Cosmological solutions of the Einstein-Friedmann equations ...

Cosmology
Appendix: Λ 0
The issue about the true value of the cosmological constant, which likely is
non-vanishing as mentioned earlier, will be reconsidered later. In any case we
have to discuss the solution of the cosmological equations for the case on
non-zero cosmological constant. The consequences for the empty world case we
already discussed: flat “background space” gets replaced by de Sitter or anti-de
Sitter space. The generalization to the matter dominated scenario is almost trivial.
A glimpse at the Friedmann equation shows that one can treat the cosmological
constant as a contribution to the energy density:
κρmat + Λ → κρtot,
where ρtot = ρtot + ρΛ with ρΛ = Λ
κ . Provided p = 0, all solutions remain unchanged,
except for a different interpretation of the energy density, which in this case is not
identical with the “normal” mass density of baryonic plus dark matter. Note that
the cosmological constant in general enters the equation of state in a not a priori
c○ 2009, F. Jegerlehner ≪❘ Lect. 7 ❘≫ 479