Enhanced CMBR non-Gaussianities from Lorentz violation

Abstract

We study the effects of Lorentz symmetry violationon the scalar CMBR bispectrum. We deal with dispersion relations modified by higherderivative terms in a Lorentz breaking effective action and solve the equations via approximation techniques,in particular the WKB method. We quantify thedegree of approximation in the computation of the bispectrum and showhow the absolute and relative errors can be made small at will, making the results robust.Our results show thatthere can be enhancements in the bispectrum for specific configurationsin momentum space, whenthe modified dispersion relations violate the adiabatic condition fora short period of time in the early Universe. The kind of configurations that are enhanced andthe pattern of oscillations in wavenumbers that generically appearin the bispectrum strictly depend on the form of the modifieddispersion relation, and therefore on the pattern of Lorentz violation. Theseeffects are found to be distinct from those that appear when modelling very high-energy(transplanckian) physics via modified boundary conditions (modifiedvacuum). In fact, under certain conditions, the enhancements can beeven stronger, given equal interactions, and possibly open a door tothe experimental study of Lorentz violation through these phenomena.After providing the general analysis, we also discuss briefly a specific example based on a healthymodification of the Corley-Jacobson dispersion relation with negativecoefficient, and plot the shape of thebispectrum in that case.