Quasi Single Field Inflation in the non-perturbative regime

TL;DR

This work analyzes quasi single-field inflation with a massive scalar S coupled to the inflaton through a derivative mixing, focusing on the nonperturbative regime $(\mu/H)^2+(m/H)^2>9/4$ and $m/H=O(1)$ or smaller. It combines nonperturbative numerics in de-Sitter space with analytic large-$\mu/H$ EFT to compute the power spectrum and non-Gaussianities, mapping when EFT is reliable (roughly $\mu/H\gtrsim10$) and how the parameters $\mu$ and $m$ affect $n_S$ and $r$ for $V_\phi(\phi)=\tfrac{1}{2}m_\phi^2\phi^2$. The bispectrum is evaluated in equilateral and squeezed configurations, yielding quantitative constraints on $V_S'''$ and $\mu$, and revealing oscillatory squeezed signals tied to the heavy-mode dynamics. The results demonstrate that larger $\mu$ can improve agreement with Planck data and highlight distinctive, potentially observable non-Gaussian features in this nonperturbative regime.

Abstract

In quasi single field inflation there are massive fields that interact with the inflaton field. If these other fields are not much heavier than the Hubble constant during inflation ($H$) these interactions can lead to important consequences for the cosmological energy density perturbations. The simplest model of this type has a real scalar inflaton field that interacts with another real scalar $S$ (with mass $m$). In this model there is a mixing term of the form $μ{\dot π} S$, where $π$ is the Goldstone fluctuation that is associated with the breaking of time translation invariance by the time evolution of the inflaton field during the inflationary era. In this paper we study this model in the region $(μ/H )^2 +(m/H)^2 >9/4$ and $m/H \sim {\cal O}(1)$ or less. For a large part of the parameter space in this region standard perturbative methods are not applicable. Using numerical and analytic methods we derive a number of new results. In addition we study how large $μ/H$ has to be for the large $μ/H$ effective field theory approach to be applicable.

Figures (10)

• Figure 1: The correction of the power spectrum of curvature perturbation ${\Delta\cal P}_\zeta$ in units of $(H^4/\dot\phi_0^2)(1/2k^3)$ due to the mixing with the new field ${s}$. The red, blue, green, orange and magenta curves are for $m = 0, 0.5H, H, 1.5$ and $2H$. The black dashed curve shows the result from the effective theory and the colored dashed lines are perturbation theory.
• Figure 2: Power spectrum of the $\pi$ and $s$ fields in the unit of $H^2/2k^3$. The solid, dotted, and dashed curves are for $(\mu/H, m/H) = (10,2), (1, 2)$ and $(1.2,0.9)$, respectively.
• Figure 3: Left: Absolute values of the field values with $m = 2H$ and $\mu = 10H$. The solid black and the dashed red curves are for the $\pi$ and ${s}$ mode with the index $\alpha = 0$. The dot-dashed blue curve illustrates the $\pi$ and $s$ modes whose dominant small $-\eta$ behavior comes from the index $\alpha = 3/2\pm (9/4- (m^2+\mu^2)/H^2)^{1/2}$. Right: Showing the absolute value of the real parts of each mode corresponding to the ones in the left panel.
• Figure 4: Numerical result of ${\cal P}_\pi(k)$ as a function of $\eta$ in the unit of $H^2/(2k^3)$ for $m=0$ and $\mu = 100 H$. For comparison in blue we show the result for standard single field inflation.
• Figure 5: Impact on the scalar spectrum index $n_S$ and the tensor-to-scalar ratio $r$ for the $\phi^2$ inflation model with $\mu$ from 0 to 100$H$ and $m$ from 0 to 6$H$, and $(\mu^2 + m^2)^{1/2} > 3H/2$. The blue and red regions are for $N_{\rm cmb} = 50$ and 60 respectively. The dotted, dashed and solid curves are for $m$ fixed to be $0,3H/2$ and $6 H$ respectively. The gray regions are the one-sigma and two-sigma constraints from the combination of the Planck data and the BICEP2/Keck data Array:2015xqh.