A Cosmological Model Based on a Quadratic Equation of State Unifying Vacuum Energy, Radiation, and Dark Energy. (21st August 2013) - Chavanis, Pierre-Henri
Abstract : We consider a cosmological model based on a quadratic equation of statep / c 2 = - 4 ρ 2 / 3 ρ P + ρ / 3 - 4 ρ Λ / 3 (whereρ P is the Planck density andρ Λ is the cosmological density) "unifying" vacuum energy, radiation, and dark energy. Forρ → ρ P, it reduces top = - ρ c 2 leading to a phase of early accelerated expansion (early inflation) with a constant density equal to the Planck densityρ P = 5.16 · 10 99 g/m 3 (vacuum energy). Forρ Λ ≪ ρ ≪ ρ P, we recover the equation of state of radiationp = ρ c 2 / 3 . Forρ → ρ Λ, we getp = - ρ c 2 leading to a phase of late accelerated expansion (late inflation) with a constant density equal to the cosmological densityρ Λ = 7.02 · 10 - 24 g/m 3 (dark energy). The temperature is determined by a generalized Stefan-Boltzmann law. We show a nice "symmetry" between the early universe (vacuum energy + radiation) and the late universe (radiation + dark energy). In our model, they are described by two polytropic equations of state with indexn = + 1 andn = - 1, respectively. Furthermore, the Planck densityρ P in the early universe plays a role similar to that of the cosmological densityρ Λ in the late universe. They represent fundamental upper and lower density bounds differing by 122 orders of magnitude. We add the contribution of baryonic matter and dark matter considered as independent species and obtain a simple cosmological model describing the whole evolution of the universe. We study the evolution of the scale factor, density, and temperature. This model gives the same results as the standardΛ CDM model fort > 23.3 t P, wheret P = 5.39 · 10 - 44 s is the Planck time and completes it by incorporating the phase of early inflation in a natural manner. Furthermore, this model does not present any singularity att = 0 and exists eternally in the past (although it may be incorrect to extrapolate the solution to the infinite past). Our study suggests that vacuum energy, radiation, and dark energy may be the manifestation of a unique form of "generalized radiation." By contrast, the baryonic and dark matter components of the universe are treated as different species. This is at variance with usual models (quintessence, Chaplygin gas, ...) trying to unify dark matter and dark energy.