Non-Extensive Entropy and Power-Law Inflation: Implications for Observations

TL;DR

This paper investigates how non-extensive entropic cosmology models, such as Tsallis and Rényi entropies, influence power-law inflation, showing they can produce viable inflationary scenarios consistent with observational data and address limitations of standard models.

Contribution

It introduces the application of non-extensive entropies to inflationary cosmology, demonstrating their ability to produce viable inflation and better fit observational constraints compared to Bekenstein-Hawking entropy.

Findings

Tsallis entropy allows for power-law inflation with n=1 to 2, matching Planck 2018 data.

Extremely small Rényi and Sharma-Mittal entropy parameters enable successful inflation with 55-65 e-folds.

Non-extensive entropies provide a viable alternative to standard entropic cosmology models.

Abstract

This study explores the interaction between non-extensive entropic FLRW cosmology and the power-law inflationary model, with a focus on the overlap between the scalar spectral index `$n_s$' and the tensor-to-scalar ratio `$r$'. Based on a conjecture that non-extensive entropy alters the energy-momentum content of the cosmic fluid, the analysis examines how these overlaps shift with different model parameters and compares the findings to those from Bekenstein-Hawking (BH) entropic cosmology. The study highlights the impact of Tsallis, R\'{e}nyi, and Sharma-Mittal entropies, uncovering a significant correlation between `$n_s$' and `$r$' that suggests a deeper connection in power-law inflationary dynamics. The results demonstrate that non-extensive entropies not only enable viable inflation with a graceful exit but also address limitations inherent in the standard BH entropic framework, emphasizing the importance of precise parameter estimation. Specifically, Tsallis entropy allows for power-law inflation with $n = 1$ to $n = 2$ in alignment with Planck 2018 data. Moreover, the $\alpha$ parameter in R\'{e}nyi and Sharma-Mittal entropy models must be extremely small ($\alpha \leq 10^{-8}$ in Planck mass units) to achieve successful power-law inflation with an e-folding number around 55-65, suggesting a unified thermodynamic perspective in cosmological studies.