# Question about the Horizon Problem

1. Jan 9, 2005

### NumberTenOx

I'm familiar with the Horizon Problem and how it is solved by the theory of Inflation. I also know that Inflation solves some other cosmological problems and fits well with the current CMB data.

Just focusing on the Horizon Problem, however, I'm curious about one thing. It seems to me that one solution to the Horizon Problem is to assert that whatever first created the universe did so with complete homogeneity, without the need for different parts of the universe to interact and become uniform.

Imagine, for example, that the universe was created at time t=0 with a size of one light year, and with complete homogeneity, because the process of creation required a specific energy density with extreme precision.

I'm not suggesting that this is a valid theory, I'm just curious as to what leads us to reject this hypothesis. As far as I know, no one has a conclusive answer as to what process actually created the universe - how do we know it didn't require homogeneity?

2. Jan 9, 2005

### Mike2

Are you suggesting that there was an instant creation of everything all at once of a given size? That would seem to deny a cause for it, and this offends our sense of reasoning. That might also negate the symmetry between time and space, t=0 but space = something not zero. We have a sense that at t=0 when space=0 in order to maintain causality. This leave no alternative but that the universe started with a singularity at t=0. Or it may have been a singularity at t= - infinity.

Last edited: Jan 9, 2005
3. Jan 9, 2005

### NumberTenOx

Actually, nevermind. I found this in Alan Guth's The Inflationary Universe. Should have looked there before I posted.

But the uniformity is explained by inflation.

4. Jan 10, 2005

### Garth

1. The horizon problem is related to these others.
2. The smoothness problem: why is the universe homogeneous but not completely smooth in which case there would have been no gravitational collapse of galaxies, stars or planets?
3. The density problem: why is the observed density of the universe close to, if not equal to, the critical density that occurs naturally in GR?
It is that precision that is the problem. Unless you invoke 'God' or some other 'transcendent' (faster than light) process to arrange the density with "extreme precision", there is no reason why different regions of the universe should have had the same density. These regions, which we can see today in different parts of the sky, would have been causally unconnected in those early moments as then there had not been enough time for light to travel around even a very small early universe.

The problem arises when we travel back in time and factor in a universe that decelerates in its expansion.

Take the density problem. If the actual density was originally close to the critical density at the earliest Planck time, 10-44 sec. then by now, if the universe decelerates the actual density would be a factor of about 1060 different from the critical density. However, if the universe had accelerated in its expansion then the opposite would now be true. Inflation resolves the density problem by accelerating the expansion of the universe, at an early stage, by a factor of over 1060, which had the effect of driving the actual density onto the critical density so closely that the subsequent decelerating expansion hasn't separated them yet.

It is interesting that the most recent standard model actually requires acceleration at some stage, which might alleviate the problem and thus not require Inflation, however it is thought that this accelerating expansion has not been there throughout cosmic history, it has been 'turned on and off'. (Why? How?)

I must mention here, (to everybody's amazement!), that if the universe never decelerated in its expansion in the first place, but simply expanded in a strictly linear fashion, R = ct, this is http://arxiv:org/abs/astro-ph/0209209, then these problems would not arise and Inflation would not be necessary.

Such a model requires a modification of GR to provide the mechanism to explain this behaviour and one viable published theory that delivers such a mechanism is http://arxiv:org/abs/gr-qc/0405094.

Garth

Last edited by a moderator: Apr 21, 2017
5. Jan 10, 2005

### Chronos

The horizon problem is what made inflation [first championed by Alan Guth IIRC] so attractive in the first place. It also works well with the smoothness problem. It became a crowd favorite after the CMB anisotropy [WMAP results] was found to be highly consistent with predictions of the inflationary model.

6. Jan 11, 2005

### Garth

That is WMAP revealed that the CMBR fluctuations were scale invariant and this is consistent with a flat universe. Inflation predicts k = 0, flatness. However as the WMAP data is angular in nature it is also consistent with a conformally flat universe, such as the freely coasting model.

Garth

Last edited: Jan 11, 2005
7. Nov 12, 2007

### Mortran

I don't understand the problem of the "Horizon Problem".
As far as I understand it, scientists wonder why the universe looks so homogeneous when we look 14 billion light years to the left and 14 billion light years to the right. They assume that since the total distance of these two points would be 28 billion light years, there was no way how light could travel from one point to the other.
But in fact the distance between the two points is not 28 billion light years, it is actually zero. The simple fact that, when we look in a distance of 14 billion light years, we also look 14 billion light years back in time seems to be ignored by the "Horizon Problem". The point that we see when we look 14 billion light years to the left is actually the big bang when the universe had a diameter close to zero. The same is true for the point that we see 14 billion light years to the right. It is the same point in space. There is no distance between them, so light has no problem to travel between them.
If we assume that the universe did never expand with a speed faster than light (rejecting the Inflation theory, which has no need in such a model), then there are no two locations in the universe which are more distant from each other than 14 billion light years, which can perfectly explain the smoothness and homogeneity of the universe.
I don't see any need for an Inflation theory, which creates only more questions than it answers.

