Inflation and size of the Universe

[Ranku]

Among other things, inflation explains the horizon problem, as to why even though the proper distance between two antipodal points on the last scattering surface is greater than the horizon distance, and therefore causally disconnected, yet the two points have the same temperature. So is this then also equivalent to saying that the size of the observable universe itself would also have been smaller without inflation, since the two antipodal points would have been closer to each other and lesser than the horizon distance, wherein temperature homogeneities would naturally exist?

 

[timmdeeg]

If the observable universe wouldn't have been blown up by a factor of around #10^26# then yes it's size would have been smaller accordingly and the horizon problem wouldn't be resolved.

 

[Ranku]

If the observable universe wouldn't have been blown up by a factor of around #{10^26}# then yes it's size would have been smaller accordingly and the horizon problem wouldn't be resolved.

You mean "the horizon problem would be resolved".

 

[timmdeeg]

I mean without the inflation assumption the horizon problem would not be resolved.

 

[elcaro]

Among other things, inflation explains the horizon problem, as to why even though the proper distance between two antipodal points on the last scattering surface is greater than the horizon distance, and therefore causally disconnected, yet the two points have the same temperature. So is this then also equivalent to saying that the size of the observable universe itself would also have been smaller without inflation, since the two antipodal points would have been closer to each other and lesser than the horizon distance, wherein temperature homogeneities would naturally exist?

See Ned Wright's cosmology tutorial on the horizon problem.

 

[Ranku]

If the observable universe wouldn't have been blown up by a factor of around #10^26# then yes it's size would have been smaller accordingly and the horizon problem wouldn't be resolved.

So would it not then be possible to tell by looking at the size of the observable universe whether inflation occurred or not.

 

[timmdeeg]

So would it not then be possible to tell by looking at the size of the observable universe whether inflation occurred or not.

No, we can't conclude that from the actual size of the observable universe. We conclude that inflation has occurred form the observed homogeneity on large scales and from the CMB power spectrum which is in accordance with predictions of the theory of inflation.

 

[Ranku]

"If the observable universe wouldn't have been blown up by a factor of around #10^26# then yes it's size would have been smaller accordingly.."

Since without inflation the size of the observable universe would have been smaller by a factor 10^26, why can we then not conclude if inflation had occurred from the size of the observable universe?

 

[timmdeeg]

Since without inflation the size of the observable universe would have been smaller by a factor 10^26, why can we then not conclude if inflation had occurred from the size of the observable universe?

I see your point, perhaps post #2 caused a misunderstanding. We compare our homogeneous observable universe with a hypothetical observable universe of the same size which is not homogeneous and which didn't inflate by this factor.

 

[Bandersnatch]

So is this then also equivalent to saying that the size of the observable universe itself would also have been smaller without inflation, since the two antipodal points would have been closer to each other and lesser than the horizon distance, wherein temperature homogeneities would naturally exist?

If the observable universe wouldn't have been blown up by a factor of around #10^26# then yes it's size would have been smaller accordingly and the horizon problem wouldn't be resolved.

No, it's not equivalent, and it doesn't mean that the observable universe would be smaller.
The extent of the observable universe is determined by the post-inflationary dynamics of the standard hot big bang expansion.
It is what it is because that's how far light can travel in the time it has had since recombination, through space that is expanding like it is.

It's important to keep in mind that we're tracking the evolution of the universe from present towards the past, with uncertainty growing towards the earlier epochs. We're not starting from some early t0 and guessing how the universe looks now - the now is measurable, and therefore fixed.
I.e. tacking on inflation to the pre-big bang era doesn't modify what happens during the big bang era. Without inflation, the particle horizon is where we see it. With inflation, it is also where we see it.

In a way, what you (Ranku) write there is topsy-turvy. If you want the OU to once have been smaller (i.e. causally connected), you add inflation. Not remove it.

 

[Ranku]

Without inflation, the particle horizon is where we see it. With inflation, it is also where we see it.

This is the answer l was looking for. Thanks.

 

[Ranku]

No, it's not equivalent, and it doesn't mean that the observable universe would be smaller.
The extent of the observable universe is determined by the post-inflationary dynamics of the standard hot big bang expansion.
It is what it is because that's how far light can travel in the time it has had since recombination, through space that is expanding like it is.

It's important to keep in mind that we're tracking the evolution of the universe from present towards the past, with uncertainty growing towards the earlier epochs. We're not starting from some early t0 and guessing how the universe looks now - the now is measurable, and therefore fixed.
I.e. tacking on inflation to the pre-big bang era doesn't modify what happens during the big bang era. Without inflation, the particle horizon is where we see it. With inflation, it is also where we see it.

