Cosmological correlators from the Inflation end to CMB sky via reheating

Abstract

We investigate the imprint of post-inflationary evolution on primordial cosmological correlators by relaxing the standard assumption of instantaneous reheating. We compute the power spectrum and bispectrum for a conformally coupled and non-minimally coupled ($ξ\neq \frac{1}{6},0$) scalar field with cubic self-interaction, across a finite reheating epoch characterized by an effective equation of state $w$, and reheating temperature $T_{\rm reh}$. We find that for a conformally coupled scalar field, the signatures of reheating, such as the modification to oscillatory features, are strictly confined to the subhorizon regime. On superhorizon scales, the correlators receive negligible corrections at leading order. In sharp contrast, for a non-minimally coupled field, we identify a distinct phenomenology where non-trivial values of $ξ$ and reheating equation of state $w$, can induce a tachyonic enhancement of the field modes on superhorizon scales. This enhancement modifies both the power spectrum and bispectrum, marking a sharp deviation from the instantaneous transition limit. Our results demonstrate that to the leading order while conformal coupling shields large-scale correlations from the expansion history, non-minimal coupling breaks this degeneracy and opens an observable window into the physics of reheating.

Figures (51)

• Figure 1: Schematic illustration emphasizing that while cosmological correlators are often evaluated at the end of inflation, observables at later times can differ due to subsequent dynamical evolution.
• Figure 2: Schematic illustration of the evolution of the comoving Hubble radius across different cosmological eras.
• Figure 3: Evolution of the dimensionless power spectrum $k^3\mathcal{P}_k$ across the inflationary and radiation-dominated epochs. During inflation ($\eta < \eta_{\text{inf}}<0$), all modes follow a universal power-law decay, highlighting the absence of scale invariance for a conformally coupled scalar. In the subsequent radiation-dominated era ($\eta > \eta_{\text{inf}}$), the spectral evolution becomes mode-dependent, where the degree of suppression is dictated by the horizon-exit scale $k/k_{\text{inf}}$.
• Figure 4: Graphical illustration of the in-in contour extended beyond $\eta=\eta_{\text{inf}}$ into some instant $\eta$ during the radiation era. The contour has small imaginary parts at early times which relates the interacting vacuum to the free vacuum.
• Figure 5: Diagrammatic representation of $\overline{\ev{\phi_{k_1}\phi_{k_2}\phi_{k_3}}}$ during instantaneous reheating. Unlike standard treatments, the correlator is evaluated at a time $\eta>\eta_{\rm inf}$, incorporating the matching conditions at the transition.