B How can the Big Bang model apply to the entire universe?

[icantevenn]

The ubiquity of the big bang holds no matter how big the universe is or even whether it is finite or infinite in size. How are we so confident that the part of the universe that is unobservable also falls under the Big Bang model?

 

[Ibix]

The bit of the universe we can see is well modeled by FLRW spacetime. We have no reason to believe the rest of the universe would be any different

So are we confident? I don't think that's really a question we can answer. We have no experience of the rest of the universe, or of other universes, on which we could base an estimate of confidence. All we can say is that, so far, everything we've seen is consistent with the non-visible parts of the universe being the same as the visible bits. But we have no idea how we might go about testing that.

 

[kimbyd]

The ubiquity of the big bang holds no matter how big the universe is or even whether it is finite or infinite in size. How are we so confident that the part of the universe that is unobservable also falls under the Big Bang model?

Generally, we aren't. The Big Bang model probably holds for some distance outside the observable, but there's no way to say how far.

 

[pervect]

The ubiquity of the big bang holds no matter how big the universe is or even whether it is finite or infinite in size. How are we so confident that the part of the universe that is unobservable also falls under the Big Bang model?

I'd agree with the other posters who say that it would be a misrepresentation of the current state of knowledge to say that we are confident about the behavior of the unobservable parts of the universe.

I would say that the general viewpoint is that because the unobservable part of the universe are unobservable, questions about these parts of the universe cannot be addressed by the scientific method. This means answering questions about the unobservable parts of the universe gets into the realm of philosophy (or possibly even religion), so to address those aspects, one would need to find a forum that talks about philosophy and/or religion. That forum isn't Physics Forum, however. Religious discussions were never allowed on PF , and philosophical discussions, which were initially limited to their own sub-forum (the Philosphy forum), became problematical in terms of academic quality and their tendency to spread to sections of the forum that were not dedicated to philosophy, so eventually the philosophy section of the forums was closed.

We can study scientifically what the big bang has to say about the observable part of the universe, and there has been quite a bit of rather impressive work done in the area. A key feature of the big bang model is that it predicts cosmic microwave background radiation (CMB) which we actually observe. Other cosmological models do not predict this radiation, and have fallen by the wayside as a result of this failure. I believe there have been at least two Nobel prizes awarded for such studies, the initial discovery of the cosmic microwave background radiation (CMB) with the prize awarded to Penzias and Wilson, and the COBE results, the award going to Smoot and Mather. The work did not stop with these Nobel-winning results, even more sophiticated studies (such as WMAP) have been done. The very short management level summary of all this work would be to say that the detailed predictions of our cosmological models are consistent with these experimental observations. So we must be doing something right.

Something else that can probably be talked about here is that the current scientific conception of the big bang is not that of a single event at a single point. This gets to be potnetially off-topic, and rather long, and I probably haven't worded this precisely enough. I believe Ned Wright discusses this somewhere in his cosmology tutorial, but I don't have an exact quote on this point.

 

[Chronos]

Generally speaking unobservable regions of the universe are veiled by some sort of horizon that causally separates them from the observable universe. We do not have a scientific basis to understand the laws of physics that apply to causally disconnected regions.

 

[phinds]

The ubiquity of the big bang holds no matter how big the universe is or even whether it is finite or infinite in size. How are we so confident that the part of the universe that is unobservable also falls under the Big Bang model?

Occam's Razor says that it's likely that the rest of the universe is the same as the observable part because otherwise there has to be something fairly weird going on that we have no clue about. That is NOT, of course, any guarantee of sameness, just highly suggestive.

 

[PeterDonis]

Generally speaking unobservable regions of the universe are veiled by some sort of horizon that causally separates them from the observable universe.

You have to be careful here. A more careful statement would be: regions of the universe that we cannot observe are behind a horizon with respect to us. But that horizon is only a horizon for us. It is not a horizon for an observer in a different galaxy a billion light-years from us.

 

[kimbyd]

Occam's Razor says that it's likely that the rest of the universe is the same as the observable part because otherwise there has to be something fairly weird going on that we have no clue about. That is NOT, of course, any guarantee of sameness, just highly suggestive.

