[Paper Review] Tsallis holographic inflation in $f(R,T)$ gravity: CMB constraints, reheating, and swampland implications

S. Taghavi, Golanbari, T.+1 more|arXiv (Cornell University)|Jan 5, 2023

Cosmology and Gravitation Theories6 citations

TL;DR

This paper proposes Tsallis holographic dark energy (THDE) with a Granda-Oliveros (GO) cutoff as the inflaton in $f(R,T)$ gravity, deriving observable constraints and swampland consistency. It finds that $\lambda \gtrsim 10^2$ ensures both swampland conjectures are satisfied, with inflation occurring below the Planck scale and model parameters consistent with CMB data when $\lambda \gtrsim 300$. The reconstructed potential depends critically on $\lambda$, which controls field excursion and potential gradient.

ABSTRACT

Understanding how early-universe inflation may emerge from generalized holographic energy densities within modified gravity motivates the present analysis. We develop a self-consistent inflationary scenario in which the Tsallis holographic dark energy (THDE) density effectively acts as the inflaton potential in $f(R,T)$ gravity. Using the Granda-Oliveros infrared cutoff, we derive the corresponding slow-roll relations and identify a broad region of the parameter space $(α,β,δ,λ)$ that remains consistent with ACT DR6 (P-ACT-LB) constraints. By exploiting the dependence of the THDE density on the Hubble rate, we reconstruct the inflaton potential $V(ϕ)$ and show that both the field excursion $Δϕ$ and the normalized potential gradient $|V'|/(V M_{p})$ are predominantly controlled by the matter-geometry coupling $λ$. We demonstrate that $λ\gtrsim \mathcal{O}(10^{2})$ suppresses the field excursion below the Planck scale and ensures $|V'|/(V M_{p}) \ge 1$, thereby satisfying both the distance conjecture and the refined de Sitter swampland bound. We also analyze the reheating stage. In addition to the primordial nucleosynthesis requirement $T_{ m BBN} \approx 4~\mathrm{MeV}$, which sets a lower limit on the reheating temperature, the observational bound $ΔN_{ m eff} \le 0.17$ imposes an additional constraint from primordial gravitational waves (PGWs). During stiff reheating phases with $ω_{ m re} > 1/3$, the high-frequency PGW spectrum is significantly enhanced, producing a distinct signature that may fall within the sensitivity of upcoming detectors. Overall, this work provides an observationally consistent realization of holographic inflation in $f(R,T)$ gravity, jointly constrained by CMB data, swampland criteria, reheating physics, and PGW limits.

Motivation & Objective

• To investigate whether Tsallis holographic dark energy (THDE) with a Granda-Oliveros (GO) cutoff can drive inflation in $f(R,T)$ gravity.
• To constrain the model parameters using CMB observational data and Python-based numerical fitting.
• To reconstruct the scalar field potential from the Hubble parameter and assess its consistency with swampland criteria.
• To determine the energy scale of inflation and evaluate whether the model satisfies the swampland conjectures.

Proposed method

• Adopt $f(R,T)$ gravity with non-minimal coupling between curvature and matter, using the modified Friedmann equations to describe the background evolution.
• Apply slow-roll approximations to simplify the dynamical equations, assuming kinetic energy is negligible compared to potential energy.
• Define the inflaton potential as Tsallis holographic dark energy (THDE) with the GO cutoff, which includes both $H^2$ and $\dot{H}$, to model early-universe inflation.
• Derive the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$ at horizon crossing using perturbation theory in the slow-roll regime.
• Use observational CMB data (Planck 2018) to constrain the free parameters $\alpha$, $\beta$, and $\lambda$ via numerical fitting.
• Reconstruct the potential $V(\phi)$ in terms of the scalar field $\phi$ and test its consistency with the swampland de Sitter and distance conjectures.

Experimental results

Research questions

• RQ1 Can Tsallis holographic dark energy with a GO cutoff serve as a viable inflaton in $f(R,T)$ gravity?
• RQ2 What range of model parameters ($\alpha$, $\beta$, $\lambda$) ensures consistency with Planck 2018 CMB data for $n_s$ and $r$?
• RQ3 What is the energy scale of inflation in this model, and is it below the Planck scale?
• RQ4 Does the reconstructed potential satisfy the swampland conjectures, particularly the distance and de Sitter conjectures?
• RQ5 How does the parameter $\lambda$ influence field excursion and potential gradient, and what value ensures swampland consistency?

Key findings

• The model achieves good agreement with Planck 2018 CMB data for scalar spectral index $n_s$ and tensor-to-scalar ratio $r$ when the free parameters lie within a specific range.
• Inflation occurs at an energy scale of approximately $10^{-3}M_p$, confirming the model operates at a low-energy effective field theory scale.
• To satisfy the first swampland conjecture (field excursion $\Delta\phi < 1$), $\lambda \gtrsim 10^2$ is required, with $\Delta\phi \approx 0.642$ for $\lambda = 500$.
• To satisfy the second swampland conjecture ($|V''/V| \geq c_2$), $\lambda \gtrsim 300$ is necessary, as $V'/V \approx 2.058$ at $\lambda = 500$, exceeding the threshold.
• The potential gradient $V'/V$ increases with $\lambda$, and for $\lambda \gtrsim 300$, it exceeds unity throughout inflation, satisfying the second conjecture.
• The parameter $\lambda$ plays a decisive role: $\lambda \gtrsim 300$ ensures both swampland criteria are met, with $V'/V \gtrsim 1.8$ and $\Delta\phi \lesssim 0.65$.