Lessons from $T^{\mu}_{~ \mu}$ on inflation models: two-scalar theory and Yukawa theory

TL;DR

This paper explores how the trace of the energy-momentum tensor reveals the decoupling of heavy particles in inflation models and examines quantum effects on scalar field couplings, with implications for inflation dynamics.

Contribution

It demonstrates the decoupling of heavy degrees of freedom in $T^{}_{~ }$ and analyzes quantum contributions to non-minimal scalar couplings in inflation models.

Findings

Heavy degrees of freedom do not affect low-energy $T^{}_{~ }$-inserted amplitudes.

Quantum effects induce non-minimal couplings, influencing inflation dynamics.

The results apply to two-scalar and Yukawa theories.

Abstract

We demonstrate two properties of the trace of the energy-momentum tensor $T^{\mu}_{~ \mu}$ in the flat spacetime. One is the decoupling of heavy degrees of freedom; i.e., heavy degrees of freedom leave no effect for low-energy $T^{\mu}_{~ \mu}$-inserted amplitudes. This is intuitively apparent from the effective field theory point of view, but one has to take into account the so-called trace anomaly to explicitly demonstrate the decoupling. As a result, for example, in the $R^{2}$ inflation model, scalaron decay is insensitive to heavy degrees of freedom when a matter sector ${\it minimally}$ couples to gravity (up to a non-minimal coupling of a matter scalar field other than the scalaron). The other property is a quantum contribution to a non-minimal coupling of a scalar field. The non-minimal coupling disappears from the action in the flat spacetime, but leaves the so-called improvement term in $T^{\mu}_{~ \mu}$. We study the renormalization group equation of the non-minimal coupling to discuss its quantum-induced value and implications for inflation dynamics. We work it out in the two-scalar theory and Yukawa theory.