has its own horizon problem: in order for inflation to happen at all, you need to have a small, nearly-uniform region dominated by a certain type of quantum field (dubbed the inflaton). That makes for its own horizon problem, but many theorists feel it's less of a problem because it's over a much, much smaller volume of space (much smaller than a proton). But from a theoretical standpoint it's not always clear that is a solution.

And on the side of flatness, the above argument for flatness implicitly assumes a certain kind of initial condition for the big bang model, one in which curvature is a free parameter whose natural range at the "start" is between -1 and 1 in some natural units, which would make values around one part in a hundred billion seem really, really odd. But what if that's the wrong way to look at things? It's possible that by being a bit more careful about reasonable values for the curvature at the start, the problem might go away. And indeed, some have come up with models where it's entirely natural for the curvature to be pretty much zero, even without invoking inflation.

For even more fun, inflation also doesn't solve the singularity problem: it has its own past singularity to deal with. This is largely interpreted as a statement that inflation had to start via some physical process, and that we can't just extrapolate backward in time to determine that process.

That's interesting.
I was (naively?) under the impression that from this graphic (originally taken from Guth's book, The Inflationary Universe) that the Standard Big Bang model uses only GR and this breaks down where the upper grey line intersects the Y axis. At about 10-5. So you seem to be saying that an initial singularity isn't just an artifact of the breakdown of GR?

https://ned.ipac.caltech.edu/level5/Guth/Figures/figure3.jpeg

--------------------------------------------------------------------------------------

Fyi, the context of my questions has to do with an e-mail debate I'm currently involved in with someone who claims that the Standard Model is the best that cosmology can offer. I've raised the Horizon and Flatness problems and now await their reply. From what you've said to me, it looks like I can also legitimately ask them how the Standard Model accounts for the observed CMB power spectrum - seeing as it doesn't say anything at all.

Two further points that I'd like to check with you beforehand are these.
Since the Standard Model uses only GR then surely there is no way it can predict or account for the Planck-scale quantum fluctuations that the Inflationary Model uses to act as 'seeds' of galaxy formation?
Also, Baryon Acoustic Oscillations are caused by quantum-scale phenomenon aren't they? So presumably the Standard Model is also silent about them too, for the very same reason?

Thank you,

Cerenkov.

Orodruin
Staff Emeritus
Homework Helper
Gold Member
I am sorry, but it is unclear to me how you are using the term "standard model". The current "standard model of cosmology" is the $\Lambda$CDM universe and it certainly predicts the CMB temperature power spectrum correctly.

Bandersnatch
@Cerenkov I think you might be misinterpreting what is being said here. LCDM, while it does have limitations, is on a much firmer ground than inflation. The latter is still waiting for any concrete data to support it.
As such, LCDM is a robust theory in its domain of applicability (where issues like the horizon problem or initial singularity indicate where the domain ends).
Whereas inflation covers a different domain, and due to the dearth of data is more of a promising hypothesis at this point.

My apologies to Orodruin and Bandersnatch for any confusion caused.
I fully realize that the LCDM is the 'current' Standard Model of cosmology and that it adequately covers the various points raised so far in this thread. To explain further, please let me refer you back to the two graphics that I posted .

https://www.researchgate.net/figure...ies-and-observations-motivated_fig2_308806912

[URL]https://ned.ipac.caltech.edu/level5/Guth/Figures/figure3.jpeg[/URL]

The first one shows the evolution of cosmological models over time with the uppermost box being the earliest and the lowest being the 'current' Standard model. The second shows Alan Guth's usage of the word 'Standard', where he contrasts it with the Inflationary model that he introduced. In both cases the word 'Standard' is not referring to today's current LDCM model, but the General Relativity-only 'Standard' model that Inflation replaced.

Yes, I know and accept that this is an anachronistic usage of the word Standard and my bad for not explaining this at the outset.
However, the person I'm debating with maintains a stubborn position on what constitutes, 'Standard'. This is his definition, as far as I understand it.

The Standard Hot Big Bang model uses only General Relativity, the Friedmann-Robertson-Walker metric and was proved to be correct by Penrose and Hawking with their singularity theorems. It takes no account of quantum physics.

So you see, he's stuck in the first or second boxes of the Concordance flow chart of cosmology.
I'm attempting to point out that his so-called Standard model is not today's 'current' LCDM model. That it cannot solve the Horizon and Flatness problems as the LCDM model can. Hence this thread and hence the angle of my questions.

Once again, apologies for not being clearer from the outset.

Has this clarified what things for you, Orodruin and Bandersnatch?