I don't think that's entirely accurate. Occam's Razor is a statement about how many unevidenced assumptions underlie a theory or idea.

I think the correct statement is that we can be reasonably sure that the universe is about the same as our observable part for some distance beyond the observable (because having a universe that changes just beyond the limits of our observation would be a very specific configuration that would be an amazing coincidence: why wouldn't we see some of the change start to occur inside the horizon?). How far do things stay the same? It's unclear and unfortunately may never become clear. But stating that it goes on forever requires additional assumptions, so we shouldn't say that's the simplest answer.

 

[PeterDonis]

stating that it goes on forever requires additional assumptions

No, it doesn't; it just requires the same solution of the Einstein Field Equation that we already use to describe our observable universe. What would require additional assumptions is the claim that some other solution becomes the correct one at some point beyond the boundary of our observable universe.

 

[kimbyd]

No, it doesn't; it just requires the same solution of the Einstein Field Equation that we already use to describe our observable universe. What would require additional assumptions is the claim that some other solution becomes the correct one at some point beyond the boundary of our observable universe.

The problem with that is that we know that the Einstein Field Equations cannot be entirely accurate. So we know that there must be some other, underlying physical law to which the EFE are just an approximation. We can't guarantee that that approximation will work in regions we haven't observed, such as the very early universe and far beyond our horizon. Assuming that the approximation holds to infinite distance is an unevidenced assumption.

 

[PeterDonis]

The problem with that is that we know that the Einstein Field Equations cannot be entirely accurate.

If you mean we know there must be some underlying quantum theory of which the EFE is the classical limit in an appropriate sense, sure. But that doesn't change any of what I was saying. Quantum gravity effects are negligible in our observable universe, and so they should be negligible everywhere else in the model as well. So saying they somehow become non-negligible at some point outside our observable universe is still an additional assumption.

To put it another way: saying that the entire universe is like our observable universe is just saying that the universe is homogeneous. But that assumption is already built into the model anyway. So it's not an "additional" assumption you have to make; it's the simplest assumption you can make that is consistent with the evidence we have, which is why our current model makes it. Saying that the universe stops being homogeneous at some point outside our observable universe is what would be an additional assumption.

 

[kimbyd]

If you mean we know there must be some underlying quantum theory of which the EFE is the classical limit in an appropriate sense, sure. But that doesn't change any of what I was saying. Quantum gravity effects are negligible in our observable universe, and so they should be negligible everywhere else in the model as well. So saying they somehow become non-negligible at some point outside our observable universe is still an additional assumption.

Quantum effects could very well have had a large impact in the very early universe, which could lead to very different behavior sufficiently far beyond our horizon. And you don't even have to consider the more exotic possibilities of varying low-energy physics: absent some mechanism to make the universe uniform, we should expect very large deviations in temperature across sufficiently large distances. This is one of the things that inflation purports to explain: by blowing up a tiny region of the universe to cosmic scales, cosmic inflation guarantees that any temperature differences that may have existed before inflation began will be smoothed out to nothing within the observable region. But it doesn't guarantee that the variations won't be large on scales beyond the observable universe.

And when you get to things like the standard model of particle physics, which includes spontaneous symmetry breaking, the possibility of far-away regions of the universe having different low-energy laws of physics becomes apparent. And that comes without adding new assumptions to the theory: it's just combining the standard model of particle physics with the standard cosmology which predicts Planck-scale temperatures in the finite past.

Theories beyond the standard model tend to include many more ways in which the low-energy laws of physics might vary. I'm not aware of any BSM proposal that genuinely predicts unique low-energy laws of physics (the ones we observe), though I know many theorists would dearly like to discover such a theory.

To put it another way: saying that the entire universe is like our observable universe is just saying that the universe is homogeneous. But that assumption is already built into the model anyway. So it's not an "additional" assumption you have to make; it's the simplest assumption you can make that is consistent with the evidence we have, which is why our current model makes it. Saying that the universe stops being homogeneous at some point outside our observable universe is what would be an additional assumption.

This is overly-reductive.

