Non-minimally coupled loop quantum inflation with inverse-volume corrections

TL;DR

This paper investigates slow-roll inflation with a non-minimally coupled scalar field in Loop Quantum Cosmology, deriving analytic inflationary predictions, numerically solving dynamics, and analyzing initial condition probabilities within observational constraints.

Contribution

It provides the first analytic expressions for inflationary observables in non-minimally coupled LQC with inverse-volume corrections and analyzes the impact of non-minimal coupling on initial conditions.

Findings

Model compatible with Planck and ACT data.

Non-minimal coupling enlarges favorable initial condition phase space.

Likelihood of sufficient inflation depends on pre-inflationary dynamics.

Abstract

We study slow-roll inflation driven by a scalar field non-minimally coupled to gravity within the effective framework of Loop Quantum Cosmology (LQC), including inverse-volume corrections. We consider two physically motivated classes of potentials, a Higgs-like quartic potential $V\propto\phi^{4}$ and string-inspired fractional monomial potentials $V\propto\phi^{p}$ with $p<1$. Working at first order in the slow-roll expansion, we derive analytic expressions for the inflationary observables, namely the scalar spectral index $n_s$, the tensor-to-scalar ratio $r$, and the running $\alpha_s\equiv dn_s/d\ln k$, and then solve the corrected background dynamics numerically to obtain quantitative predictions. Confronting these results with current observational constraints from Planck 2018 and ACT DR6, we find that the model can lie within the allowed region of the $(n_s,r,\alpha_s)$ parameter space, including a mild preference for slightly larger $n_s$, as suggested by recent ground-based measurements. We also compute the probability of achieving sufficient slow-roll inflation in this setting. Although effective LQC replaces the initial singularity with a nonsingular quantum bounce, the likelihood of a sufficiently long inflationary phase depends on the pre-inflationary dynamics and on the inflaton potential. Using the canonical Liouville measure on the effective phase space, we determine the fraction of post-bounce trajectories that yield sufficient inflation and find that the non-minimal coupling parameter $\xi$ substantially enlarges the phase-space volume of favorable initial conditions relative to the minimally coupled case, exhibiting an attractor-like enhancement that saturates at large $\xi$.