Effects of nonlinear dispersion relations on non-Gaussianities

Abstract

We investigate the effect of non-linear dispersion relations on thebispectrum. In particular, we study the case were the modifiedrelations do not violate the WKB condition at early times, focusing on aparticular example which is exactly solvable: the Jacobson-Corleydispersion relation with quartic correction with positivecoefficient to the squared linearrelation. We find that the corrections to thestandard result for the bispectrum are suppressed by a factorH2/pc2 where pc is the scale where the modification to thedispersion relation becomes relevant. The modification is mildlyconfiguration-dependent and equilateral configurations are moresuppressed with respect to the local ones, by a factor of onepercent. There is no configurationleading to enhancements. We then analyze the results in the framework of particlecreation using the approximate gluing method ofBrandenberger and Martin, which relates more directly to the modelingof the trans-Planckian physics via modifications of thevacuum at a certain cutoff scale. We show that the gluing methodoverestimates the leading order correction to the spectrum andbispectrum by one and two orders, respectively, in H/pc. Wediscuss the variousapproximationand conclude that for dispersion relations not violating WKB atearly times the particle creation is small and does not lead toenhanced contributions to thebispectrum. We also show that in many cases enhancements do not occurwhen modeling the trans-Planckian physics via modifications of thevacuum at a certain cutoff scale. Most notably they are only of orderO(1) when the Bogolyubov coefficients accounting for particle creation are determined bythe Wronskian condition and the minimization of the uncertaintybetween the field and its conjugate momentum.