Thank you,

Cerenkov.

kimbyd
Gold Member
What about LiteBird? http://litebird.jp/eng/ Would that mission have a chance of collecting the data in question?
It has a chance for sure. The problem in accurately measuring B-mode polarization is three-fold:
1) You need to be able to have an instrument which is very good at measuring polarization with minimal systematic error. The rotating half wave plate they mention achieves this.
2) Foreground signals are brighter than the CMB B modes. That means you need to have an instrument that is really good at separating foreground from background signals, and that means lots of frequency bands. Six bands from 50 to 320GHz may not be enough. This is compared with Planck which has nine bands from 30GHz to 857GHz.
3) Nobody knows just how dim the B-mode signal actually is. It might be too dim to detect.

I understand why they're going for a small design (cost), which requires some sacrifices. The rotating half wave plate design certainly makes it better than Planck for polarization. The small design probably means it won't be anywhere close to Planck in terms of resolution, but you don't need high resolution to measure B-mode polarization (primordial B modes are only apparent at large angular scales). They might be able to combine their results with Planck's to get better foreground subtraction to help cope with the limited number of frequency bands.

My guess is that if this satellite is launched and successfully detects primordial B modes, then that will spur investment in another, bigger design that will do a better job of it.

I didn't know that, kimbyd.
About the failure of the Standard Big Bang model to predict anything about the (CMB?) power spectrum. Is this related to the near-perfect agreement between prediction and observation of the CMB blackbody radiation curve?

And surely, if the Standard Model says nothing about the power spectrum, that's another strike against it?
Making the tally three things that Inflation does say something about, but the Standard Model doesn't - the Horizon, Flatness and Power Spectrum problems?
The standard big bang model has no mechanism to produce anisotropies. It does predict the CMB given the assumption of a homogeneous universe, and does strongly predict its black body radiation curve. But it says nothing at all about the power spectrum. The simplest idea is that the spectrum would have been scale-invariant. The scale-invariant power spectrum is one that is typically used as a null hypothesis to test inflation against, as inflation predicts that it can't be exactly scale-invariant (a scale invariant spectrum would result from a constant energy scale during inflation, but inflation has to end, so it can't have an exactly constant energy scale).

I don't think it's so much that the power spectrum was ever a "problem" with the big bang model, but just another signal that it was incomplete. It was known a long time ago that there had to be some physical mechanism to produce density variations throughout the universe, and the Big Bang model had literally nothing to say on the matter.

The nearly scale-invariant power spectrum can also be produced by some inflation alternatives, by the way. So it isn't strong evidence for inflation by itself.

That's interesting.

I was (naively?) under the impression that from this graphic (originally taken from Guth's book, The Inflationary Universe) that the Standard Big Bang model uses only GR and this breaks down where the upper grey line intersects the Y axis. At about 10-5. So you seem to be saying that an initial singularity isn't just an artifact of the breakdown of GR?

https://ned.ipac.caltech.edu/level5/Guth/Figures/figure3.jpeg
The thing is, inflation doesn't do away with General Relativity. It relies upon General Relativity being correct, and that we can accurately understand the early universe by using quantum field theory in curved space-time, without taking into account the effects of quantum gravity. And General Relativity predicts that there is a past singularity in any expanding universe, regardless of contents. The difference between the standard big bang and inflation is that inflation posits a new type of matter (typically a scalar field).

In the context of inflation, during the course of inflation the universe is rapidly diluted. This is what made inflation so attractive to so many theorists from the start: you could start with a universe that was completely irregular and full of all kinds of crap, and inflation would smooth all of that out, creating a uniform universe. Furthermore, it creates a set of perturbations in a statistically-uniform way that are easy to measure.

But if you reverse that logic and run the clock backward in time, then that means that if you have a universe at the end of inflation with anything in it at all besides the inflaton, then running back in time it will make that non-inflaton stuff get more dense at an extremely rapid pace, eventually to the point of creating a singularity.

What that means is that inflation has to have a start, and it's probable that quantum gravity has an impact on what that start looks like. Some of the critiques of inflation involve theorists who are concerned about the fact that quantum gravity isn't included (because, well, we don't really know the right theory of quantum gravity yet).

Fyi, the context of my questions has to do with an e-mail debate I'm currently involved in with someone who claims that the Standard Model is the best that cosmology can offer. I've raised the Horizon and Flatness problems and now await their reply. From what you've said to me, it looks like I can also legitimately ask them how the Standard Model accounts for the observed CMB power spectrum - seeing as it doesn't say anything at all.
FYI, the standard model of cosmology generally includes inflation. Specifically, single-field slow-roll inflation (note: this isn't a single model, but a classification that includes a number of models). Usually this is parameterized with two parameters: the scalar spectral index (which relates to how close the model is to scale invariance) and the tensor to scalar ratio (which is related to the attempts to measure B-modes, which would come from the tensor perturbations).

