Horizon problem - why do we need inflation?

• Dmitry67
In summary, the horizon problem is a paradox in cosmology that states that regions in space that are separated by vast distances and moving away from each other rapidly, should not have similar properties. This is known as the homogeneity problem and it was initially thought that some amount of departures from homogeneity at very large scales would be observed, but the observations of the Cosmic Microwave Background (CMB) have shown that the tension with theory is growing out of control. The addition of quantum mechanics (QM) to general relativity (GR) suggests that small deviations could have occurred around the Planck time or earlier, which would have been greatly amplified by gravity and could explain the observed smoothness of the CMB. Inflation theory, which proposes
Dmitry67
Why do we need an inflation to solve the horizon problem?
http://en.wikipedia.org/wiki/Horizon_problem

If O(t) is omnuim ((c) Frederik) - wavefunction of the whole Universe then initial conditions like

O(t=0) = const

solve the problem?

I had wondered about this myself. GR by itself doesn't predict any particular spectrum for how energy was distributed in early times. How then can someone claim that the observed smoothness of the CMB is "too smooth" ? It doesn't seem to contradict GR.

However, if QM is added, small deviations could occur around the Planck time or earlier that would be now be of comparable length scale to a large fraction of the Universe and larger. These deviations would have been greatly amplified by gravity and might be manifested now as a much greater variation in mass density than is observed, although I haven't actually tried to calculate that hypothetical density spectrum.

The horizon problem simply states that regions in space that are separated by vast distances and moving away from each other rapidly, ought not to share similar properties. They are not in causal contact with each other at any time in the universe's history(and we know how much time they had to communicate, given roughly by the age of the universe and we know the speed of light), so its damn peculiar that their observed temperatures are so similar.

So for a long time scientists thought that ultimately we would see some amount of departures from homogeneity at very large scales, but the observations kept piling in, and they realized that the tension with theory was growing rapidly out of control.

The idea that remote regions of space "ought not to share similar properties" is vague. How similar should the properties of two separated regions be? Without a model that predicts a specific spatial energy density spectrum, we have nothing to compare the observed (smooth) spectrum against, and so the "smooth" observation wouldn't contradict anything.

In other words, the opinion that it's "too uniform" is just a value judgment until the uniformity is compared against a model that has a specific prediction.

It seems you are almost arguing that the uniformity in the CMB is not that surprising.

Considering two causally disconnected regions of spacetime, would you expect them to have the same temperature to one part in a hundred thousand? I do not think one needs a precise model of what one expects these things to look like to say "in general, no." After reaching that conclusion you can say one of two things:
1) Well that's fortuitous! I'll call it a day.
2) Since that's extremely unlikely, what made it that way?

Inflation is obviously the theory of someone in camp #2.

Suppose I told you that a certain ball bearing factory was producing steel bearings whose density varied from piece to piece with a variance of 1/100,000. Without any guideline or standard to consult, would you call that "high" or "low" variance? 1/100,000 sounds like a small number, but for all we know this may be an out-of-spec batch, and 1/1,000,000 or less would be normal.

GR by itself (without QM or inflation) doesn't give us any guideline as to what variance to expect. Someone who examines GR alone might conclude that there is not necessarily any conflict with GR theory vs. the observed uniformity.

However, I think that adding QM to GR makes it clear that there is a conflict, which inflation (I presume) solves.

I haven't examined another possibility, however: that gaussian statistical fluctuations in early photon numbers (inverse square root of N) might have caused large-scale fluctuations which could have been amplified by expansion. In this case, GR by itself might predict too much variation, and inflation would be needed.

Last edited:
I think your example is an incorrect representation of the situation. I think the appropriate thing to say would be this:
I find 10,000 random ball bearings from all over the place. I find that their densities are all the same to one part in one hundred thousand. Would I consider this odd? I think anyone would say "Certainly! These ball bearings must have been produced in the same factory/by the same company/from the same mould/etc" But would have to admit some correlation between them. No such correlation exists in the standard framework of GR, which is why we appeal to inflation to solve the problem.

