The inflationary era of the universe via Tsallis cosmology

Abstract

In this paper, using the first law of thermodynamics (FLT), we derive a modification of the Friedmann equation from the nonadditive Tsallis entropy associated with the apparent horizon of the Friedmann–Robertson–Walker (FRW) Universe, where matter inside the apparent horizon is represented by a scalar field with a potential. We suggest that the inflationary era of the universe may phenomenologically consist of the two phases. We determined that the first phase is an inflate under the slow-roll condition known as exponential accelerated expansion, and the second one is an expansion phase containing the kinetic term of the scalar field, leading to a quintessential era. After expressing the observable inflation indices for both phases in terms of e-foldings number with choosing power-law scalar potential, we have compared the results with the latest Planck observation data. With some restrictions on the nonadditive Tsallis parameter and power-term of the potential, we observe that inflation can occur with the two phases. It is determined that while the nonadditive Tsallis parameter is positive in the slow-roll phase, it takes negative values in the kinetic energy dominating phase. Nonetheless, for the apparent horizon of the universe, an increasing entropy exists in the first phase, while a decrease in entropy is observed for the second phase, which indicates that the universe is ready for the creation of matter. In addition, a correlation between slow-roll and kinetic inflation is shown by determining the kinetic energy-potential relationship via the exponential term of the potential.