Anisotropic inflation in Finsler spacetime

TL;DR

This paper proposes a Finslerian model of the universe during inflation, introducing anisotropy and parity violation, and derives the resulting effects on primordial power spectrum and angular correlations.

Contribution

It introduces a Finslerian inflationary framework that incorporates anisotropy and parity violation, deriving new gravitational field equations and angular correlation predictions.

Findings

Primordial power spectrum depends on both wavenumber magnitude and direction.

Angular correlation coefficients exhibit anisotropic effects with specific parity violation features.

Numerical results demonstrate the impact of Finslerian anisotropy on observable correlations.

Abstract

We suggest the universe is Finslerian in the stage of inflation. The Finslerian background spacetime breaks rotational symmetry and induces parity violation. The primordial power spectrum is given for quantum fluctuation of the inflation field. It depends not only on the magnitude of wavenumber but also on the preferred direction. We derive the gravitational field equations in the perturbed Finslerian background spacetime, and obtain a conserved quantity outside the Hubble horizon. The angular correlation coefficients are presented in our anisotropic inflation model. The parity violation feature of Finslerian background spacetime requires that the anisotropic effect only appears in angular correlation coefficients if $l'=l+1$. The numerical results of the angular correlation coefficients are given to describe the anisotropic effect.