Non-Gaussianity from Lifshitz Scalar

TL;DR

A Lifshitz scalar with z=3 can produce scale-invariant, non-Gaussian primordial fluctuations with large f_NL, potentially detectable in future CMB observations, due to its unique scaling and self-couplings.

Contribution

This work demonstrates that Lifshitz scalars can generate large non-Gaussianity in primordial fluctuations, with analytically computed bispectrum and trispectrum shapes.

Findings

Primordial non-Gaussianity of order f_NL=O(100) can arise from Lifshitz scalars.

The bispectrum exhibits local, equilateral, and orthogonal shapes.

Analytic calculations of the in-in formalism integrals were achieved.

Abstract

A Lifshitz scalar with the dynamical critical exponent z = 3 obtains scale-invariant, super-horizon field fluctuations without the need of an inflationary era. Since this mechanism is due to the special scaling of the Lifshitz scalar and persists in the presence of unsuppressed self-couplings, the resulting fluctuation spectrum can deviate from a Gaussian distribution. We study the non-Gaussian nature of the Lifshitz scalar's intrinsic field fluctuations, and show that primordial curvature perturbations sourced from such field fluctuations can have large non-Gaussianity of order f_NL = O(100), which will be detected by upcoming CMB observations. We compute the bispectrum and trispectrum of the fluctuations, and discuss their configurations in momentum space. In particular, the bispectrum is found to take various shapes, including the local, equilateral, and orthogonal shapes. Intriguingly, all integrals in the in-in formalism can be performed analytically.