A Mess of Cosmic Coincidences: Problems With the Big Bang Theory

The furthest bodies
To which man sends his
Beyond which God is;
The cosmic motes
Of yawning lenses.
~Robert Frost, I Will Sing You One-0

Awe! She's so cute!
Although it shares the same name, cosmic inflation is very different from inflating a balloon. Cosmic inflation referst to the speed of expansion. (Image from wikipedia.)

I apologize for the long time of silence! I graduated from the University of Colorado about a month ago and was immediately assaulted by a huge amount of family affairs… and then caught up in moving. Sorry about this, everyone! My regular Sunday update schedule should resume next week.

Last time, I described the theory of the Big Bang. I gave some history of the theory, and some reasons for why we believe it. The Big Bang theory beautifully aligns with observations. We know the universe is expanding, which means it must have been much smaller in the past. If we plug this into the equations of general relativity, the mathematics of the Friedmann-Lemaitre-Robertson-Walker cosmology (FLRW cosmology) predict the Big Bang singularity. Furthermore, a Big Bang should have left an echo, which we observe now as the cosmic microwave background.

Unfortunately, the Big Bang theory is shadowed by some strange almost problems. What I mean by “almost problem” will become more clear after I explain what they are.

The Flatness Problem

We know from Einstein that space and time are both part of a united spacetime. We also know that this spacetime can be curved. Indeed, not only is the spacetime curved, but at a given fixed time, space can be curved too. To visualize things, let’s move down to two dimensions. Imagine that spacetime is the surface of a hollow sphere. Spheres are curved, and so is spacetime. Now, at a given time, the spatial extent of the universe forms a circle. Circles are curved too, and each spatial slice is thus curved.

The universe in a nutshell: the universe IS a nutshell!
If we imagine that spacetime is a sphere, it’s made up of circles, which form the spatial extent of the universe at a given time. The bigger the circle, the less curved it is.

But not all slices are made equal. Each circle has a radius associated with it; and the curvature of a circle is inversely proportional to its radius. In other words, the smaller circles have more curvature! So the biggest circle has the least curvature and the smallest circle has the most curvature.

Of course, this is a pretty simple model. In reality, the curvature of the spatial extent of the universe at a given time is determined by the distribution of mass and energy in the universe at this time and in the moments before and after it. This in turn is determined by the densities of mass and energy at the beginning of the universe, and by how much time has passed.

The FRLW model—the same mathematics that predict the Big Bang—tells us that the the spatial portion of the universe should have become more and more curved as time passed. And herein lies the problem. Current measurements show the universe to be almost totally flat as far as we can tell… which would mean the universe was even flatter right after the Big Bang. The odds of the early universe being so colossally flat are are astronomically—pun intended—low. We call this the flatness problem.

The Horizon Problem

At the instant of the Big Bang, the universe was singular. Distance had no meaning, and everything was—in a sense—located at the same place. However, right after the Big Bang, parts of the universe were thrown out of causal contact with each other. Light originating at one end of the universe didn’t have time since the beginning of time to reach the other side of the universe. As time passed, light had the time to travel further distances, and distant parts of the universe were able to interact.

Cauchy and Euler were both instrumental in putting Calculus on firm rigorous ground.
In the moments after the Big Bang, Augustin Louis Cauchy and Leonhard Euler are thrown out of causal contact. Light doesn’t have enough time since the beginning of the universe to travel from Cauchy to Euler. But, as time passes, light can travel further and, eventually, Cauchy and Euler can see each other. The red and blue lines represent Cauchy and Euler’s lines of sight respectively. The y axis is time and the x axis is space.

As I described in my previous post, the cosmic microwave background (CMB) is important evidence in favor of the Big Bang theory. The CMB is a sea of photons permeating everywhere in space left over from the big bang. Moments after the big bang, the universe was too dense and too hot for atoms to form. The charged particles that formed up all the matter in the universe moved around very quickly—and moving particles create light. After the universe expanded and cooled, this light remained, and this is the CMB.

In recent years, we’ve measured the CMB to a very high level of precision… and discovered something strange. Everywhere we look in the sky, the CMB is exactly the same. The distribution of colors (wavelengths) of light in the CMB is the same everywhere in the universe. The reason this is unsettling is because we should see random fluctuations. The only way the CMB could look the same everywhere, is if photons from one end of the sky, mixed with photons from the other end of the sky, until they all formed a homogenous mixture.

Think of this like Thai iced tea. For those of you who don’t know, Thai iced tea is a very strong tea from thailand. It is often sweetened by condensed milk, which you pour over the top. Since milk and tea have different densities, the milk floats happily on top of the tea, as shown in the figure below. Much like photons on different sides of the universe, the milk and the tea can’t mix with each other on their own. However, if I stir the beverage, the milk and the tea mix together and homogenize. No one stirred the CMB, however; so how did it become so homogenous?

Thai iced tea is a lot like the cosmic microwave background. At first (as shown on the right), different parts of the beverage—condensed milk and tea—have very different qualities. However, after mixing (on the left), the tea becomes homogenized. (Image source).

Perhaps the answer is simple. Enough time must have passed after the big bang for photons on one side of the sky to have interacted with photons on the other side of the sky. Unfortunately, that amount of time STILL hasn’t passed! On each side of the sky, new photons reach us ever instant that have been traveling towards us since they were formed in the hot early universe. They haven’t had time to reach the other side of the sky.

Of course, we could just be incredibly lucky. By pure random change, all the random fluctuations in the CMB in the early hot universe could have resulted in a very homogeneous CMB now. However, this is incredibly unlikely. We call this the horizon problem.

The Problem With Our Problems

Now I can explain what I meant when I said there were “almost problems” with the Big Bang theory. There’s nothing obviously wrong with the Big Bang theory. No evidence contradicts it. However, if we assume that the Big Bang occurred as I described last time, it’s incredibly unlikely that the universe would have evolved in the way we observe it to have. Chalking the observations of the flatness problem and the horizon problem up to a colossal coincidence is not very satisfying. So cosmologists have looked for another solution. The solution is Cosmic Inflation, which I’ll talk about next time.

8 thoughts on “A Mess of Cosmic Coincidences: Problems With the Big Bang Theory

  1. Two things:

    Firstly can I just shout out how much I love your blog! As an undergraduate physics student myself, I can understand (from the theoretical perspective) some of the material and I have heard of the rest, but it’s wonderful to read your take on things.

    Secondly, love it how you manage to namedrop famous scientist here and there cf. Cauchy and Euler.

    Hope to see more fantastic blog entries soon!

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