Consistent initial data for CMD perturbations

TL;DR

This paper derives an exact formula for the spectrum transfer-function, ensuring initial conditions are consistent across radiation and matter-dominated epochs in cosmological perturbation theory.

Contribution

It introduces a method to set initial conditions that are consistent with perturbation equations in both epochs, improving accuracy in cosmological models.

Findings

Derived an exact formula for the spectrum transfer-function.

Established initial conditions consistent across different cosmological epochs.

Enhanced the accuracy of perturbation analysis in cosmology.

Abstract

We investigate the initial condition which are simultaneously consistent with perturbation equations in both the radiation-dominated and the mater-dominated epochs. The exact formula for the spectrum transfer-function is derived.