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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

A Cosmological Model Based on a Quadratic Equation of State Unifying Vacuum Energy, Radiation, and Dark Energy