Agreed. 1/100,000 is a small number. A question should be raised here-- what order of magnitude of fractional variation in temperature (to give a specific example, let's say over about a 10 degree angle) would you expect to see with GR only if there were no inflation, at the last scattering surface (CMB)?

Right. That's the logical next question to ask, and I can't give a calculation or reference to one, but I think the point is: significantly larger than 10^-5. My point is that I don't believe we need an exact prediction from GR to say that the homogeneity is more than could be expected.

I feel like we should be able to do a back-of-the-envelope calculation as to what kind of distribution could be expected, but I don't know of one off the top of my head and am not strong enough in this type of thing to produce one.

Edit: Spent half an hour looking for something to no avail.

Nabeshin said:
It seems you are almost arguing that the uniformity in the CMB is not that surprising.

Considering two causally disconnected regions of spacetime, would you expect them to have the same temperature to one part in a hundred thousand? I do not think one needs a precise model of what one expects these things to look like to say "in general, no."

If initial conditions were the same everywhere (the simplest form of initial conditions, otherwise extra information is encoded in these initial conditions) and laws of physics are the same, then there is absolutely no surprise that from the same initial conditions spacetime+matter everywhere we get identical states later

For me it is much more difficult to explain that there are still some variations.

Dmitry67 said:
Why do we need an inflation to solve the horizon problem?
http://en.wikipedia.org/wiki/Horizon_problem

If O(t) is omnuim ((c) Frederik) - wavefunction of the whole Universe then initial conditions like

O(t=0) = const

solve the problem?
The problem is this: parts of the universe separated by distance scales that, in standard big bang theory, have never been in contact, are highly-correlated. Postulating initial conditions for which this is so doesn't solve the problem, it merely ignores it.

Why? Initial conditions are also the part of the laws of physics and they have the same status.

Do you find surprising that Fine structure constant is 1/137.035999679... everywhere?
Did different parts of the Universe need to be 'in casual contact' in order to 'synchronize' the value?

Dmitry67 said:
Why? Initial conditions are also the part of the laws of physics and they have the same status.
In what sense do they have the same status? For every physical theory I am aware of, initial conditions are entirely separate from the theory, and dependent upon which system you're studying.

Dmitry67 said:
Do you find surprising that Fine structure constant is 1/137.035999679... everywhere?
Did different parts of the Universe need to be 'in casual contact' in order to 'synchronize' the value?
That's not the same thing as initial conditions, unless you want to posit a theory wherein alpha is allowed to vary.

Initial conditions are a particular configuration of the system in question, a configuration that, in general, won't be the same afterwards.

By contrast, alpha is a parameter in the theory for Quantum Electro-Dynamics (as well as a few others). It is just a number, a number which the theory does not predict but which must be measured experimentally.

With that little bit of semantics out of the way, yes, I strongly suspect that alpha is actually a parameter which can vary from place to place, that there is a set of physical laws more fundamental than QED of which we are not yet aware that allows this parameter to take various values, and ensures that it remains relatively constant at low energies. Therefore I strongly suspect that parts of the universe that are not in causal contact with one another take different values for the fine structure constant.

Finally, let me just point out that even if you don't like my semantics here, the point remains that positing initial conditions doesn't solve the horizon problem: in order to explain something, by Occam's Razor, your explanation must have fewer parameters than that which it explains. But simply stating what we think needs explaining is actually just the initial conditions doesn't do this, so it isn't an explanation, and we are still left with the problem.

Chalnoth said:
In what sense do they have the same status? For every physical theory I am aware of, initial conditions are entirely separate from the theory, and dependent upon which system you're studying.

Say, equations of toe are:

TOE(Omnium(t)) = 0
(1)

Now we want to define initial conditions at t=0:

Omnium(t=0) = 0
(2)

So we just have 2 equations defining the behavior of Omnium. We can call (1) 'physical laws' and (2) 'initial conditions' but in fact, there is no difference.

I don't think you answered my post at all.

