Non-Gaussian Density Fluctuations from Entropically Generated Curvature Perturbations in Ekpyrotic Models

Abstract

We analyze the non-gaussian density perturbations generated in ekpyrotic/cyclic models based on heterotic M-theory. In this picture, two scalar fields produce nearly scale-invariant entropic perturbations during an ekpyrotic phase that are converted into curvature modes {\it after the ekpyrotic phase is complete} and just before the big bang. Both intrinsic non-linearity in the entropy perturbation and the conversion process contribute to non-gaussianity. The range of the non-gaussianity parameter $f_{NL}$ depends on how gradual the conversion process is and the steepness of the scalar field potential during the ekpyrotic phase. Although a wider range is possible, in principle, natural values of the ekpyrotic parameters combined with a gradual conversion process lead to values of $-60 \lesssim f_{NL} \lesssim +80$, typically much greater than slow-roll inflation but within the current observational bounds.

Figures (2)

• Figure 1: The background trajectory in scalar field space is straight everywhere except for a brief period after the ekpyrotic phase around the time of reflection. The shaded region indicates the geometrically forbidden region bounded by the axis $\phi_2=0.$ In the presence of brane-bound matter, the trajectory reflects smoothly off this boundary. Also shown are the directions of adiabatic ($\delta \sigma$) and entropic ($\delta s$) fluctuations, as well as the angle of the trajectory before and after the reflection.
• Figure 2: The predicted value of the non-gaussianity parameter $f_{NL}$ as a function of the duration of the reflection. The shaded range represents results for the simplest ekpyrotic and reflection potentials allowing $\kappa_3$ to range from $+5$ (top) to $-5$ (bottom). The upper and lower boundaries can be extended (dashed and dotted curves) by carefully tuning the reflection potentials, but the change is not significant for typical durations ${\cal O} (1)$.