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

Figure 11

Evolution of the scale factor 𝑎 with the time 𝑡 in logarithmic scales. This figure clearly shows the transition between the matter era (EdS) and the dark energy era (de Sitter). In the dark energy era, the radius increases exponentially rapidly on a timescale of the order of the cosmological time 𝑡_Λ=1.46⋅10¹⁸s. This corresponds to a phase of late inflation. The universe is decelerating for 𝑎<𝑎^′_𝑐 and accelerating for 𝑎>𝑎^′_𝑐 with 𝑎^′_𝑐=7.11⋅10²⁵m. The transition between the matter era and the dark energy era takes place at 𝑎₂=8.95⋅10²⁵m. Coincidentally, the present universe turns out to be close to the transition point (𝑎₀∼𝑎₂).