In a way, what you (Ranku) write there is topsy-turvy. If you want the OU to once have been smaller (i.e. causally connected), you add inflation. Not remove it.

I realized just now that the question I should really be asking is would the proper distance between two antipodal points in the last scattering surface be lesser than the horizon distance, if no inflation occurred? If so, can we deduce whether inflation occurred or not by observing if last scattering surface is greater or lesser than the horizon?

 

[timmdeeg]

I.e. tacking on inflation to the pre-big bang era doesn't modify what happens during the big bang era. Without inflation, the particle horizon is where we see it. With inflation, it is also where we see it.

This seems to suggest that we presuppose that the average energy density of the ingredients of the universe does not depend on whether or not the OU was causally connected at the time of big bang, correct?

 

[kimbyd]

Since without inflation the size of the observable universe would have been smaller by a factor 10^26, why can we then not conclude if inflation had occurred from the size of the observable universe?

It's not hard to conceive of the universe being more than 10^26 times larger than the observable part of it alone.

 

[Ranku]

It's not hard to conceive of the universe being more than 10^26 times larger than the observable part of it alone.

I have superseded that question with this question: Would the proper distance between two antipodal points in the last scattering surface be lesser than the horizon distance, if no inflation occurred? If so, can we deduce whether inflation occurred or not by observing if last scattering surface is greater or lesser than the horizon?

 

[Bandersnatch]

I realized just now that the question I should really be asking is would the proper distance between two antipodal points in the last scattering surface be lesser than the horizon distance, if no inflation occurred? If so, can we deduce whether inflation occurred or not by observing if last scattering surface is greater or lesser than the horizon?

I'm not sure I understand your intent, since this looks to me like exactly the same question as before.
For the purposes of this topic, the particle horizon and the last scattering surface are pretty much the same thing. Where they are is determined solely by what happens during regular expansion.
So, 1) You can't make them be in different places by adding or removing inflation; 2) Since they're closely related, what you're asking here boils down to: can a (positive) distance be more than twice the same distance.

I suspect your overarching reasoning here goes as follows (please, clarify otherwise):
- we have these regions that look connected
- the expansion model suggests they should be disconnected
- inflation spread them apart
Therefore removing inflation should mean they'd be closer (and possibly connected), as there would have been nothing to increase their separation before BB.

In which case the error would be in that the first two steps cannot be changed, as they are fixed by observation. These regions definitely look connected, and the BB expansion definitely would have them disconnected.
What you can change is the hypothetical third step, but all it does is provide a reason for steps one and two to not be at odds. I.e. flipping inflation on/off means that you see the same problem either way, but you either have or don't have a possible solution.
It's an issue with logic. It's like saying: I see a blue cow. Cows are not blue. This is the cow colour problem. To attempt to solve the problem I hypothesise somebody painted the cow. Now, does it make any sense to propose that maybe nobody painted the cow, since then the cow wouldn't be blue, thus solving the problem?

You could assume the third step to be true in our universe, and ask what would change in some hypothetical universe, where inflation didn't occur, but expansion proceeded normally (i.e. you relax the first step). In such universe, the distant regions would look like the expansion model alone suggests - they wouldn't look causally connected. But they definitely do.
The cow wouldn't be blue in the absence of the sneaky bovine painter. But it definitely is.

 

[Bandersnatch]

This seems to suggest that we presuppose that the average energy density of the ingredients of the universe does not depend on whether or not the OU was causally connected at the time of big bang, correct?

It's not that what happens during inflation cannot hypothetically affect the distribution of the contents of a universe. It's that we are not at liberty to modify the distribution in >our< universe. Whatever we hypothesise must conform to observations. So whether we assume inflation or not, the end result must be the hot big bang expansion that is observed.

 

[Jorrie]

Maybe another way to explain this is as follows. I have taken a 'standard' inflation+LCDM expansion and plotted it on a double log scale.

;
Where t is cosmic time and r the separation between two comoving particles and t[SUB]p[/SUB] and r[SUB]p[/SUB] are the corresponding Planck values. Then I naively extrapolated the radiation dominated era (slope 0.5) linearly back to earlier times, to reach a singularity. This could have been the case with no inflation.

This would have made no difference to current observations of distances and horizons. The isotropy of the CMB would have been different.

