Energy content of the universe

For a homogeneous and isotropic universe, one can show that the tensor energy-impulse is that of a true fluid (weinberg1972, chapter 2). One a:

$$T^{\mu \nu} = (\rho + P) V^\mu V^\nu -Pg^{\mu \nu}$$ (1.10)

Where $P$ are respectively the quadrivitess, the density and the pressure of the fluid. One can consider two kinds of traditional fluids `` '' and a new fluid, respectively:

1. Fluids made up of particles not-relativists for which one can consider that the pressure is null. $\rho$ is thus mainly the energy of mass of this fluid. It is the case of the ordinary baryon matter. One will speak in this case about matter.

2. Fluids made up of relativistic particles whose pressure is $\rho \propto \lambda a^{-1 }$. One will speak then about radiation.

3. A new type of fluid of the cosmological constant type, of which the density does not vary with time.

Let us note that one can pass continuously from the one to the other of these fluids, and that nothing prohibits their mixture.