homogeneity and inflation

[Perpetual Student]

Why is inflation required to explain the homogeneity of the universe? Why would the universe not be homogeneous without inflation?
In any physical situation, if the conditions are the same why would not the results expected to be the same? Why would we need parts of the universe to be in contact (as postulated by a microscopic early universe and inflation) to explain homogeneity? Any knowledgeable comments are welcome.

 

[BonkingBear]

As I understand - there is no reason to assume that the very early conditions ( prior to inflation) were everywhere the same and you have to allow for quantum fluctuations anyway

 

[Perpetual Student]

That is my understanding of the reasoning, but I wonder, why would it not be the same everywhere anyway?

 

[sol invictus]

Why is inflation required to explain the homogeneity of the universe? Why would the universe not be homogeneous without inflation?

Suppose two people each send you a letter, both of which arrive on the same day. One is from Uzbekistan, the other from Chile. You have a theory that the letter writers have never met or communicated in any way, or ever had access to any of the same information. You open the letters and discover they are long, detailed, specific... and absolutely identical in every way, every letter and punctuation mark the same, down to exactly the same handwriting and mis-spellings. Would you continue to believe those two people never communicated or copied from the same source?

Take the universe today and run it back in time. Without inflation, you arrive at a big bang which is incredibly homogeneous - the matter density is independent of location to an extremely high precision, and the temperature is exactly the same across space - even though those different locations were causally disconnected and never could have exchanged even a single particle, let alone equilibrated thermally.

Inflation removes whatever inhomogeneities were there in the initial state, and at the same time creates new ones with a very particular spectrum - precisely like the ones we observe. You don't need inflation to explain the universe, but it does so for many different aspects very simply and elegantly, whereas anthing else requires some sort of huge and incredibly improbable coincidence (which cries out for an explanation).

 

[Perpetual Student]

s. i.:
Your comments are quite clear, thanks. Just to be certain there is no misunderstanding, I am not debating inflation theory and I am generally familiar with the CMB and other evidence supporting the theory.
Your description of taking "the universe today and run(ning) it back in time" is very compelling.
I simply don't understand why the universe would not be homogeneous anyway without inflation.
When cosmologists discuss inflation, homogeneity is always mentioned in addition to the other evidence for inflation. You said, "Inflation removes whatever inhomogeneities were there in the initial state." But, if the initial state was a singularity, would it not be completely homogeneous anyway? How could a singularity be inhomogeneous? I guess that's my problem. What am I missing?

 

[KingMerv00]

Watch these two vids to get the idea:





A bit long I know but worth it. Pay special attention to the paint balloon analogy. (The analogy starts near the end of the first vid.)

 

[arthwollipot]

Perpetual Student is here articulating a question that I have myself had in my mind for a long time.

The big bang theory states that at one time, all points in the universe were at zero distance from each other. In other words, in contact. I have never seen any reason to expect that distant parts of the universe wouldn't or shouldn't be homogenous.

I once received a very vague answer to this question to the effect that general relativity suggests that the smaller the universe, the less likely it is that the universe would be homogenous, but surely at T=0, everything is right on top of everything else?

 

[KingMerv00]

Perpetual Student is here articulating a question that I have myself had in my mind for a long time.

The big bang theory states that at one time, all points in the universe were at zero distance from each other. In other words, in contact. I have never seen any reason to expect that distant parts of the universe wouldn't or shouldn't be homogenous.

I once received a very vague answer to this question to the effect that general relativity suggests that the smaller the universe, the less likely it is that the universe would be homogenous, but surely at T=0, everything is right on top of everything else?

At T=0, nothing makes any sense.

 

[arthwollipot]

At T=0, nothing makes any sense.

Point.

 

[sol invictus]

I simply don't understand why the universe would not be homogeneous anyway without inflation.
When cosmologists discuss inflation, homogeneity is always mentioned in addition to the other evidence for inflation. You said, "Inflation removes whatever inhomogeneities were there in the initial state." But, if the initial state was a singularity, would it not be completely homogeneous anyway? How could a singularity be inhomogeneous? I guess that's my problem. What am I missing?

Singularities are often wildly inhomogeneous. Here's a mathematical example (I'll give a physics one below). Take the function f(z)=e^-1/z. That function has an essential singularity at z=0. One fact about it is that as one approaches the origin of the complex plane z=0 from different directions, f takes every finite value (except 0) an infinite number of times. In other words, it oscillates more and more wildly the closer one comes to the origin, even though it's just a single point in a plane.

The big bang theory states that at one time, all points in the universe were at zero distance from each other. In other words, in contact.

No, it doesn't. In an infinite universe, the only sensible definition of the volume of the singularity (which is the limit of the volume as t->0) is infinity. In a finite universe it's true that the volume goes to zero at t=0 - but what's more relevant here is the distance d between two points at time t, divided by t - i.e. d/t. If that ratio is greater than c it means light hasn't had time to propagate between those two points since the bang. But it turns out that d/t>c for all points as t->0 (except in certain special cases). So in the early universe no pair of points can have had any contact at all until some time after the bang - and without inflation that still hasn't happened to the pair of points we're looking at when we look in opposite directions on the cosmic microwave background sky.

