# Why is the horizon problem a problem?

I am curious about physics and astrophysics in particular, although I have no academic basis.

Usually, I find it easy to understand the concepts and explanations, but I have particular difficulty in understanding the premises of why the CMB observation leads to the horizon problem.

In general, the explanations I see start from the premise that different areas of primordial space should have different temperatures, and, as light would not have had time to travel between all corners of space and homogenize temperature, the CMB should not be so uniform.

My problem is: where does the premise come from that primordial space should have different temperatures in each region?

My mental image is of a singularity that starts the big bang. This singularity, unless there is a reason to the contrary, should have given rise to a homogenous universe, even before particles would exist themselves.

If space starts to expand from a homogeneous environment, it should remain homogeneous until something happens to change that.

Therefore, for me, what would be expected is precisely that the CMB would be homogeneous, and not the other way around.

What am I missing? How we are certain that the universe “should” have been heterogeneous in temperature?

• I might have asked exactly that Question, and I appreciate Sten's and TimRias' Answers. Isn't it true, though that in lay terms, more stuff happens in less time as we look further back? Then can it really be known that what Physics thinks of as the first syllable of recorded time, in fact came rather later and there wasn't (a lot more) stuff happening before that? Commented Feb 29 at 14:32

## 5 Answers

The other answers are good, but I want to address this idea specifically:

This singularity, unless there is a reason to the contrary, should have given rise to a homogeneous universe, even before particles would exist themselves.

Indeed, it seems pretty natural that the Universe should be initially homogeneous. The Universe must ultimately have some initial conditions. Why not let them be the simplest ones?

However, the Universe is not initially homogeneous! The primordial curvature power spectrum is measured to be $$\mathcal{P}_\zeta(k)\simeq 2.2\times 10^{-9} \, \left(\frac{k}{0.05 \text{ cMpc}^{-1}}\right)^{-0.04}$$ (where cMpc is "comoving megaparsec"). Very roughly speaking, this describes the squared fractional amplitudes of initial density variations as a function of the reciprocal length scale $$k$$. The interpretation is that on scales that are too large to be in causal contact, there are density variations with fractional amplitudes of around $$\sqrt{2.2\times 10^{-9}}\simeq 5\times 10^{-5}$$ (one part in 20 thousand), and moreover, these variations have slightly scale-dependent amplitudes, such that on a 10-times-larger length scale, the initial density variations have amplitudes $$\sqrt{10^{0.04}}\simeq 1.05$$ times larger (5% larger).

Those are perhaps not so natural initial conditions after all! (In fact, the $$10^{-9}$$ in there is technically unnatural.) Why would the Universe pick them?

(Technical note: when I refer to superhorizon density variations, I'm speaking in Newtonian gauge.)

• What I understand from your answer is that our observations of the universe, when applied to the models we have, indicate an early universe that should have been heterogeneous. I can accept this. But looking at the articles I read on the subject, this being the case, I would write them differently. I wouldn't say that the universe should be heterogeneous. I would say that our best models, when applied to our observations and extrapolated back to the past, indicates a heterogeneous primordial universe. This makes sense to me. Commented Feb 27 at 15:56
• Yeah, I think the primordial density variations represent some often-missed context about what is really driving the science in this area. Scientists working on the origins of the Universe are not trying to explain a homogeneous universe. They are trying to explain the precisely measured primordial power spectrum, as well as other observed features of the primordial perturbations, like their precisely Gaussian distribution and the presence of only scalar modes (density variations) and not tensor modes (gravitational waves).
– Sten
Commented Feb 27 at 22:45

Consider this analogy instead. Suppose you were to invite a hundred different people to your birthday party. They all show up wearing the same clothes (not just the same type of clothes, but literally the same clothes, with the same brand, same color, etc.) Do you conclude that they must have communicated with each other before coming?

I suspect most people will say yes. After all, there is no reason to expect that they will wear the same clothes. If they all decided independently, then the odds that all of them choosing the same clothes should be astronomically small. But note that it is in theory possible that it really is sheer coincidence. It might be contrived, but it's possible.