Obviously I made a mistake in my argumentation, but I don't see where it is. Assuming that the universe has a diameter of less than 14 billion light years, why is there a horizon problem? Light could have easily crossed the universe. And assuming that the background radiation is actually the remnant of the Big Bang, it is the proof that we can see across the universe, right to its beginning. The entire universe is apparently within our visual horizon, because we can see back to the Big Bang, and there is no part of the universe beyond it.
Where is the error in my thought?

Can anybody help me to answer this question and to explain the horizon problem to me?

8. Nov 13, 2007

### chronon

There are two problems with your argument. Firstly you are thinking in terms of 'Radar coordinates', in which distance and time are given by looking at the behaviour of light. These coordinates disagree with 'Comoving coordinates' which are those used by cosmologists. You can get an idea of the differences between coordinate systems from my Cosmological Distances applet .

Of course the behaviour of the universe doesn't depend on the coordinates we use to describe them, but when distances are mentioned it is vital to be clear about what coordinate system they relate to. One big problem with radar coordinates is that you end up with an infinite amount of universe within a finite coordinate size. The other problem is that it is harder to do general relativistic calculations using these coordinates.

The second and more serious problem with your argument is that you claim we are looking back to the big bang. In fact we are only looking back to the CMBR, which comes from matter a few hundred thousand years after the big bang. The parts on opposite sides of the sky for us would have been much closer together, but they were certainly not next to each other, and you would find that the equations of general relativity tell you that no matter how far back you go a signal would not be able to travel between them. This is the horizon problem.

If you could ignore gravity (the (0,0) model of the universe) then you would be correct, there would be no particle horizon and the entire (infinite) universe would be in our past light cone.

Last edited: Nov 13, 2007
9. Nov 13, 2007

### PRDan4th

Let me say first that I am not a Physicist. I am a retired Chemical Engineer with an interest in physics. Reading this thread has given me a thought that may explain our perception of what we see in the universe. I am probably wrong, but here goes:

Imagine the universe as an expanding sphere with everything we see on the surface. Light travels in this model parallel to the surface. There is no up or down! With our most powerful telescopes we can see the CMBR in all directions that we look, which is a spot close to the opposite side of the sphere. This sphere is expanding at some rate explaining the expansion of the universe. If we could see farther than the CMBR we would see the big bang event.

Does this idea make sense?

Peter Danforth

10. Nov 13, 2007

### Mortran

@chronon:
So does my mistake lie in the fact that space has already expanded 14 billion years ago (at the point where the CMBR originates) at a speed so that light wasn't able to catch up?

But what about assuming that space never expanded faster than light? In this case light would always have been able to catch up with the expansion of the universe.

You are right of course, the 3K background radiation that we see, is not exactly the Big Bang but shortly after the Big Bang, when the density of the universe became low enough to make the universe transparent for the radiation. As you explained it, this is a few hundred thousand years after the Big Bang. But this is not actually a big difference. A millisecond or one hundred thousand years are equally insignificant time spans compared to the age of the universe of 14 billion years.
Under the assumption that space did not expand faster than light, the size of the universe at this point of time would have been just about hundred thousand light years. Therefore all points of the visible horizon that we can see today are less than hundred thousand light years away from each other. This would be close enough for light to travel across this distance and to explain the homogeneity of the visible universe.
Or is there any evidence that the universe expanded faster than light that I am not aware of?
Actually I am using the same model as you, PRDan4th in order to imagine the situation. This is why I don't get it. In this model, when I inflate the sphere, I never run into the horizon problem. It is a fact that we can see the CMBR. So we can obviously see almost to the spot on the other side of the sphere (just lacking 100,000 light years.) If we can see this spot, then there is no point on the surface of the sphere which would be beyond our horizon.

But perhaps this model neglects the fact that this spot has also vastly expanded.....
May be here is my mistake. It is really hard to imagine. You cannot just take a 3D model, you have also to take time into consideration.

Perhaps I get it with another approach: As I understand it, the visible horizon of the universe is about 14 billion light years. Is the estimated size of the universe actually bigger than 14 billion light years? And if yes, how big is it supposed to be?