 

[Ranku]

I'm not sure I understand your intent, since this looks to me like exactly the same question as before.
For the purposes of this topic, the particle horizon and the last scattering surface are pretty much the same thing. Where they are is determined solely by what happens during regular expansion.
So, 1) You can't make them be in different places by adding or removing inflation; 2) Since they're closely related, what you're asking here boils down to: can a (positive) distance be more than twice the same distance.

I suspect your overarching reasoning here goes as follows (please, clarify otherwise):
- we have these regions that look connected
- the expansion model suggests they should be disconnected
- inflation spread them apart
Therefore removing inflation should mean they'd be closer (and possibly connected), as there would have been nothing to increase their separation before BB.

In which case the error would be in that the first two steps cannot be changed, as they are fixed by observation. These regions definitely look connected, and the BB expansion definitely would have them disconnected.
What you can change is the hypothetical third step, but all it does is provide a reason for steps one and two to not be at odds. I.e. flipping inflation on/off means that you see the same problem either way, but you either have or don't have a possible solution.
It's an issue with logic. It's like saying: I see a blue cow. Cows are not blue. This is the cow colour problem. To attempt to solve the problem I hypothesise somebody painted the cow. Now, does it make any sense to propose that maybe nobody painted the cow, since then the cow wouldn't be blue, thus solving the problem?

You could assume the third step to be true in our universe, and ask what would change in some hypothetical universe, where inflation didn't occur, but expansion proceeded normally (i.e. you relax the first step). In such universe, the distant regions would look like the expansion model alone suggests - they wouldn't look causally connected. But they definitely do.
The cow wouldn't be blue in the absence of the sneaky bovine painter. But it definitely is.

This much is clear to me now: since both particle horizon and last scattering are set in the post-inflationary big bang universe, they do not offer evidence of inflation.

As for the horizon problem, I have some issues: on the one hand an observer A cannot observe beyond particle horizon, and yet temperature homogeneity of last scattering beyond particle horizon is considered to be a 'problem', when A cannot even observe it. Suppose the particle horizon of another observer B overlaps a part of particle horizon of A and also covers a region beyond the particle horizon of A, then of course temperature in that region (beyond A) would be homogenous for observer B - and therefore, by extension, the temperature of the whole region of particle horizon A and B would be naturally homogenous. Thus, it seems to be unnecessary to identify a horizon 'problem', that needs to be 'solved' with inflation.

 

[Bandersnatch]

and yet temperature homogeneity of last scattering beyond particle horizon is considered to be a 'problem'

No, that's not what the problem is. The problem is that the scale of homogenized regions is larger than what laws of physics permit. Imagining additional observers doesn't help, as each has to work with the same laws of physics, and each sees the same disparity of scales.

 

[Ranku]

No, that's not what the problem is. The problem is that the scale of homogenized regions is larger than what laws of physics permit. Imagining additional observers doesn't help, as each has to work with the same laws of physics, and each sees the same disparity of scales.

How was the scale of homogenized regions derived?

 

[Ranku]

Maybe another way to explain this is as follows. I have taken a 'standard' inflation+LCDM expansion and plotted it on a double log scale.
View attachment 289834;
Where t is cosmic time and r the separation between two comoving particles and t[SUB]p[/SUB] and r[SUB]p[/SUB] are the corresponding Planck values. Then I naively extrapolated the radiation dominated era (slope 0.5) linearly back to earlier times, to reach a singularity. This could have been the case with no inflation.

View attachment 289835
This would have made no difference to current observations of distances and horizons. The isotropy of the CMB would have been different.

It would be interesting to check if retracing back from present particle horizon length does end up in Planck length at Planck time within 13.8 Gy. If there is a mismatch, that would indicate inflation would be necessary to bridge it.

 

[PeterDonis]

retracing back from present particle horizon length

This would be meaningless since the present particle horizon length is not a direct observable; it is extrapolated forward from our best estimate of the state in the past. So retracing it back into the past would just give you the state you started from; it would not tell you anything new.

 

[Ranku]

Maybe another way to explain this is as follows. I have taken a 'standard' inflation+LCDM expansion and plotted it on a double log scale.
View attachment 289834;
Where t is cosmic time and r the separation between two comoving particles and t[SUB]p[/SUB] and r[SUB]p[/SUB] are the corresponding Planck values. Then I naively extrapolated the radiation dominated era (slope 0.5) linearly back to earlier times, to reach a singularity. This could have been the case with no inflation.

