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

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.