When we talk about some subsystem of the Universe, there is a difference between 'laws' and 'boundary conditions'. At least the difference is obvious.

When we talk about the WHOLE UNIVERSE there are no boundaries, so 'boundary' or 'initial' conditions are just additional limitations. So if TOE equations do not give the unique solutions for the Omnuim, then we add additional conditions, in a form of additional equations.

So we have a longer list of equations - nothing more.

Regarding your point about the Ocamms razor. It is on MY side. Compare 2 cases:
a) void initial conditions Omnium(x,y,z,0)=0
b) void except 73 pre-existing particles forming 4 triangles. Why 73? Not 74? Why triangles? isn't that obvious that only a) is the simples case and is resistent to Ocamms razor?

'Initial' conditions should not necessarily define the state of the Universe at t=0.
For example, because time might be not well defined at the Big Bang.
So again, they are just additional equations.

Dmitry67 said:

When we talk about some subsystem of the Universe, there is a difference between 'laws' and 'boundary conditions'. At least the difference is obvious.

When we talk about the WHOLE UNIVERSE there are no boundaries, so 'boundary' or 'initial' conditions are just additional limitations. So if TOE equations do not give the unique solutions for the Omnuim, then we add additional conditions, in a form of additional equations.
Except initial conditions are just a particular type of boundary condition. So you're contradicting yourself.

Dmitry67 said:
So we have a longer list of equations - nothing more.
There's a fundamental difference between an equation that lists a relationship between components of the universe at any place or time, and one that specifically lays out a particular configuration of the universe at one time (or place, for that matter).

Dmitry67 said:
Regarding your point about the Ocamms razor. It is on MY side. Compare 2 cases:
a) void initial conditions Omnium(x,y,z,0)=0
b) void except 73 pre-existing particles forming 4 triangles. Why 73? Not 74? Why triangles? isn't that obvious that only a) is the simples case and is resistent to Ocamms razor?
First you'd have to show that those 73 pre-existing particles extend necessarily from setting that particular initial condition, instead of some other. As near as I can tell, you gain nothing at all in the theory from setting that initial condition.

Chalnoth said:
There's a fundamental difference between an equation that lists a relationship between components of the universe at any place or time, and one that specifically lays out a particular configuration of the universe at one time (or place, for that matter).

No. Take Newtonian Universe.

Fg = G * M1*M2 / r^2

This is a physical law. Now we can examine how 2 bodies will behaive:

M1=1, M2=0.1
at t=0: X1=.. Y1=.. Z1=.. Vx1=.. Vy1=.. Vz1=...
X2=.. Y2=.. Z2=.. Vx2=.. Vy2=.. Vz2=...

These are initial conditions.

The boundary (t=0) is artificial of course. Boundary conditions can define the state of the system at t=0, or any other property.

For example, "and at least 2 masses of N will ever collide". This condition is also a boundary one, even it does not define the state of the system at some t, it just claims that system reaches some property at some t.

Now what's about QM where we can not in principle know the complete state of the system? Or when no 'global' physical t can be defined (like in cosmology).

Lets say that in TOE the very notion of TIME is emergent. What are you going to do if you don't have t=0? In TOE very likely you have neither time nor spatial boundary. How, in principle, you can define 'boundary' conditions?

The very words 'boundary' or 'initial' (=boundary at earlier time) in general do not make any sense if we think about the whole universe. They are 'boundary' or 'initial' only in mathematical sense, defining some additional restrictions of the solution.

You can choose very, very specific initial conditions in a standard big bang picture to 'solve' the horizon problem, but note:

Those conditions can't be completely homogenous everywhere (otherwise you won't create any sort of clumping), so at least some amount of initial perturbation is needed to create the seeds for structure formation, galaxies and so forth.

And then you are back to asking the question. Why do two causally disconnected regions, presumably not quite, but very nearly homogenous and that are never allowed to equilibriate, both possesses a set of quantities (temperature, density, etc) that match so closely? The initial conditions must be tuned to fantastic accuracy, at every point in space to make it so.

