Quantum-Corrected ${\varphi }^4$ Inflation in Light of ACT Observations

Abstract

Recent measurements from the Atacama Cosmology Telescope (ACT), combined with Planck and DESI data, suggest a scalar spectral index $n_s$ higher than the Planck 2018 baseline, thereby placing conventional attractor-type inflationary models such as Starobinsky $R^2$ and Higgs inflation under increasing tension at the $\gtrsim 2\sigma$ level. In this work, we examine quantum-corrected ${\varphi }^4$ inflation with a non-minimal coupling to gravity. Introducing an anomalous scaling parameter $\gamma$ to capture quantum corrections to the effective potential, we derive analytic expressions for the inflationary observables $n_s$ and $r$. Confronting these predictions with ACT, Planck, and BAO+lensing constraints, we demonstrate that modest values of $\gamma$ can raise $n_s$ into the ACT-preferred range while maintaining a strongly suppressed tensor-to-scalar ratio. For instance, with $N=60$ and $\gamma \simeq 0.006$, the model predicts $n_s\simeq 0.974$ and $r\simeq 0.007$, in excellent agreement with current bounds. We further investigate preheating dynamics, focusing on particle production via parametric resonance in quantum-corrected ${\varphi }^4$ inflation with a non-minimal coupling to gravity. In this scenario, the inflaton $\varphi$ couples to an additional scalar $\chi$ through an interaction $g^2{\varphi }^2{\chi }^2$. In Minkowski spacetime, the resonance dynamics reduce to the Mathieu equation, and we find that broad resonance can be readily achieved, leading to efficient particle production.

v1: 13 pages, 3 figures

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