More on Pre-Inflationary Non Gaussianities

TL;DR

The paper investigates pre-inflationary non-Gaussianities in a bounce cosmology motivated by string-theory SUSY breaking, focusing on climbing dynamics driven by an exponential potential $V(\phi)=\frac{T}{2\kappa^2}e^{\sqrt{6}\,\lambda\phi}$. It generalizes previous $\lambda=1$ results to generic $\lambda$, deriving turning-point scalar contributions $\langle O_i\rangle_t^{\lambda}$ with a scale factor $h(\lambda)$ and showing that the inflationary e-fold window $N$ shifts with $\lambda$, while smoothing via a bounce eliminates certain singular contributions. The tensor sector is computed in the same bounce background, demonstrating the absence of turning-point contributions and yielding Maldacena-like results in the $\Delta\to0$ limit, with bounce-induced oscillations appearing only in scalar channels. Collectively, the results connect string-theory-inspired pre-inflationary dynamics to observable non-Gaussian signatures, potentially testable through the equilateral bispectrum and the evolution of $f_{NL}$ around a narrow window of $e$-folds near $N\sim 63$.

Abstract

I generalize the three-point amplitude of curvature perturbations in the climbing scenario inspired by ten-dimensional non-supersymmetric strings to a broader class of exponential potentials, under some assumptions on the smoothing effects of String Theory that favor a bounce Cosmology. The extension can encompass the SO(16)xSO(16) model, together with other scenarios related to supersymmetry breaking in String Theory. The e-fold ranges compatible with Planck data move toward lower values of N for milder potentials and toward larger values for steeper ones. I also compute the three-point amplitudes involving graviton modes in the same bounce scenario, showing in detail their lack of peculiar contributions from the turning point.

Figures (5)

• Figure 1: The deformed Mukhanov-Sasaki potential that resolves the initial singularity considered in ms (blue, solid), where the Bunch--Davies condition is imposed at $\eta_0$, together with a typical $W$ for a climbing cosmology (red,dashed) and the attractor potential lowered by $\Delta^2$ (black, dotted).
• Figure 2: $h(\lambda)$ around the critical value $\lambda_c=1$ and beyond.
• Figure 3: Left panel: the turning--point contribution $f_t$ to $f_{NL}$ as a function of the number of e-folds $x=N-60$ for $\lambda = 0.02$ (red, dot-dashed), for $\lambda = 0.1$ (purple, dashed) and $\lambda = \lambda_c = 1$ (dark blue, solid), for $k=1.2 \, \Delta$. Right panel: the turning--point contribution $f_t$ to $f_{NL}$ as a function of the number of e-folds $x=N-60$ for $\lambda = \lambda_c = 1$ (dark blue, solid), for $\lambda = 2$ (brown, dot-dashed) and $\lambda = 6$ (black, dashed) for $k=1.2 \, \Delta$. The results displayed correspond to the choice $\epsilon=0.03$, with the reference value $\eta_t = -\frac{5}{\Delta}$.
• Figure 4: The turning--point contribution $f_t$ to $f_{NL}$ as a function of the number of e-folds $x=N-60$ for $\lambda = 2/3$ (orange, dashed), for $\lambda = \lambda_c = 1$ (dark blue, solid) and $\lambda = 5/3$ (brown, dot-dashed), for $k=1.2 \, \Delta$. The results displayed correspond to the choice $\epsilon=0.03$, with the reference value $\eta_t = -\frac{5}{\Delta}$.
• Figure 5: $f_{t}$ (black solid) vs $f_{t}^{\text{lim}}$ (red, dashed) as functions of $\frac{k}{\Delta}$. Left panel: $\lambda = 2/3$; central panel: $\lambda = \lambda_c = 1$; right panel: $\lambda = 1.65$. The results correspond to the choice $\epsilon = 0.03$, with reference values $\eta_t = -\frac{5}{\Delta}$ and $N = 63$.