The odds of this happening by chance are so astronomically large, I don't even know how to write that number down.

Dmitry67 said:
Lets say that in TOE the very notion of TIME is emergent. What are you going to do if you don't have t=0? In TOE very likely you have neither time nor spatial boundary. How, in principle, you can define 'boundary' conditions?

The very words 'boundary' or 'initial' (=boundary at earlier time) in general do not make any sense if we think about the whole universe. They are 'boundary' or 'initial' only in mathematical sense, defining some additional restrictions of the solution.
Which makes your whole idea of setting the initial conditions to be a bit contradictory.

Chalnoth,
Let go from the other side. Say, I'm wrong, you're right
initial conditions are not homogenous
Could you provide (write) any example of any non-homogenous initial conditions in infinite flag 3D+t universe (for simplicity let's assume there is just one varibale - p (density) and universe is Newtonian)

Dmitry67 said:
Chalnoth,
Let go from the other side. Say, I'm wrong, you're right
initial conditions are not homogenous
Could you provide (write) any example of any non-homogenous initial conditions in infinite flag 3D+t universe (for simplicity let's assume there is just one varibale - p (density) and universe is Newtonian)
Sure, you could have random initial conditions.

But I don't see that this is a useful exercise, because there is no reason to believe that the t=0 in the big bang theory relates to anything physical at all. Put another way, there is no reason to believe that the beginning of our region of space-time represents the beginning of everything.

no matter what happened at t=0, It is useful if we believe that there are ANY initial conditions.

Ok, let's forget about BB. We have flat Newtonian universe with density function P(x,y,z,t).

Please provide an example any non-homogenous initial conditions. Dont say 'random'. It is a word, not a formula. There is a reason why I am asking not a description of initial conditions, but any (simple) example of such conditions.

Dmitry67 said:
no matter what happened at t=0, It is useful if we believe that there are ANY initial conditions.

Ok, let's forget about BB. We have flat Newtonian universe with density function P(x,y,z,t).

Please provide an example any non-homogenous initial conditions. Dont say 'random'. It is a word, not a formula. There is a reason why I am asking not a description of initial conditions, but any (simple) example of such conditions.
You don't know how to write down random initial conditions? Um, okay.

$$P(\vec{r},0)$$ is a realization of a Gaussian random field with covariance:

$$C(\vec{r_1}, \vec{r_2}) = \sigma^2 \delta^3(\vec{r_2} - \vec{r_1})$$

This means that the field value at any point in space is uncorrelated with the value at any other point in space, while the variance over all points is $$\sigma^2$$.

Cool

This is what I expected even you did not specify the initial conditions correctly, because based on your formula I can not CALCULATE the value for any given point (isnt it a point for having the initial conditions?)

But look, $$\sigma^2$$ is a parameter. So if we begin from the simplest:

P(0,x,y,z)=0

and when we try to create more complicated initial conditions, we nececcerily inject more and more parameters, making it less and less likely because of the ocamm?

Dmitry67 said:
Cool

This is what I expected even you did not specify the initial conditions correctly, because based on your formula I can not CALCULATE the value for any given point (isnt it a point for having the initial conditions?)
That's an arbitrary and useless requirement.

Dmitry67 said:
But look, $$\sigma^2$$ is a parameter. So if we begin from the simplest:

P(0,x,y,z)=0

and when we try to create more complicated initial conditions, we nececcerily inject more and more parameters, making it less and less likely because of the ocamm?
Not specifying any initial conditions would be even simpler.

Edit: But regardless, initial conditions similar in form to those I supplied above are those that would be required by our current observations of the inhomogeneities of the universe, if you want to throw out inflation.

Ok, looks like we have reached the constructive disagreement

But just 1 another question:

Do you agree that in the form how you wrote it:

$$C(\vec{r_1}, \vec{r_2}) = \sigma^2 \delta^3(\vec{r_2} - \vec{r_1})$$

There is no difference between that formula (except it is valid for t=0) and other formulas, responsible for Newtonian laws is our toy universe?

