Lessons from Tμμ on inflation models: Two-scalar theory and Yukawa theory

Abstract

We demonstrate two properties of the trace of the energy-momentum tensor T μμ 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 μμ-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 R2 inflation model, scalaron decay is insensitive to heavy degrees of freedom when a matter sector minimally couples to gravity (up to a nonminimal coupling of a matter scalar field other than the scalaron). The other property is a quantum contribution to a nonminimal coupling of a scalar field. The nonminimal coupling disappears from the action in the flat spacetime, but leaves the so-called improvement term in T μμ. We study the renormalization group equation of the nonminimal coupling to discuss its quantum-induced value and implications for inflation dynamics. We work it out in the two-scalar theory and Yukawa theory.