View attachment 289835
This would have made no difference to current observations of distances and horizons. The isotropy of the CMB would have been different.

Also I notice you made inflation start from zero size universe, when in fact the universe was already expanding at regular rate, before it started to expand exponentially. Correcting for that, clearly that slope wouldn't match post-inflationary slope of expansion.

 

[Jorrie]

Also I notice you made inflation start from zero size universe, when in fact the universe was already expanding at regular rate, before it started to expand exponentially. Correcting for that, clearly that slope wouldn't match post-inflationary slope of expansion.

No, not a "zero size universe", but what I wrote: "... r [is] the separation between two comoving particles", which pre-inflation could have been on top of each other. The parameter r could also simply be the separation between two arbitrary spatial locations. Space could have been infinite throughout.

Please give a reference for your "in fact the universe was already expanding at regular rate, before it started to expand exponentially..."?

 

[Ranku]

No, not a "zero size universe", but what I wrote: "... r [is] the separation between two comoving particles", which pre-inflation could have been on top of each other. The parameter r could also simply be the separation between two arbitrary spatial locations. Space could have been infinite throughout.

Please give a reference for your "in fact the universe was already expanding at regular rate, before it started to expand exponentially..."?

Please refer to page 185 of the book The Inflationary Universe (Vintage Pub.) by Alan Guth. In the diagram, you'll notice that the slope of expansion of the pre-inflationary universe is parallel to the slope of expansion of the post-inflationary universe.

 

[Jorrie]

Please refer to page 185 of the book The Inflationary Universe (Vintage Pub.) by Alan Guth. In the diagram, you'll notice that the slope of expansion of the pre-inflationary universe is parallel to the slope of expansion of the post-inflationary universe.

Thanks for the reference. I do not have access to Guth's book, but I guess the diagram is the same as the one in the Caltech pages "WAS COSMIC INFLATION THE 'BANG' OF THE BIG BANG?" by A.Guth

As far as I could see, there was no discussion of the expansion before inflation, but he did remark:

"There are many versions of inflationary theories but generically they assume that some small patch of the early Universe somehow came to be in a false vacuum state. Various possibilities have been discussed, including supercooling during a phase transition in the early Universe, or a purely random fluctuation of the fields. A chance fluctuation seems reasonable even if the probability is low, since the inflating region will enlarge by many orders of magnitude, while the non-inflating regions will remain microscopic. Inflation is a wildfire that will inevitably take over the forest, as long as there is some chance that it will start."

In any case, this did not matter in what I was trying to illustrate by means of separation between spatial locations.

 

[Ranku]

Thanks for the reference. I do not have access to Guth's book, but I guess the diagram is the same as the one in the Caltech pages "WAS COSMIC INFLATION THE 'BANG' OF THE BIG BANG?" by A.Guth

View attachment 289904
As far as I could see, there was no discussion of the expansion before inflation, but he did remark:

"There are many versions of inflationary theories but generically they assume that some small patch of the early Universe somehow came to be in a false vacuum state. Various possibilities have been discussed, including supercooling during a phase transition in the early Universe, or a purely random fluctuation of the fields. A chance fluctuation seems reasonable even if the probability is low, since the inflating region will enlarge by many orders of magnitude, while the non-inflating regions will remain microscopic. Inflation is a wildfire that will inevitably take over the forest, as long as there is some chance that it will start."

In any case, this did not matter in what I was trying to illustrate by means of separation between spatial locations.

Yes it is the same diagram.

Even though the diagram is indicative, I am still curious to check if you plot the slope of expansion starting with the particle horizon now, and all the way back to Planck length at Planck time, with the same rate of expansion throughout, whether it fits within 13.8 Gy. If it overshoots, then to fit it within 13.8 Gy, how much inflation has to be introduced, and whether that number matches the number that is usually presented.

 

[Jorrie]

Yes it is the same diagram.

Even though the diagram is indicative, I am still curious to check if you plot the slope of expansion starting with the particle horizon now, and all the way back to Planck length at Planck time, with the same rate of expansion throughout, whether it fits within 13.8 Gy. If it overshoots, then to fit it within 13.8 Gy, how much inflation has to be introduced, and whether that number matches the number that is usually presented.

If the present rate of change of the LCDM particle horizon is extrapolated backwards, it would actually have fallen short of 14 Gly by a few Gy, as you can deduce from this chart.

I think your question has been answered quite a few times already.

 

[Ranku]

Here's to hoping I do not ever have to scratch the inflation itch again.