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Slow-roll Hilltop Inflation in $f(φ,T)$ gravity

Biswajit Deb, Atri Deshamukhya

TL;DR

The paper investigates slow-roll Hilltop inflation within the modified gravity framework $f(\phi,T)$, where the scalar field $\phi$ non-minimally couples to the trace $T$ of the energy-momentum tensor via $f(\phi,T) = \sqrt{\kappa}\,\lambda\,\phi\,T$. By deriving the modified Friedmann equations and inflaton dynamics, it computes the slow-roll parameters $\epsilon_V$ and $\eta_V$, along with the observables $n_s$ and $r$, for Hilltop potentials $V(\phi)=\Lambda^4\left[1-(\phi/\mu)^m+\dots\right]$ at horizon exit ($N=50$). The results show that for positive coupling $\lambda$, the four representative Hilltop models with $m=\{3/2,2,3,4\}$ can be consistent with Planck 2018 constraints, and crucially, the inflationary scale can be lowered from super-Planckian values to $\mu=10M_p$ or even $5M_p$ depending on $\lambda$. This work broadens the viable parameter space for hilltop inflation in modified gravity and invites further exploration with alternative matter couplings and multi-field extensions.

Abstract

Over the last four decades, a number of modified gravity theories have been proposed to study cosmological phenomena as they can provide solutions for some of the shortcomings of Einstein's gravity in explaining early and late time accelerations of the observed Universe, the existence of dark matter, singularities at center of Black holes etc. The theoretical and observational challenges faced by the $Λ$CDM model also point towards the necessity for looking beyond General Relativity. In this direction, recently $f(φ, T)$ gravity has been proposed in literature where the non-minimal coupling of the scalar field $φ$ with the trace of energy-momentum tensor $T$ has been introduced in the Einstein-Hilbert action. Considering the Hilltop potential, we have studied the slow-roll inflation in the framework of $f(φ, T)$ gravity. It is found that Hilltop inflationary models in $f(φ, T)$ gravity are viable when seen in the light of latest Planck data.

Slow-roll Hilltop Inflation in $f(φ,T)$ gravity

TL;DR

The paper investigates slow-roll Hilltop inflation within the modified gravity framework , where the scalar field non-minimally couples to the trace of the energy-momentum tensor via . By deriving the modified Friedmann equations and inflaton dynamics, it computes the slow-roll parameters and , along with the observables and , for Hilltop potentials at horizon exit (). The results show that for positive coupling , the four representative Hilltop models with can be consistent with Planck 2018 constraints, and crucially, the inflationary scale can be lowered from super-Planckian values to or even depending on . This work broadens the viable parameter space for hilltop inflation in modified gravity and invites further exploration with alternative matter couplings and multi-field extensions.

Abstract

Over the last four decades, a number of modified gravity theories have been proposed to study cosmological phenomena as they can provide solutions for some of the shortcomings of Einstein's gravity in explaining early and late time accelerations of the observed Universe, the existence of dark matter, singularities at center of Black holes etc. The theoretical and observational challenges faced by the CDM model also point towards the necessity for looking beyond General Relativity. In this direction, recently gravity has been proposed in literature where the non-minimal coupling of the scalar field with the trace of energy-momentum tensor has been introduced in the Einstein-Hilbert action. Considering the Hilltop potential, we have studied the slow-roll inflation in the framework of gravity. It is found that Hilltop inflationary models in gravity are viable when seen in the light of latest Planck data.
Paper Structure (6 sections, 31 equations, 2 figures, 2 tables)

This paper contains 6 sections, 31 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Slow-roll inflation in $f(\phi,T)$ gravity
  3. A case study with Hilltop potentials
  4. When $\mu = 10 M_p$
  5. When $\mu = 5 M_P$
  6. Conclusion

Figures (2)

  • Figure 1: The $n_s-r$ plot predicted by the hilltop potentials corresponding to $m = \{3/2,2,3,4\}$ marked by black, blue, orange and pink colour respectively at $N=50$ and $\mu=10M_p$. The marginalized joint 68% and 95% C.L. regions for $n_s$ and $r$ at $k=0.002 Mpc^{-1}$ from Planck 2018 data are shown in red and green colour respectively r39.
  • Figure 2: The $n_s-r$ plot predicted by the hilltop potentials corresponding to $m = \{3/2,2,3,4\}$ marked by black, blue, orange and pink colour respectively at $N=50$ and $\mu=5M_p$. The marginalized joint 68% and 95% C.L. regions for $n_s$ and $r$ at $k=0.002 Mpc^{-1}$ from Planck 2018 data are shown in red and green colour respectively r39.