The expected anisotropy in solid inflation

TL;DR

Solid inflation predicts an unavoidable level of statistical anisotropy in the power spectrum due to superhorizon scalar field fluctuations, with potential observational signatures if the bispectrum amplitude is near current limits.

Contribution

This paper calculates the expected anisotropy level in solid inflation's power spectrum, linking it to inflation duration and bispectrum amplitude, highlighting observable predictions.

Findings

Expected anisotropy can reach over 3% for extended inflation periods.

Anisotropy arises from superhorizon scalar field fluctuations, even with isotropic initial conditions.

The model's predictions are similar to those involving vector field couplings during inflation.

Abstract

Solid inflation is an effective field theory of inflation in which isotropy and homogeneity are accomplished via a specific combination of anisotropic sources (three scalar fields that individually break isotropy). This results in specific observational signatures that are not found in standard models of inflation: a non-trivial angular dependence for the squeezed bispectrum, and a possibly long period of anisotropic inflation (to drive inflation, the "solid" must be very insensitive to any deformation, and thus background anisotropies are very slowly erased). In this paper we compute the expected level of statistical anisotropy in the power spectrum of the curvature perturbations of this model. To do so, we account for the classical background values of the three scalar fields that are generated on large (superhorizon) scales during inflation via a random walk sum, as the perturbation modes leave the horizon. Such an anisotropy is unavoidably generated, even starting from perfectly isotropic classical initial conditions. The expected level of anisotropy is related to the duration of inflation and to the amplitude of the squeezed bispectrum. If this amplitude is close to its current observational limit (so that one of the most interesting predictions of the model can be observed in the near future), we find that a level of statistical anisotropy $\gtrsim 3\%$ in the power spectrum is to be expected, if inflation lasted $\gtrsim 20-30$ e-folds more than the final $50-60$ efolds required to generare the CMB modes. We also comment and point out various similarities between solid inflation and models of inflation where a suitable coupling of the inflaton to a vector kinetic term $F^{2}$ gives frozen and scale invariant vector perturbations on superhorizon scales.