Cosmological Inflation in $f(Q,\mathcal{L}_{m})$ Gravity

TL;DR

This paper explores cosmological inflation within the $f(Q, ext{L}_m)$ gravity framework, deriving analytical predictions for inflationary parameters and comparing them with observational data to assess viability as an alternative to General Relativity.

Contribution

It formulates slow-roll inflation in $f(Q, ext{L}_m)$ gravity and analyzes the observational viability of linear and nonlinear coupling models against Planck and other data.

Findings

Linear model compatible with observational constraints for positive parameters.

Nonlinear model viable mainly for negative parameters.

Distinct inflationary regimes emerge from different $f(Q, ext{L}_m)$ models.

Abstract

Cosmological inflation remains a key paradigm for explaining the earliest stages of the Universe, yet the theoretical limitations of General Relativity (GR) motivate the development of alternative formulations capable of addressing both early and late cosmic acceleration. In this work, we investigate cosmological inflation within the $f(Q,\mathcal{L}_{m})$ gravity framework based on symmetric teleparallel geometry, where the non-metricity scalar $Q$ couples directly to the matter Lagrangian. We formulate the slow-roll dynamics and derive analytical predictions for the scalar spectral index $n_{s}$ and tensor-to-scalar ratio $r$ in both linear and nonlinear non-minimal coupling models, assuming a power-law inflaton potential. Our findings show that the linear case, $f(Q,\mathcal{L}_{m})=-\alpha Q + 2\mathcal{L}_{m}+\beta$, becomes compatible with Planck+BK15+BAO constraints for positive $\alpha$ and $\beta$, producing narrow viable contours in parameter space. In contrast, the nonlinear model, $f(Q,\mathcal{L}_{m})=-\alpha Q+(2\mathcal{L}_{m})^{2}+\beta$, achieves observational viability only for negative $\alpha$ and $\beta$, and its predictions predominantly fall inside the $68\%$ confidence region of joint data. These results demonstrate that $f(Q,\mathcal{L}_{m})$ gravity produces distinct inflationary regimes, providing a highly competitive alternative to GR.