The infinite homogeneity and isotropy that we find in the Friedmann equations is a result of one thing and one thing only: it makes the math simple. We should not assume that the fact that it makes the math simple means that this should be considered a guide to the behavior of the universe beyond the observable.

 

[PeterDonis]

Quantum effects could very well have had a large impact in the very early universe, which could lead to very different behavior sufficiently far beyond our horizon.

Only if the universe is non-homogeneous on cosmological scales. Which is an additional assumption.

absent some mechanism to make the universe uniform, we should expect very large deviations in temperature across sufficiently large distances

But there is no reason to expect "sufficiently large" distances to just happen to be a little bit larger than the size of our observable universe. Which means we should expect significant deviations in temperature across the region we can see. But we don't see that. Hence proposals like inflation to explain the observed homogeneity of the universe.

In other words, you're saying that we should expect the universe to not be homogeneous on large scales. Absent inflation, or some other mechanism to produce homogeneity, that's true; but it also contradicts observation. Occam's Razor doesn't tell you to force your theory to be so simple that it contradicts observation.

when you get to things like the standard model of particle physics, which includes spontaneous symmetry breaking, the possibility of far-away regions of the universe having different low-energy laws of physics becomes apparent. And that comes without adding new assumptions to the theory: it's just combining the standard model of particle physics with the standard cosmology which predicts Planck-scale temperatures in the finite past.

This is a valid point; however, it doesn't mean what you appear to think it means. Regions with different low-energy laws of physics, in terms of the classical approximation model on which our standard cosmology is based, are different universes. So whether they are present or not is a separate question from the spatial extent and spatial homogeneity of the universe we are in.

it makes the math simple

Because it's the simplest assumption consistent with the data. In other words, Occam's Razor.

We should not assume that the fact that it makes the math simple means that this should be considered a guide to the behavior of the universe beyond the observable.

This amounts to saying: we should not assume Occam's Razor. But your whole argument is based on Occam's Razor.

 

[rootone]

I am enjoying this guys, please continue.

 

[kimbyd]

Only if the universe is non-homogeneous on cosmological scales. Which is an additional assumption.

According to the current mainstream model, the universe is non-homogeneous on all scales. Hence the existence of galaxies. The homogeneity is just an approximation.

In the context of cosmic inflation, for example, the homogeneity only arises because the early expansion rapidly grows Planck-scale fluctuations to be cosmic in scale. As long as inflation lasts long enough, this guarantees that the observable universe will be approximately homogeneous. But it makes very little statement about how far that approximate homogeneity extends. In fact, according to many inflation models, the prediction is that the universe far beyond the observable will be wildly inhomogeneous (as quantum effects will cause the average energy of the inflaton field during inflation to change enough to impact the rate of expansion). There are lots of caveats and mathematical difficulties with these models, but the overall picture is clear: if cosmic inflation is real, then the universe on scales much larger than our horizon cannot be assumed to be remotely homogeneous.

But there is no reason to expect "sufficiently large" distances to just happen to be a little bit larger than the size of our observable universe. Which means we should expect significant deviations in temperature across the region we can see. But we don't see that. Hence proposals like inflation to explain the observed homogeneity of the universe.

In other words, you're saying that we should expect the universe to not be homogeneous on large scales. Absent inflation, or some other mechanism to produce homogeneity, that's true; but it also contradicts observation. Occam's Razor doesn't tell you to force your theory to be so simple that it contradicts observation.

By "sufficiently large" I mean scales much, much greater than our cosmic horizon. You should note that I made precisely this point earlier that what we can expect is that, given observation, the universe remains approximately homogeneous for a significant distance beyond our cosmic horizon. My naive estimate would be to expect approximate homogeneity for at least a few tens of Hubble radii for there to be no observational consequences. I'm sure that given a specific model, it would be possible to make somewhat more careful estimates, but there will be a lot of speculation put into any such estimate so we should always take them with a grain of salt. One way to make some progress with this would be to take the failure of observational searches for cosmic superstrings to put a lower bound on the estimated distance to the nearest domain wall (besides, modeling an expanding universe with domain walls might be a very difficult exercise; I'm not aware of it being done to any significant degree).

