Abstract
We consider a cosmological model based on a quadratic equation of state (where is the Planck density and is the cosmological density) “unifying” vacuum energy, radiation, and dark energy. For , it reduces to leading to a phase of early accelerated expansion (early inflation) with a constant density equal to the Planck density g/m3 (vacuum energy). For , we recover the equation of state of radiation . For , we get leading to a phase of late accelerated expansion (late inflation) with a constant density equal to the cosmological density g/m3 (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 index and respectively. Furthermore, the Planck density in the early universe plays a role similar to that of the cosmological density 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 standard CDM model for , where 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 at 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.
Highlights
The evolution of the universe may be divided into four main periods [1]
The universe is composed of approximately 5% baryonic matter, 20% dark matter, and 75% dark energy [1]
We propose that vacuum energy, radiation, and dark energy may be the manifestation of a unique form of “generalized radiation”
Summary
The evolution of the universe may be divided into four main periods [1]. In the vacuum energy era (Planck era), the universe undergoes a phase of early inflation that brings it from sthizeePalan∼ck10si−z6emlP. Observations tend to select the constant pressure equation of state p = −ρΛc2 (a = 0, n = −1) among the whole family of Chaplygin gas models of the form p = −A/ρa.) In [34,35,36], we proposed to describe the transition between the vacuum energy era and the radiation era in the early universe by a unique equation of state of the form p/c2 = −4ρ2/3ρP + ρ/3 This equation of state may be viewed as a generalized polytropic equation of state (1) with polytropic index n = 1, polytropic constant k = −4/(3ρP), and linear coefficient α = 1/3. They represent fundamental upper and lower density bounds differing by 122 orders of magnitude
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