Why did dark energy play a subdominant role in the radiation and matter dominated era?

Question

After inflation, the Universe passed through radiation dominated (RD) and matter dominated (MD) era during both of which the evolution of the scale factor (or the Hubble parameter) was decreasing with time as $H\sim t^{-1}$. These were phases of cosmic deceleration. However, the present Universe is undergoing an accelerated expansion. Whatever agent causes this expansion is termed as dark energy. It may be constant, or perhaps, it has been evolving with time.

If we assume that dark energy was always in the form of a constant energy density which doesn't dilute with expansion- a cosmological constant, why didn't it play a dominant role in the RD and MD era?

Answer 1

Because the Universe was much smaller at that time. Both matter and radiation is diluted as the volume it occupies expands, but the dark energy (DE) density is constant.

The density of matter decrease with increasing volume $V \propto a^3$, where $a$ is the scale factor, or the "size", of the Universe. Radiation is also redshifted, and the redshift is linearly proportional to the expansion, so there's an extra factor of $a$; hence its energy density decreases as $a^4$.

But dark energy (DE) is a property of space itself and has a constant energy density. That means that when you increase the volume, the density of matter and radiation decreases, while the density of DE stays the same. Hence, at some point it will start to dominate.

You can calculate backwards and find that matter and DE contributed equally when the Universe was roughly 10 billion years old; before that, matter dominated. You can then go on and find that matter and radiation contributed equally when the Universe was roughly 50,000 yr old; before that, you have the radiation-dominated epoch.