There's where the horizon problem comes from. Calculations show that in the naive Big Bang model, different patches of the sky are causally disconnected - that is, they could not possibly have communicated, because doing so would require speeds that are greater than the speed of light. There is no reason to think they would have the same temperature, yet we measure them to do. It could be coincidence - which is equivalent to postulating that "primordial space has exactly the same temperature in each region" - but it seems much more reasonable to conclude that the Big Bang model without inflation is incorrect. Once you assume inflation, then you do have reason to expect these patches of the sky to show the same temperature. Phrased alternatively, the naive Big Bang model cannot explain why the CMB is so uniform, while the Big Bang model with inflation naturally leads to that result.

If you're willing to accept the postulate that a few hundred (I don't remember the exact number) causally-disconnected patches of the sky can somehow have the same temperature through random coincidence, then the horizon problem isn't a problem for you. For most people, however, they will consider that improbable enough to be a problem.

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– Buzz
Commented Mar 3 at 17:13

My mental image is of a singularity that starts the big bang. This singularity, unless there is a reason to the contrary, should have given rise to a homogenous universe, even before particles would exist themselves.

This intuition seems based on thinking of the initial singularity as a point, which effectively brings back all the points into contact, allowing for the choosing of a common initial condition.

However, the initial singularity in FLRW universes is not a point but a spacelike surface. So, even at the singularity the different patches do not come into contact. Consequently, we should expect the initial conditions in each patch (whether chosen at the singularity, or sometime there after) the be chosen independently.

• In fact, I tend to imagine the singularity as a single point. This view probably comes from the understanding that the expansion of the universe is not simply a stretching, but the creation of space itself (hence the redshift effect). Then, rewinding, I tend to imagine less and less space until a homogeneous singularity. Commented Feb 27 at 15:51
• The singularity is spacelike in the sense that timelike curves terminate at it, but it's not a surface in the sense of being a submanifold of lower dimension
– Sten
Commented Feb 29 at 4:54
• @Sten Agree. The main point I'm making is that causally disconnected patches stay causal disconnected all the way to singularity, and therefore have independent initial conditions. Commented Feb 29 at 8:23

What you need to understand is that physicists think of the big bang backwards (in a sense). The current universe is expanding, and the statement of the big bang is that if you wind that back far enough (about 14 billion years or so) the universe is very dense, and very hot. Thats the big bang. If we run this back far enough the energy density eventually goes above a plank mass per plank area, that's when we run into "singularities". While the big bang is certainly a beginning to our universe (i.e. everything we see now, was once there) no one knows that this is the beginning of everything.

Now we see a patch of our universe, that is at a uniform(ish) temperature. So unless someone set it up like that, and the universe was very homogeneous in the past (which seems like a very special case that would need some justification) we expect that the uniformity in temperature came from the universe interacting with itself. But for that to happen, the different parts of the universe must be in causal contact. This leads to the horizon problem you started with. Of course you can postulate that it "just was" homogeneous, but then I would want a reason why, which is hard given that we dont know the physics at play at those energy densities

• If our patch of universe didn’t have uniform temperature we would not need to know why also? How is that different, if we don’t really understand the state that lead to it (the universe before Planck scale)? Commented Feb 27 at 7:57

(I'll add this as a separate answer, since it provides an answer along completely different lines.)

In important element of the horizon problem is that we observe the CMB to be in almost perfect thermal equilibrium (the CMB spectrum closely resembles a black body spectrum). There is no particularly good reason to think the universe started out in thermal equilibrium. The much more likely explanation is that it reached this equilibrium through thermalizing over a period of time. Prior to this thermalization the temprature would not even be well defined.

It would be extremely unlikely for this rather chaotic process to lead to all causally disconnected patches of the CMB having almost exactly the same temperature.

• How is the fact that we do observe the CMB to be in almost perfect thermal equilibrium not in itself a good reason to think the universe started out in thermal equilibrium? What could prior to thermalization the temperature would not even be well defined actually mean? I wasn't there but how could the necessity for thermalization not mean that some factor you're not naming caused the early universe not to be consistent? Who says anything would be at all, let alone extremely unlikely? Commented Feb 27 at 22:20