# Finslerian dipolar modulation of the CMB power spectra at scales $2<l<600$

## TL;DR

This paper proposes a Finslerian model of the early universe to explain the observed dipolar asymmetry in the CMB power spectra, deriving a three-dimensional primordial spectrum with a preferred direction and analyzing its effects on angular correlations.

## Contribution

It introduces a Finslerian framework for primordial power spectra, linking dipolar modulation amplitude to Finslerian parameters and providing numerical anisotropic correlation results.

## Key findings

- Finslerian parameters influence dipolar modulation amplitude.
- Derived a 3D primordial power spectrum with directional dependence.
- Numerical analysis shows anisotropic correlations in CMB for $2<l<600$.

## Abstract

A common explanation for the CMB power asymmetry is to introduce a dipolar modulation at the stage of inflation, where the primordial power spectrum is spatially varying. If the universe in the stage of inflation is Finslerian, and if the Finsler spacetime is non-reversible under parity flip, $x\rightarrow-x$, then a three dimensional spectrum which is the function of wave vector and direction is valid. In this paper, a three dimensional primordial power spectrum with preferred direction is derived in the framework of Finsler spacetime. It is found that the amplitude of dipolar modulation is related to the Finslerian parameter, which in turn is a function of wave vector. The angular correlation coefficients are presented, and the numerical results for the anisotropic correlation coefficients over the multipole range $2<l<600$ are given.