Hamilton-Jacobi analysis of noncanonical inflation in $f(R,T)$ gravity: Constraints from Planck/ACT data, and theoretical bounds

Abstract

The latest CMB data from ACT DR6, combined with Planck, DESI, and BICEP/Keck, indicate a slight upward shift in the scalar spectral index, placing several previously favored inflationary models under tension. We study an inflationary scenario within the framework of $f(R,T)$ gravity, featuring a nonminimal matter-curvature coupling, where the inflaton is a noncanonical scalar field with a generalized kinetic energy. Using the Hamilton-Jacobi formalism, we express the Hubble parameter as a function of the scalar field and consider two forms of $H(\varphi )$, a power-law and an exponential one, deriving the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$. Comparison with ACT DR6 allows us to explore the parameter space, showing that the power-law case is compatible with the data across a wide range, while the exponential form requires a large number of e-folds. We then study reheating, noting its close link with the inflationary dynamics. By imposing the bound on overproduction of primordial gravitational waves encoded in the constraint on $\Delta N_{\text{eff}}$, we obtain a lower limit on the reheating temperature, which becomes particularly restrictive for the stiff reheating equation of state ${\omega }_{\text{re}}$. This bound implies that the total number of e-folds should not exceed $N\lesssim 64(65)$. The predicted gravitational-wave spectrum shows an enhanced high-frequency amplitude, potentially observable by future detectors. We also examine consistency with the Swampland conjectures and the Trans-Planckian Censorship Conjecture, finding that combining $f(R,T)$ gravity with noncanonical dynamics provides a rich and testable framework for the early universe.

arXiv comment22 pages, 11 figures, 4 tables

References in corpus (86)

• Dynamics of dark energy
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified Gravity and Cosmology
• Extended Theories of Gravity
• f(R,T) gravity
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Towards the Theory of Reheating After Inflation
• A Dynamical Solution to the Problem of a Small Cosmological Constant and Late-time Cosmic Acceleration
• Particle Physics Models of Inflation and the Cosmological Density Perturbation
• k-Inflation
• Essentials of k-essence
• Reheating after Inflation
• Exponential potentials and cosmological scaling solutions
• Observational Probes of Cosmic Acceleration
• Beyond the Cosmological Standard Model
• Perturbations in k-inflation
• DBI in the Sky
• Encyclopaedia Inflationaris
• Inflation Dynamics and Reheating
• Universe Reheating after Inflation
• Cosmological Backgrounds of Gravitational Waves
• The Swampland: Introduction and Review
• Big-Bang Nucleosynthesis and Hadronic Decay of Long-Lived Massive Particles
• Scalar Speed Limits and Cosmology: Acceleration from D-cceleration
• Distance and de Sitter Conjectures on the Swampland
• Cosmological Tests of Modified Gravity
• Quintessence: A Review
• Reheating in Inflationary Cosmology: Theory and Applications
• Inflationary Cosmology
• Testing General Relativity in Cosmology
• Bounds on Slow Roll and the de Sitter Swampland
• Reconstruction of f(R, T) gravity describing matter dominated and accelerated phases
• Big-Bang Nucleosynthesis After Planck
• Signatures of Supersymmetry from the Early Universe
• Stellar equilibrium configurations of compact stars in $f(R,T)$ gravity
• Improved Calculation of the Primordial Gravitational Wave Spectrum in the Standard Model
• Reheating constraints to inflationary models
• Trans-Planckian Censorship and the Swampland
• Primordial gravitational waves, precisely: The role of thermodynamics in the Standard Model
• Reheating predictions in single field inflation
• Modelling wormholes in $f(R,T)$ gravity
• f(R,T) Cosmological Models in Phase Space
• Trans-Planckian Censorship and Inflationary Cosmology
• The simplest non-minimal matter-geometry coupling in the $f(R,T)$ cosmology
• Analytical general solutions for static wormholes in $f(R,T)$ gravity
• Equation-of-State Parameter for Reheating
• Dark Matter From f(R,T) Gravity
• Probing reheating temperature of the universe with gravitational wave background
• Static Spherically Symmetric Solutions in F(R) Gravity
• The cosmic gravitational wave background in a cyclic universe
• Precision calculations of the gravitational wave background spectrum from inflation
• The dS swampland conjecture and the Higgs potential
• A Hamilton-Jacobi approach to non-slow-roll inflation
• Gravitational waves in the $f(R,T)$ theory of gravity
• Radiative decay of a massive particle and the non-thermal process in primordial nucleosynthesis
• Stellar equilibrium configurations of white dwarfs in the $f(R,T)$ gravity
• Constraints on α-attractor inflation and reheating
• A note on Inflation and the Swampland
• Primordial Gravitational Waves in Nonstandard Cosmologies
• Refining inflation using non-canonical scalars
• Gravitational wave production from preheating: parameter dependence
• Decoding the phases of early and late time reheating through imprints on primordial gravitational waves
• Slow-roll inflation in f(R,T) gravity and a modified Starobinsky-like inflationary model
• Fractional attractors in light of the latest ACT observations
• Inflation in $f(R,T)$ Gravity
• Polarized primordial gravitational waves in the ghost-free parity-violating gravity
• Cosmology in modified $f(R,T)$-gravity
• Primordial non-Gaussianities after Planck 2015: an introductory review
• Observational Constraints and Cosmological Implications of Scalar-Tensor $f(R,T)$ Gravity
• Inflaton phenomenology via reheating in light of primordial gravitational waves and the latest BICEP/$Keck$ data
• Hamilton-Jacobi formalism to warm inflationary scenario
• Kinetically Modified Palatini Inflation Meets ACT Data
• Brane Constant-roll Inflation
• Evaluation of cosmological models in $f(R,T)$ gravity in different dark energy scenario
• Intermediate inflation driven by DBI scalar field
• Beta-function formalism for k-essence constant-roll inflation
• Viscous Warm Inflation: Hamilton-Jacobi formalism
• Observational constraints on inflationary models with non-minimally derivative coupling by ACT
• Brane inflation and Trans-Planckian censorship conjecture
• Study of Goldstone Inflation in the domain of Einstein-Gauss-Bonnet gravity
• Revisiting $f(R,T)$ cosmologies
• Constraining the history of reheating with the NANOGrav 15-year data
• Constraints on the reheating phase after Higgs inflation in the hybrid metric-Palatini approach
• Reheating constraints on mutated hilltop inflation
• Inflationary Dynamics in Einstein-Gauss-Bonnet Gravity Using New Slow-Roll Approximations considering Generalised Reheating
• Observational Constraints on Extended Starobinsky and Weyl Gravity Model of Inflation