This is a valid point; however, it doesn't mean what you appear to think it means. Regions with different low-energy laws of physics, in terms of the classical approximation model on which our standard cosmology is based, are different universes. So whether they are present or not is a separate question from the spatial extent and spatial homogeneity of the universe we are in.

That's a matter of semantics that I'm not sure is relevant. For one, it would imply a finite universe, which breaks the assumption of infinite homogeneity.

This amounts to saying: we should not assume Occam's Razor. But your whole argument is based on Occam's Razor.

Hardly. The problem with this is that this is an argument based upon the FLRW universe. But the FLRW universe is not completely accurate. This is necessarily true because our universe is not perfectly homogeneous and isotropic (if it were, the Earth and Sun couldn't exist: the entire universe would be a uniform gas).

The most accurate theory we have right now to describe the universe on cosmic scales is described by Cosmological perturbation theory, where the FLRW metric is taken as a baseline with deviations from that baseline included. This is still an approximation, but it also breaks the fundamental assumption that you're relying upon: that the universe is homogeneous and isotropic.

The thought process you are describing is the same as a person who lives in the US Midwest and never travels more than five miles claiming that the simplest explanation is that the entire Earth is just like their local area. Within that area, the only bodies of water are a few ponds and streams. There are no hills of note, and no mountains are visible. Some stands of trees dot the landscape, mostly associated with farm houses. There are a large number of corn fields plus a handful of soybean fields. Were they resourceful and dedicated enough, they might conclude that the Earth is spherical. But without traveling further or talking to people outside their area, they would have no concept of lakes, mountains, or oceans. Cliffs and waterfalls would never occur to them. The universe far beyond our cosmological horizon might be even more diverse than this analogy would suggest.

Certainly if you just look at the simplest possible model of our universe, the FLRW model, it looks like homogeneity is the simplest. But if you dig a little bit beneath the surface and examine more precise models, that apparent simplicity evaporates as it becomes clear that any model more complex than FLRW actually requires more parameters to describe a universally-homogeneous model than one that varies on scales much larger than the observable.

 

[PeterDonis]

According to the current mainstream model, the universe is non-homogeneous on all scales. Hence the existence of galaxies. The homogeneity is just an approximation.

This is not correct. According to the current mainstream model, the universe is homogeneous on very large scales--basically large compared to the size of clusters of galaxies. And that is the only distance scale the model of the universe as a whole addresses. That model is an approximation, yes, in the same way that the model of a real fluid as a continuum is an approximation, since the real fluid is made of atoms. But that still doesn't change anything I said before.

if cosmic inflation is real, then the universe on scales much larger than our horizon cannot be assumed to be remotely homogeneous

And if that turns out to be true--because we collect additional evidence that convinces us that cosmic inflation is real--then which model is the simplest model consistent with the evidence will change, because the evidence changed. But we're not currently in that position.

For one, it would imply a finite universe

I think that depends on the model; AFAIK there are models in which each "bubble" formed by spontaneous symmetry breaking is spatially infinite. But all of these models are speculative at this point.

this is an argument based upon the FLRW universe. But the FLRW universe is not completely accurate

I already addressed this. Yes, the FLRW universe is an approximation. But the approximation you are talking about here, as I said above, breaks down on distance scales smaller than the scale of homogeneity, not larger. So it's irrelevant to the discussion here, which is about what happens on scales larger than the observable universe.

The most accurate theory we have right now to describe the universe on cosmic scales is described by Cosmological perturbation theory

Reference, please?

if you dig a little bit beneath the surface and examine more precise models

References, please?

 

[kimbyd]

To narrow the discussion (as it's gotten rather verbose), and because I think that this point is the most concrete, I'm only going to respond to the first paragraph.

This is not correct. According to the current mainstream model, the universe is homogeneous on very large scales--basically large compared to the size of clusters of galaxies. And that is the only distance scale the model of the universe as a whole addresses. That model is an approximation, yes, in the same way that the model of a real fluid as a continuum is an approximation, since the real fluid is made of atoms. But that still doesn't change anything I said before.

