Rapid field excursions and the inflationary tensor spectrum

TL;DR

This paper probes whether sudden nonadiabatic excitations of a spectator scalar field $\\chi$ during inflation can significantly modify the inflationary tensor spectrum. Using a gauge-invariant, analytical in-in formalism, it computes loop corrections to tensor modes from $\\chi$ excitations and isolates the parts tied to particle production via a nonzero Bogoliubov coefficient $\\beta(k)$. The main result is a small one-loop tensor correction of order ${{k_*^3}/{(H M^2)}}$ modulated by functions peaked near horizon scales, with a key bound $E^4 \sim k_*^4 \ll V_{inf}$ ensuring perturbativity; consequently, the standard relation between tensor amplitude and the Hubble scale $H$ remains intact in these scenarios. The analysis also covers classical $\\chi$ backgrounds and multi-field extensions, concluding that sizable tensor enhancements are unlikely without breaking perturbation theory, thereby reinforcing the utility of tensor measurements as probes of $H$.

Abstract

We consider the effects of fields with suddenly changing mass on the inflationary power spectra. In this context, when a field becomes light, it will be excited. This process contributes to the tensor power spectrum. We compute these effects in a gauge-invariant manner, where we use a novel analytical method for evaluating the corrections to the tensor spectrum due to these excitations. In the case of a scalar field, we show that the net impact on the tensors is small as long as the perturbative expansion is valid. Thus, in these scenarios, measurement of tensor modes is still in one-to-one correspondence with the Hubble scale.

Figures (5)

• Figure 1: Left: Non-adiabaticity parameter $| \dot{\omega}/\omega^2|$ as a function of time for various wavelengths. Right: Corresponding numerical time evolution of the $\chi$ correlation function $\langle \hat{\chi}_k(t) \hat{\chi}_{-k}(t) \rangle = | \chi_k(t) |^2$. Long wavelengths (blue) have $| \dot{\omega}/\omega^2 | \gg 1$ near $t_0$ (in this picture, $t_0 \approx 300$); these modes undergo a sharp non-adiabatic evolution, leading to interference between the positive and negative frequency mode functions, cf. (\ref{['chilate']}). Shorter-wavelength modes have weaker effects (red, $k \approx k_{*}$) or evolve completely adiabatically (yellow, $k \gg k_{*}$). Notice that all mode functions have a nontrivial evolution beyond the usual redshifting: they scale like $\omega^{-1/2}$, which is enhanced near $t_0$.
• Figure 2: Diagrams contributing to $\langle h_k h_k \rangle$ at leading order ($1/M^2$). The scalar lines are $\chi$ correlators and the curly lines are gravitons. Later we denote the first diagram by $A$ and the second by $B$.
• Figure 3: Dimensionless functions $F$ and $G$ appearing in the answer. $F$ enters into the tadpole diagram while $G$ enters into the other diagram.
• Figure 4: Some typical diagrams involving background $\chi$ fields, insertions of which we denote with crosses and double lines. Dashed lines are $\delta \chi$ propagators and solid lines are $\zeta$ propagators.
• Figure 5: Contour used for evaluating $\beta$.