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Dark energy is density is constant and that's something like 75% of the universe, so I am pretty sure that the net change must be positive. But photons redshift and so loose energy. I assume other wave-like particles (all of them?) also redshift and so energy is lost. On the other hand matter (galaxies, dark matter etc) moves apart and so we have more gravitational potential energy and so more energy. So a proper accounting would be interesting.

Perhaps the answer is different at different cosmological epochs, since the energy change depends on the inflation rate.

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A few things:

1) it is in principle unknowable what's happening outside the cosmological horizon. Because notions of total energy depend on boundary conditions (or conditions at infinity), there are several different possible scenarios for "the total energy of the universe", all of which are completely consistent with observation

2) Assuming that homogeniety and isotropy extend forever, then the notion of "total energy of the universe" is actually logically inconsistent. The right answer is to say either infinity, or that the energy is not defined. The root reason for this is that a consistent definition of energy depends on having a locally time-invariant physics. A (non steady-state) expanding universe is inherently time-dependent, and therefore, cannot have a consistent energy. We are only able to do so in the solar system because the stress-energy density of the universe is relatively small when compared with the binding energies of the sun and planets, which makes our local space look approximately like empty space.

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  • $\begingroup$ in some sense, the total energy of a homogeneous isotropic universe is well-defined: FLRW spacetime comes with a privileged set of observers, making Pirani's expression for energy well-defined; that energy is trivially 0 in any finite volume as the density vanishes identically, yielding a vanishing total energy as limit $\endgroup$ – Christoph Feb 8 '15 at 21:43
  • $\begingroup$ @Christoph: and you can do various extensions from the Schwarzschild-de Sitter universe to an expanding universe and get some sort of notion of energy that way, too. None of it really meaningfully answers the OP's question, though. $\endgroup$ – Jerry Schirmer Feb 8 '15 at 21:46
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The total energy of the Universe is a sticky subject. First of all do you mean the total Universe? If the Universe is infinite surely the total energy is infinite, but we can't know if it is inifinite or not anyway. Do you mean the observable Universe? In which case the size of the observable Universe is increasing in terms of proper volume and comoving volume. Do you try you try to include gravitational energy? In which case you encounter huge problems defining gravitational energy in general terms. For this reason I think it is better to speak of the energy density (and not worry about trying to shoe-in a concept of gravitational energy).

In an expanding Universe with cosmological constant the energy density per proper volume will decrease with cosmological time, approaching a constant which will be the energy density of the cosmological constant. This is as the energy density per proper volume due to matter and radiation decreases (with the energy density due to radiation decreasing quicker than the energy density due to matter), whereas the energy density due to the cosmological constant stays the same.

In some ways to see how the different energy densities it is instructive to look at the energy density per comoving volume. Per comoving volume, the energy density due to radiation decreases (due to redshift), the energy density due to mater (modeled as a dust) is constant and the energy density due the cosmological constant increases.

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There are reasonable senses where energy is constant. In a homogeneous (but evolving) universe you can imagine a series of time slice determined by the slices of the universe where things look the same everywhere. We can call these surfaces, surfaces of constant cosmological time.

For those time slices you can look at the stress-energy tensor, and note that it's integral over that surface of constant cosmological time is the same for every time. So an electromagnetic wave can get stretched out and have less energy density, but over more space so the same energy. Or it could change it's energy density, but be compensated by a change in the energy density of charged particles. So it changes from here to there, but globally it is the same (unless the universe is infinite and plays a Hilbert's Hotel kind of trick).

So that's the stress-energy tensor, it includes radiation, dark matter, and regular matter. The only thing left is dark energy, and if you postulate that that doesn't change (which you stated in your question) then energy is conserved.

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