Can We See Lorentz-Violating Vector Fields in the CMB?

TL;DR

The paper analyzes a fixed-norm, timelike Lorentz-violating vector field during inflation, deriving a consistent quantum perturbation theory and constraining the theory’s parameters ${\beta_i}$. It shows that vector perturbations are sourced by inflaton fluctuations and do not generate spin-1 modes, but they modify the spin-0 and spin-2 spectra and violate the standard inflationary consistency relation. The scalar amplitude is rescaled by factors involving ${\alpha},{\gamma}$, and the tensor amplitude can be enhanced if ${\gamma}<0$, with observable implications for the CMB, particularly in B-mode polarization. The work delineates a viable parameter space and highlights potential observational signatures, requiring full Boltzmann code modeling to predict imprints on the CMB power spectra.

Abstract

We investigate the perturbation theory of a fixed-norm, timelike Lorentz-violating vector field. After consistently quantizing the vector field to put constraints on its parameters, we compute the primordial spectra of perturbations generated by inflation in the presence of this vector field. We find that its perturbations are sourced by the perturbations of the inflaton; without the inflaton perturbation the vector field perturbations decay away leaving no primordial spectra of perturbations. Since the inflaton perturbation does not have a spin-1 component, the vector field generically does not generate any spin-1 ``vector-type'' perturbations. Nevertheless, it will modify the amplitude of both the spin-0 ``scalar-type'' and spin-2 ``tensor-type'' perturbation spectra, leading to violations of the inflationary consistency relationship.

Figures (1)

• Figure 1: Figure showing the allowed values for $\beta_i$. The arrows indicate extension to infinity. The slope of the wedge makes a 45 degrees angle with the $\beta_2-\beta_3$ plane. An example of a valid choice of parameters is $\beta_1=1$, $\beta_2=2.5$, $\beta_3=-3$.