On Pre-Inflationary non Gaussianities

Abstract

We explore the three-point amplitude of curvature perturbations in scenarios suggested by high-scale supersymmetry breaking in String Theory, where the inflaton is forced to climb a steep exponential potential. We can do it at the price of some simplifications, and more importantly with some assumptions on the softening effects of String Theory. These suggest a scenario proposed long ago by Gasperini and Veneziano, where the initial singularity is replaced by a bounce, and the resulting analysis rests on a scale $Δ$ that leaves some signs in the angular power spectrum of the CMB. The amplitude comprises two types of contribution: the first oscillates around the original result of Maldacena and gives no further prospects to detect a non-Gaussian signal, but the second, which is subtly tied to the turning point at the end of the climbing phase, within the window 62<N<66 for the inflationary e-folds could be compatible with Planck constraints and potentially observable. The amplitudes involving the tensor modes contain only the first type of contribution.

Figures (11)

• Figure 1: Typically the scale factor (red, dashed) approaches the attractor (black, dotted) while the scalar field is still in the climbing phase with medium--large values of $\epsilon$ (green, solid), but an initial singularity is readily encountered at earlier times in the region where $\epsilon \simeq 3$. The dip in the solid curve for $\epsilon$ corresponds to the turning point.
• Figure 2: The non--singular model for $\epsilon(\eta)$ (blue, dot-dashed), with a dip at $\eta_t$, where the climbing scalar inverts its motion. As $\eta$ decreases, the actual $\epsilon(\eta)$ (orange, solid) experiences a quick growth to its asymptotic value as the Universe collapses, and the dashed vertical line corresponds to the initial singularity.
• Figure 3: Left panel: a typical Mukhanov--Sasaki potential for a climbing scalar. Note that $W$ changes sign at $\eta^\star$ and experiences a short growth as $\eta$ decreases further, before tending to $-\infty$ as the initial singularity is approached. Right-panel: an attractor $W$ with $\nu=\frac{3}{2}$ lowered by $\Delta^2$, as in eq. \ref{['W_Delta']}.
• Figure 4: Left panel: an extended model for $W$ that follows the curve of eq. \ref{['W_Delta']} up to $\eta_0$, where it experiences a sudden jump to the corresponding attractor curve without $\Delta$, has the virtue of leading to simple mode functions. Right panel: the actual transition could occur smoothly, within a small window of conformal time.
• Figure 5: Left panel: a sharp transition between an earlier epoch of compression and the expansion that begins at $\eta_0$ and evolves into the inflationary scenario. Right panel: a smooth model of the transition.