What you seem to be referring to is the standard (sometimes called classical) big bang model.

Two further points that I'd like to check with you beforehand are these.
Since the Standard Model uses only GR then surely there is no way it can predict or account for the Planck-scale quantum fluctuations that the Inflationary Model uses to act as 'seeds' of galaxy formation?
As stated, it isn't about it only using GR. It's that the standard big bang model includes no mechanism to lay down those perturbations. To see why this is, consider that this model does the following:
1) Assume a homogeneous, isotropic universe.
2) Determine the contents of said universe that we can measure (including normal matter, radiation, dark matter, and the cosmological constant).
3) Extrapolate back in time.

If you just do that, you get nothing that would produce any perturbations. You have to add something else to get any. And that's what inflation does: it adds a quantum field in the early universe which modifies the way the universe expands early-on and also seeds fluctuations.

Also, Baryon Acoustic Oscillations are caused by quantum-scale phenomenon aren't they? So presumably the Standard Model is also silent about them too, for the very same reason?
Baryon acoustic oscillations are the result of sound waves propagating through the plasma of the early universe. In inflationary theory, the original seeds for those sound waves would have been quantum in nature. These would have been the exact same seeds that set the perturbations in motion I've been talking about this entire time.

But once inflation was over, that quantum nature was basically irrelevant. They were sound waves in the early-universe plasma. The reason why they're an important measurement is because they leave a signature in terms of the typical separation distances between galaxies. Those early sound waves create a little peak at a certain distance, such that galaxies are a little bit more likely to be found at that distance away from one another than you might expect given no coherent sound waves in the early universe. That distance correlates distances measured on the CMB sky with distances between galaxies in the nearby universe. That correlation allows us to very, very precisely measure the spatial curvature of the universe.

It doesn't really have much to do with inflation or quantum mechanics, though. Those were just the seeds. If there was a different seed with different statistical properties, BAO would still be a thing, it'd just have different behavior.

What about LiteBird? http://litebird.jp/eng/ Would that mission have a chance of collecting the data in question?

It has a chance for sure. The problem in accurately measuring B-mode polarization is three-fold:
1) You need to be able to have an instrument which is very good at measuring polarization with minimal systematic error. The rotating half wave plate they mention achieves this.
2) Foreground signals are brighter than the CMB B modes. That means you need to have an instrument that is really good at separating foreground from background signals, and that means lots of frequency bands. Six bands from 50 to 320GHz may not be enough. This is compared with Planck which has nine bands from 30GHz to 857GHz.
3) Nobody knows just how dim the B-mode signal actually is. It might be too dim to detect.

I understand why they're going for a small design (cost), which requires some sacrifices. The rotating half wave plate design certainly makes it better than Planck for polarization. The small design probably means it won't be anywhere close to Planck in terms of resolution, but you don't need high resolution to measure B-mode polarization (primordial B modes are only apparent at large angular scales). They might be able to combine their results with Planck's to get better foreground subtraction to help cope with the limited number of frequency bands.

My guess is that if this satellite is launched and successfully detects primordial B modes, then that will spur investment in another, bigger design that will do a better job of it.

-------------------------------------------------------------------------------------------------------------------------

Re those B-modes, isn't there another problem, when it comes to detecting them? It's my understanding that the BICEP team fell foul of foreground contamination back in 2014. So, besides not knowing how dim they might be there's the additional challenge of knowing just how much foreground contamination to subtract when looking for them.

Cerenkov.

kimbyd,

Your full reply contains much for me to mull over. I will have to put aside some time to do that. Many thanks.

Cerenkov.

kimbyd
Gold Member

Re those B-modes, isn't there another problem, when it comes to detecting them? It's my understanding that the BICEP team fell foul of foreground contamination back in 2014. So, besides not knowing how dim they might be there's the additional challenge of knowing just how much foreground contamination to subtract when looking for them.

Cerenkov.
Foregrounds will definitely be the biggest challenge, and a satellite has an immediate advantage over a ground-based measurement such as BICEP: our atmosphere.

The primary problem with measuring the CMB signal precisely from inside our atmosphere is that most of the signal is blocked by water vapor and carbon dioxide (caveat: this is from memory, so I may be mistaken on the exact components that are the main culprits, but I think this is right). The contents of our atmosphere make it so that there are only a handful of frequencies where it is relatively transparent in the range where the CMB is bright. As you can see at the associated Wikipedia article, BICEP2 only measured the sky at 150GHz. This means that their instrument relied entirely upon modeling from other observations to determine the foreground result. They got the model wrong, which resulted in the false signal.

The LiteBIRD satellite proposal is vastly superior for foreground removal. It may still not be enough. This stuff is hard. But it certainly has a chance.