The universe is approximately homogeneous on large scales. This is most clearly visible in the CMB power spectrum:
https://lambda.gsfc.nasa.gov/produc...s/nineyear/cosmology/images/med/gh9_f02_M.png

If your assertion was correct, then the power spectrum would be indistinguishable from zero at low $\ell$. Instead, it flattens out at around 1/6th the peak variance. This is because the primordial source of these perturbations created variations in density on all length scales, of approximately the same magnitude. The peak structure exists because of the details of how those perturbations evolved within our expanding observable universe, but the primordial source of those perturbations was nearly uniform across all length scales. You don't even need to consider inflation here: just look at the measured spectrum of primordial fluctuations, which is nearly flat and becomes flatter at larger scales (at least within the observable universe) [edit: This is incorrect. The flucutations become larger at larger scales. See my post below.].

The main reason why we say that the universe is homogeneous on large scales is because gravity has amplified the small-scale fluctuations dramatically (which we can observe as the formation of galaxy clusters, galaxies, and smaller structures), so that the large-scale fluctuations are much, much smaller than the small-scale ones.

So the simplest model which fits the data is not homogeneous and isotropic, but only approximately so. And when you delve into the details, it becomes clear that that approximation is very likely to break down when you go far enough beyond the observable universe.

It honestly surprises me that you're so reluctant to accept this. What I'm applying here is one of the most basic principles of inference: inference allows you to have some degree of confidence of what happens beyond the observed cases. But as you progress further and further from those observed cases, it becomes more and more likely that unanticipated effects will change the result. I do try to make some inferences as to what those effects might be based upon the nature of the physical laws we have observed, but it's not necessary to accept any of those arguments to realize that it doesn't make sense to extrapolate a theory to infinity, especially not when all of the plausible theories that we have been able to come up with predict very different behavior at distances far beyond the Hubble scale.

If you want some philosophical backing, take a look at the problem of induction, which points out that inferring some mathematical behavior based on observations will always have shortcomings, and that the more likely scenario is that there is some place beyond current observation where that induction breaks down. I'd also note that this problem of induction largely agrees with Occam's Razor as long as you are considering actually fundamental models, rather than approximations like the statement that the universe is homogeneous and isotropic, because it turns out that having a uniform universe requires more assumptions in those more fundamental models.

 

[PeterDonis]

If your assertion was correct, then the power spectrum would be indistinguishable from zero at low $\ell$.

Can you give a brief explanation of why? Or point to a reference that has one?

What I'm applying here is one of the most basic principles of inference

No, what you're applying here is a particular inference from a particular piece of data (the CMB power spectrum) that, if it's correct, changes the simplest model consistent with the data (by adding a piece of data, or more precisely an implication of a piece of data, that makes homogeneity on the largest scales no longer the "simplest assumption", as it was taken to be when the original FRW models were developed). I just need to understand better why that particular piece of data has that particular implication.

 

[kimbyd]

Can you give a brief explanation of why? Or point to a reference that has one?

The power spectrum can be interpreted as the average variance between points separated by a particular distance on the sky*. That distance is given by $\pi/\ell$ radians (or, alternatively, $180/\ell$ degrees). So for $\ell=1$, the power spectrum value can be thought of as the expected variance in temperature of the CMB at opposite points on the sky. For $\ell=2$, it would be the temperature variance of points separated by 90 degrees on the sky.

Note that these variations are quite small (of the order of one part in one hundred thousand of the average temperature), and the really large-scale fluctuations aren't amplified much by gravitational interactions as the universe expands. So the approximation of a homogeneous universe really is quite good at large length scales (more than a few hundred million light years). But it isn't perfect.

* The technical definition is that it is the variance of the amplitudes of the spherical harmonic components for each $\ell$ value.

No, what you're applying here is a particular inference from a particular piece of data (the CMB power spectrum) that, if it's correct, changes the simplest model consistent with the data (by adding a piece of data, or more precisely an implication of a piece of data, that makes homogeneity on the largest scales no longer the "simplest assumption", as it was taken to be when the original FRW models were developed). I just need to understand better why that particular piece of data has that particular implication.

