Is there a flatness problem in classical cosmology?

TL;DR

This paper reviews the flatness problem in classical cosmology, questions its existence, and presents calculations showing it does not exist across all Friedmann-Lemaître models, challenging a common cosmological assumption.

Contribution

It provides a comprehensive analysis and new calculations demonstrating the flatness problem does not exist in any Friedmann-Lemaître cosmological model.

Findings

Flatness problem is absent in all examined models

Calculations include models that will collapse and expand forever

Challenges the conventional view of the flatness problem in cosmology

Abstract

I briefly review the flatness problem within the context of classical cosmology and examine some of the debate in the literature with regard to its definition and even the question whether it exists. I then present some new calculations for cosmological models which will collapse in the future; together with previous work by others for models which will expand forever, this allows one to examine the flatness problem quantitatively for all cosmological models. This leads to the conclusion that the flatness problem does not exist, not only for the cosmological models corresponding to the currently popular values of lambda_0 and Omega_0 but indeed for all Friedmann-Lema\^itre models.