The Early Universe and Planck's Radiation Law

TL;DR

This paper revises Planck's radiation law to solve Friedmann-Lemaître equations, demonstrating a flat universe evolution without initial singularity, and resolving horizon and flatness problems in cosmology.

Contribution

It introduces a corrected Planck's law into cosmological equations, showing a flat universe evolution free of initial singularities and classical problems.

Findings

Universe evolution is only consistent for flat spatial slices (k=0).

Initial singularity is avoided in the model.

Standard expansion behavior is recovered at low temperatures.

Abstract

The classical Friedmann-Lema\^itre equations are solved using a corrected version of Planck's radiation law. The function curves of the scale parameter a(t) and the variations with temperature a(T) and t(T) are given. It is shown that a reasonable cosmological evolution is only possible in case of flat spatial slices (k=0). The initial singularity is avoided. Horizon and flatness problems do not exist. For low temperatures compared with the Planck Temperatur, the equations yield the usual course of expansion of the standard FLRW model for a radiation universe with k=0 and p=u(T)/3.