Chalnoth said:
Edit: But regardless, initial conditions similar in form to those I supplied above are those that would be required by our current observations of the inhomogeneities of the universe, if you want to throw out inflation.

Why?
Homogeneity is symmetry which can be easily broken using randomness in CI or splitting in MWI. Then dark matter had 100000 years to magnify initial tiny fluctuations.

Dmitry67 said:
Ok, looks like we have reached the constructive disagreement

But just 1 another question:

Do you agree that in the form how you wrote it:

$$C(\vec{r_1}, \vec{r_2}) = \sigma^2 \delta^3(\vec{r_2} - \vec{r_1})$$

There is no difference between that formula (except it is valid for t=0) and other formulas, responsible for Newtonian laws is our toy universe?
There's a huge difference: that formula requires a specific definition of coordinates, while any good physical law is independent of coordinate choice.

Dmitry67 said:
Why?
Homogeneity is symmetry which can be easily broken using randomness in CI or splitting in MWI. Then dark matter had 100000 years to magnify initial tiny fluctuations.
You have to have some sort of mechanism to generate the initial fluctuations, though. You can't simply say, "It's because of quantum mechanics."

This is one thing inflation does, by the way: it provides a mechanism for the generation of initial perturbations.

1. Wow! Thank you! What a nice argument that I am right!
So this formula introduces another parameter, special frame where it is valid.
Our Universe has something like that (even it is not a 'frame', but in every point of the universe there is a special frame which is 'in rest to CMB'). So this is some kind of broken symmetry.

If initial conditions are not homogenous, then in some rest frames they are anisotropic

But even more, if density=const, then the actual value of const depends on the choice of a frame. The only exception - vaccum, where energy density is canceled by vacuum tension

So the ONLY lorentz-invariant initial conditions is the vacuum

Thank you again!

2. Initial perturbations are generated in any changing gravitational field. Even now (unruh radiation from the horizon)

Dmitry67 said:
If initial conditions are not homogenous, then in some rest frames they are anisotropic
Not at all. These initial conditions aren't anisotropic either. They're approximately anisotropic, and approximately homogeneous, for some observers. Not for all, of course.

And for what observer, pray tell, would these initial conditions actually be anisotropic?

Dmitry67 said:
But even more, if density=const, then the actual value of const depends on the choice of a frame. The only exception - vaccum, where energy density is canceled by vacuum tension

So the ONLY lorentz-invariant initial conditions is the vacuum
Who cares if the initial conditions are Lorentz-invariant?

Dmitry67 said:
2. Initial perturbations are generated in any changing gravitational field. Even now (unruh radiation from the horizon)
And there would be no changing gravitational field if there were no perturbations. Your argument is circular.

It is possible that unconnected regions of the universe could have the same properties without being causally connected. What seems highly improbable is they could be so remarkably similar in all directions.

Chalnoth said:
These initial conditions aren't anisotropic either. They're approximately anisotropic, and approximately homogeneous, for some observers. Not for all, of course.
And for what observer, pray tell, would these initial conditions actually be anisotropic?

For an observer moving thru that matter distributed 'randomly'
In the direction where she moves the Universe looks contracted due to Lorentz contraction.

Chalnoth said:
Who cares if the initial conditions are Lorentz-invariant?

Occam.
Why are you introducing a preferred frame from the very beginning?
Why that particular fram is chosen?

Chalnoth said:
And there would be no changing gravitational field if there were no perturbations. Your argument is circular.

Expansion itself does not require perturbations.

• Cosmology
Replies
1
Views
1K
• Cosmology
Replies
13
Views
3K
• Cosmology
Replies
17
Views
2K
• Cosmology
Replies
37
Views
3K
• Cosmology
Replies
9
Views
2K
• Cosmology
Replies
6
Views
2K
• Cosmology
Replies
6
Views
2K
• Cosmology
Replies
4
Views
2K
• Cosmology
Replies
11
Views
2K
• Cosmology
Replies
2
Views
1K