Imprints of a Primordial Preferred Direction on the Microwave Background

TL;DR

The paper tests the robustness of inflationary predictions to a small break of rotational invariance caused by a fixed-norm vector during inflation, deriving how this yields a scale-invariant, direction-dependent modification to the primordial power spectrum and associated off-diagonal CMB correlations. The authors derive explicit expressions for the induced correlations $\langle a_{lm} a_{l'm'}^* \rangle$ in terms of a single amplitude $g_*$ and a preferred direction $\mathbf n$, together with a concrete anisotropic-inflation model based on a spacelike vector $u^\mu$ that produces a parameter $\epsilon_H$ and a log-enhanced correction $\Delta P(k) \propto \epsilon_H \log(k)$. The main contributions are (i) the general prediction framework for CMB anisotropies with a preferred direction and (ii) a solvable inflationary model that yields near-scale invariance of the effect, enabling observational constraints. The work provides a pathway to test high-energy physics of the inflation era and to constrain Lorentz-violating effects using CMB data.

Abstract

Rotational invariance is a well-established feature of low-energy physics. Violations of this symmetry must be extremely small today, but could have been larger in earlier epochs. In this paper we examine the consequences of a small breaking of rotational invariance during the inflationary era when the primordial density fluctuations were generated. Assuming that a fixed-norm vector picked out a preferred direction during the inflationary era, we explore the imprint it would leave on the cosmic microwave background anisotropy, and provide explicit formulas for the expected amplitudes $<a_{lm}a_{l'm'}^*>$ of the spherical-harmonic coefficients. We suggest that it is natural to expect that the imprint on the primordial power spectrum of a preferred spatial direction is approximately scale-invariant, and examine a simple model in which this is true.