All we have, though, is inference from data. I used the CMB here because it's the clearest picture of the largest-scale fluctuations that are within our observable universe. The simplest model that fits this data is one with a nearly-invariant power spectrum parameterized with what is known as a "scalar spectral index". See here:
https://en.wikipedia.org/wiki/Primordial_fluctuations

These primordial fluctuations scale as $k^{n_s-1}$ (with $n_s$ measured to be approximately 0.97). Looking at it more carefully, this actually contradicts my previous post, but does so in a way that supports my broader point: this function diverges at large scales (as $k$ approaches zero). That is, the best fit to current data is that large-scale fluctuations gain increasingly greater amplitudes at larger scales. This approximation certainly breaks down at some point (it is, after all, little more than a curve fit as real inflation models predict more complex behavior). But it does support my broader point that we can't guarantee that the universe remains uniform at scales much larger than the horizon.

 

[PeterDonis]

The power spectrum can be interpreted as the average variance between points separated by a particular distance on the sky*.

I understand this part. What I am looking for an explanation of is why, if the universe were homogeneous on the largest scales, we would expect the power spectrum to be indistinguishable from zero at low $\ell$. But it looks like you're now saying the data say something stronger--see below.

the best fit to current data is that large-scale fluctuations gain increasingly greater amplitudes at larger scales

I agree that this, if true, would basically invalidate the simple homogeneous FRW model when extended much beyond our observable universe. The key point, to me, is "increasingly greater". If the power spectrum just goes flat at larger and larger distance scales, at some small variance (one part in a hundred thousand or so), that would just mean the entire universe could only be treated as homogeneous to that degree of approximation--which is basically what our current model does anyway. But if the variance increases at larger and larger distance scales, then you're right, we can't reasonably infer that any region outside our observable universe, but of comparable size, has an average density similar to our observable universe.

It looks like the Wikipedia article you linked to has some good references; I'll take a look at them.

 

[haushofer]

Another link of possible interest:

https://en.m.wikipedia.org/wiki/Huge-LQG

About megastructures which seem to be in conflict with the cosm.principle.

 

[kimbyd]

I understand this part. What I am looking for an explanation of is why, if the universe were homogeneous on the largest scales, we would expect the power spectrum to be indistinguishable from zero at low $\ell$. But it looks like you're now saying the data say something stronger--see below.

The main argument I'm making with respect to this is that you can't reasonably apply Occam's Razor to an approximation in this manner, not when we know that there's a more detailed underlying model that is more precise.

I agree that this, if true, would basically invalidate the simple homogeneous FRW model when extended much beyond our observable universe. The key point, to me, is "increasingly greater". If the power spectrum just goes flat at larger and larger distance scales, at some small variance (one part in a hundred thousand or so), that would just mean the entire universe could only be treated as homogeneous to that degree of approximation--which is basically what our current model does anyway. But if the variance increases at larger and larger distance scales, then you're right, we can't reasonably infer that any region outside our observable universe, but of comparable size, has an average density similar to our observable universe.

One thing I find interesting is that this model does predict a breakdown of the simple notion of homogeneity applied to the universe as a whole, but you can still recover it if you're willing to broaden your definition of homogeneity a bit.

In the context of cosmic inflation with a simple scalar spectral index, the primordial perturbations will, at any given time, lead to very large differences in density in different Hubble volumes. However, inflation will always end at the exact same energy density, and the subsequent expansion of the universe will continue in pretty much exactly the same way in all subsequent volumes. Thus you could say that as long as something more exotic isn't going on, the universe at 14 billion years from the local end of inflation will look pretty much exactly the same to all observers in all locations that are stationary with respect to the local Hubble flow. Depending upon the model of inflation, inflation might end everywhere within a single second, or there might be billions, trillions, or any number of years between the end of inflation in different locations (in eternal inflation models). But regardless of that timing, all of the subsequent evolution will be effectively identical, just with a different pattern of matter with the same statistical properties.

This expanded notion of homogeneity is only broken if we consider more exotic possibilities, such as spontaneous symmetry breaking leading to different low-energy laws of physics. Given that spontaneous symmetry breaking is a component of the Standard Model of particle physics, I don't think we can discount these possibilities as unlikely through the use of Occam's Razor (because you'd have to add additional assumptions to the Standard Model to discount them). If you define it so that regions with different symmetry breaking are different universes, then that's fine.