Initial Friedmann universe, its spatial flatness, matter creation, and the cosmological term

TL;DR

This paper explores the initial conditions of the Friedmann universe, emphasizing the importance of spatial flatness and vacuum states in avoiding infinite density, and discusses the origin of the cosmological term from vacuum energy.

Contribution

It proposes a link between initial vacuum states, spatial flatness, and matter creation, offering a new perspective on the origin of the cosmological term in Friedmann equations.

Findings

Spatial flatness avoids infinite initial density.

Matter creation arises from Friedmann equation nonlinearity.

Effective cosmological term is due to vacuum density.

Abstract

In the Friedmann equations, an infinite initial density is avoided only when the universe is spatially flat. With such equations being then valid when the scale factor $a=0$, the universe must also be in the state of vacuum when $a$ is infinitesimal. Matter creation thus largely comes from nonlinearity of the Friedmann equations at a finite $a$. For the correspondence between such an initial vacuum and the Friedmann universe, therefore, a vacuum density is suggested to be gravitationally significant only when it could also have a matter phase. The effective cosmological term is then due to such a vacuum density.