Inflation Based on the Tsallis Entropy

Abstract

We study the inflationary scenario in the Tsallis entropy-based cosmology. The Friedmann equations in this setup can be derived by using the first law of thermodynamics. To derive the relations of the power spectra of the scalar and tensor perturbations in this setup, we reconstruct an $f(R)$ gravity model which is thermodynamically equivalent to our model in the slow-roll approximation. In this way, we find the inflationary observables, including the scalar spectral index and the tensor-to-scalar ratio in our scenario. Then, we investigate two different potentials in our scenario, including the quadratic potential and the potential associated with the natural inflation in which the inflaton is an axion or a pseudo-Nambu-Goldstone boson. We examine their observational viability in light of the Planck 2018 CMB data. We show that although the results of these potentials are in tension with the observations in the standard inflationary setting, their consistency with the observations can be significantly improved within the setup of the Tsallis entropy-based inflation. Moreover, we place constraints on the parameters of the considered inflationary models by using the current observational data.

37 pages, 9 figures

References in corpus (24)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Avoiding Dark Energy with 1/R Modifications of Gravity
• Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe
• Thermodynamic route to Field equations in Lanczos-Lovelock Gravity
• Corrected Entropy-Area Relation and Modified Friedmann Equations
• Modified cosmology from extended entropy with varying exponent
• Barrow entropic dark energy: A member of generalized holographic dark energy family
• Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons
• Unifying Holographic Inflation with Holographic Dark Energy: a Covariant Approach
• Thermodynamics of apparent horizon and modified Friedman equations
• Updated constraints on amplitude and tilt of the tensor primordial spectrum
• Consistency relation for $R^p$ inflation
• Geometrical observational bounds on a fractal horizon holographic dark energy
• Correspondence of cosmology from non-extensive thermodynamics with fluids of generalized equation of state
• Cosmic evolution and thermal stability of Barrow holographic dark energy in nonflat Friedmann-Robertson-Walker Universe
• Growth of Perturbations in Tsallis and Barrow Cosmology
• Baryogenesis in non-extensive Tsallis Cosmology
• Constraining Barrow entropy-based Cosmology with power-law inflation
• Observational constraints on Tsallis modified gravity
• Slow-roll inflation in (R+R*4) gravity
• Modified Cosmology Models from Thermodynamical Approach
• Tsallis thermostatics as a statistical physics of random chains
• Generalized interacting Barrow Holographic Dark Energy: cosmological predictions and thermodynamic considerations
• The inflationary scenario in the $f(R)$ gravity model with a $R^4$ term

Cited by in corpus (6)

• Lagrangian formulation of the Tsallis entropy
• Topological and optical signatures of modified black-hole entropies
• Gravitational wave probes of Barrow cosmology with LISA standard sirens
• Cosmological Tensions with Non-Extensive Entropic Cosmology: A Modified Stress-Energy Approach
• Observational constraints on Luciano-Saridakis entropic cosmology
• Non-Gaussian Saha's ionization in Rindler spacetime and the equivalence principle