The Inflationary with Inverse Power-Law Potential in Tsallis Entropy

Abstract

In this article, we focus on the inflation dynamics of the early Universe using an inverse power law potential scalar field (V_((ϕ))=V_0 ϕ^(-n)) within the framework of Tsallis entropy. First, we derive the modified Friedmann equations from the non-additive Tsallis entropy by applying the first law of thermodynamics to the apparent horizon of the Friedmann–Robertson–Walker (FRW) Universe. We assume that the inflationary era of the Universe consists of two phases; the slow roll inflation phase and the kinetic inflation phase. We obtained the scalar spectral index n_s and tensor-to-scalar ratio r and compared our results with the latest Planck data for these phases. By choosing the appropriate values for the Tsallis parameters, which bounded by β<2, and the inverse power-term of the potential n, we determined that the inflation era of the Universe in Tsallis entropy can only occur in the second phase (kinetic inflation), while the slow-roll inflation phase is incompatible with the Planck data.

Keywords

• Tsallis entropy
• inflationary
• inverse power law potential

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