I have never seen any reason to expect that distant parts of the universe wouldn't or shouldn't be homogenous.

Well, again, run the universe back, starting from the initial conditions today. What you'll find is an infinitely inhomogeneous solution (that's the physics example). You can imagine starting with some wiggly function, and then shrinking the scale of the x axis at the same time as you increase the amplitude. The function gets infinitely spiky - it has infinite derivative at every point. But in our universe without inflation it will be an incredibly special kind of spikyness, very carefully tuned so running forward again, by the time that would correspond to the end of inflation those spikes have moved around and combined with each other to form thermal equlibrium (which remember is a much stronger statement than mere homogeneity) to an incredibly perfect degree, but leaving behind in addition an almost precisely scale-invariant spectrum of very small (1 part in 100,000) fluctuations over a huge range of length scales. It's not impossible - but it's the kind of thing that no one would ever believe is a coincidence.

 

[Perpetual Student]

Singularities are often wildly inhomogeneous. Here's a mathematical example (I'll give a physics one below). Take the function f(z)=e^-1/z. That function has an essential singularity at z=0. One fact about it is that as one approaches the origin of the complex plane z=0 from different directions, f takes every finite value (except 0) an infinite number of times. In other words, it oscillates more and more wildly the closer one comes to the origin, even though it's just a single point in a plane.



No, it doesn't. In an infinite universe, the only sensible definition of the volume of the singularity (which is the limit of the volume as t->0) is infinity. In a finite universe it's true that the volume goes to zero at t=0 - but what's more relevant here is the distance d between two points at time t, divided by t - i.e. d/t. If that ratio is greater than c it means light hasn't had time to propagate between those two points since the bang. But it turns out that d/t>c for all points as t->0 (except in certain special cases). So in the early universe no pair of points can have had any contact at all until some time after the bang - and without inflation that still hasn't happened to the pair of points we're looking at when we look in opposite directions on the cosmic microwave background sky.



Well, again, run the universe back, starting from the initial conditions today. What you'll find is an infinitely inhomogeneous solution (that's the physics example). You can imagine starting with some wiggly function, and then shrinking the scale of the x axis at the same time as you increase the amplitude. The function gets infinitely spiky - it has infinite derivative at every point. But in our universe without inflation it will be an incredibly special kind of spikyness, very carefully tuned so running forward again, by the time that would correspond to the end of inflation those spikes have moved around and combined with each other to form thermal equlibrium (which remember is a much stronger statement than mere homogeneity) to an incredibly perfect degree, but leaving behind in addition an almost precisely scale-invariant spectrum of very small (1 part in 100,000) fluctuations over a huge range of length scales. It's not impossible - but it's the kind of thing that no one would ever believe is a coincidence.

You've given me a lot to think about, thanks.

 

[arthwollipot]

Singularities are often wildly inhomogeneous. Here's a mathematical example (I'll give a physics one below). Take the function f(z)=e^-1/z. That function has an essential singularity at z=0. One fact about it is that as one approaches the origin of the complex plane z=0 from different directions, f takes every finite value (except 0) an infinite number of times. In other words, it oscillates more and more wildly the closer one comes to the origin, even though it's just a single point in a plane.

This makes sense to me.

No, it doesn't. In an infinite universe, the only sensible definition of the volume of the singularity (which is the limit of the volume as t->0) is infinity. In a finite universe it's true that the volume goes to zero at t=0 - but what's more relevant here is the distance d between two points at time t, divided by t - i.e. d/t. If that ratio is greater than c it means light hasn't had time to propagate between those two points since the bang. But it turns out that d/t>c for all points as t->0 (except in certain special cases). So in the early universe no pair of points can have had any contact at all until some time after the bang - and without inflation that still hasn't happened to the pair of points we're looking at when we look in opposite directions on the cosmic microwave background sky.

This does not. I don't see how it is possible for a pair of points not to have had contact with each other at T=0.

Well, again, run the universe back, starting from the initial conditions today. What you'll find is an infinitely inhomogeneous solution (that's the physics example). You can imagine starting with some wiggly function, and then shrinking the scale of the x axis at the same time as you increase the amplitude. The function gets infinitely spiky - it has infinite derivative at every point. But in our universe without inflation it will be an incredibly special kind of spikyness, very carefully tuned so running forward again, by the time that would correspond to the end of inflation those spikes have moved around and combined with each other to form thermal equlibrium (which remember is a much stronger statement than mere homogeneity) to an incredibly perfect degree, but leaving behind in addition an almost precisely scale-invariant spectrum of very small (1 part in 100,000) fluctuations over a huge range of length scales. It's not impossible - but it's the kind of thing that no one would ever believe is a coincidence.

Ah, now I'm getting it.

Sol, you have been pretty much what I've been looking for all these years. This language makes a lot more sense to me than the language of two points having had to have contact in order to come into thermal equilibrium. It never made sense to me why they shouldn't be in thermal equilibrium from the very beginning, since at the beginning, all points were right on top of all other points. But you're making some sense. I probably won't grasp it all unless I take a three-year course in mathematics and cosmological physics, but to my layman's mind it is making a lot more sense than it did. Thanks.