Trying to teach myself the basics of cosmology. I can see why, in an expanding universe, radiation and matter density, and radiation and matter pressure vary with time. But why is it assumed that dark energy is independent of time?
In my textbook, it's just sort of stated as if it's blindingly obvious.
Many thanks
Time invariant dark energy is the simplest form. Time invariant dark energy appears in the GR field equations in the same way as a cosmological constant, making it easy to handle.
There are plenty of other suggested forms of dark energy that do vary with time. See for example wikipedia.org/wiki/Quintessence_(physics).
First of all, when it is said that 'dark energy is independent of time', this means that the density of dark energy is invariant, not the total amount, which does indeed increase with the size of the universe. Of course, "dark energy" or "quintessence" in the simplest models are just cosmological constants. I.e., the same "constant" that appears in Einstein's equations. Another way to get a constant contribution to the energy density is to have a scalar field which is resting at the minimum of its potential. Many popular inflationary models are based on this picture. From the perspective of elementary physics, however, the easiest explanation is that dark energy is constant because of it's equation of state. The equation of state says that the energy density is equal to the pressure, which, one may easily show, implies that the energy density is constant as the universe expands. (dE=pdV, therefore dE/dV = E/V, implying E is proportional to V, or that the energy density is constant.)
Incidentally, one might ask why the positive energy density doesn't cause the universe to collapse. Instead, dark energy fuels the expansion. The answer is that pressure outweighs the energy density in Einstein's equations since there are 3 directions of space and only one of time and pressure is related to the spatial directions while energy is related to time. This means that the pressure is basically three times as effective at expanding the universe as the energy is at contracting it, resulting in a net (accelerating) expansion.
Einstein once called the cosmological constant his biggest blunder, which he said when he was told by someone else the universe was expanding, and he then revised his theory, based on what little was known back then. He came up with it originally to explain a static, non-expanding universe, which was accepted until observations of redshift by Hubble. Energy cannot be created or destroyed, it only changes form. It is not reasonable to say with certainty that dark energy remains at constant density with time and expansion, as all other forms of energy don't, and we can't see it or measure it, except by calculations based on assumptions based on observations. Occam's Razor says that the more assumptions a solution has, the more likely it is wrong.
