# Cosmology: Inflation, rate of expansion over the first few years

The universe expanded insanely fast during inflation. But even after it ended (maybe around 10^-32 seconds) the universe still expanded extremely quickly, far faster than it does today. It went from the size of a grapefruit (or even larger, say a football stadium) to 10-40(???) light years in size after one second. After one year the observable universe had expanded to close to the size of the Milky Way galaxy, which it reached by around the third year according to this article: https://www.forbes.com/sites/startswithabang/2017/03/24/how-big-was-the-universe-at-the-moment-of-its-creation/#c710f3b4cea3

The initial rapid expansion was due to inflation and the collapse of the Inflaton field, but once the Inflaton field is gone, why would the universe still expand at such a fast rate (soccer ball to 10-40 light years in a second). What caused the universe to expand at 35LY/meter/second?

Was there a different force, such as repulsive gravity, at work for the first second, year, few years?

What I don't understand is there wasn't an explosion, like a bomb that caused particles to move away at a high velocity, it was space itself that expanded at a rate far exceeding the speed of light/unit time. Why would the expansion rate not immediately stop unless acted on by a force such as repulsive gravity after inflation ended?

From 1 second to a year the observable universe expanded from 10ish LY to 80,000 LY. From year 1 to year 3 it expanded from 80,000 to 100,000 LY. Thats clearly slowing down (why?) yet its still much faster than light and far faster than today.

Inflation ended by 10e-32 but at 10E-12 it was expanding at 10^29 what it is today.

After inflation ended, there was a period of time when the universe was radiation-dominated. During this period the scale factor increased like $$t^{1/2}$$. As the expansion continued, the universe became matter-dominated and the expansion increased like $$t^{2/3}$$. If you plot either curve, you’ll see that they start out with infinite expansion rate and slow down. The slowing down is because gravity of both radiation and matter is attractive.

After billions of years of expansion, the density of radiation and matter got so low that the density of dark energy became important. This made the expansion start speeding up, because the gravity of dark energy is repulsive. This will eventually make the expansion go back to being exponential. But, unlike during inflation, the doubling time will be billions of years rather than a tiny fraction of a second.

The expansion of the universe is the just the motion of the matter in it. The universe continued to expand because of inertia. As in Newtonian physics, there's no force needed to make objects keep moving in general relativity.

Spacetime doesn't have a state of motion in general relativity. 3D space isn't particularly well defined to begin with, but to the extent that you can define it, it doesn't have a state of motion either. There's no way to define (in a generally covariant way) a notion of expanding space. The idea that the expansion of the universe is due to some special cosmology-only behavior of space is simply false. The next time someone tells you it's true, ask them to write down a tensor field that's nonzero when space is expanding and zero when it isn't, or quantitatively define in any other generally covariant way what they mean. They won't be able to do it.

The forces acting on the matter in the early universe were the inverse-square law of gravity and a repulsion due to the cosmological constant (which behaves like a force directly proportional to distance). The cosmological constant was too small to make a difference in the early (post-inflationary) universe. The inverse-square attraction slowed the rate of expansion, but not enough to stop it. The outcome of a small scale (and extremely homogeneous) explosion could be analyzed in the same way; spacetime would locally have a FLRW geometry, and you could put FLRW coordinates on it and define a "cosmological time" and "comoving distance" and such on that basis. There's no special magic in what happens at the cosmological scale; general relativity works the same at all scales.

• The next time someone tells you it's true, ask them to write down a tensor field that's nonzero when space is expanding and zero when it isn't, or quantitatively define in any other generally covariant way what they mean. The Ricci tensor of a Friedmann universe is nonzero when space is expanding and zero when it isn’t. Jul 28, 2020 at 17:03
• @G. Smith It's nonzero when matter is present, regardless of what the matter is doing. Jul 28, 2020 at 17:09
• Sorry, I don’t know what point you are trying to make. The point I made was that your statement “They won’t be able to do it” is false. You seem to have a non-mainstream view of cosmology. A statement like “There's no way to define (in a generally covariant way) a notion of expanding space” indicates to me that you don’t accept GR. Jul 28, 2020 at 17:20
• @G. Smith, I don't understand what point you're trying to make. The Ricci tensor has nothing to do with expansion of space, it's a function of the matter that's present. If there's no matter present then it's zero. The FLRW geometry is not a rigid background into which test particles are placed. It's the gravitational field of the matter actually present. There's no such thing as a vacuum FLRW geometry, except the $\Omega=0$ case. Jul 28, 2020 at 17:20
• The Ricci tensor has nothing to do with expansion of space. That’s equally non-mainstream. We don’t have a basis for further discussion, and comments are not for discussion anyway, so I’m done. Jul 28, 2020 at 17:27