Initial directional singularity in inflationary models

TL;DR

This paper explores a cosmological model where the traditional big bang singularity is replaced by a directional singularity, affecting observers differently based on their motion, and analyzes its properties and implications.

Contribution

It introduces and examines the properties of a directional singularity in inflationary models, challenging the conventional big bang singularity concept.

Findings

Observers with zero linear momentum cannot reach the singularity.

Observers with nonzero linear momentum encounter the singularity in finite proper time.

The initial singularity can be infinitely distant in proper time for comoving observers.

Abstract

In [1] a new cosmological model is proposed with no big bang singularity in the past, though past geodesically incomplete. This model starts with an inflationary era, follows with a stiff matter dominated period and evolves to accelerated expansion in an asymptotically de Sitter regime in a realistic fashion. The big bang singularity is replaced by a directional singularity. This singularity cannot be reached by comoving observers, since it would take them an infinite proper time lapse to go back to it. On the contrary, observers with nonzero linear momentum have the singularity at finite proper time in their past, though arbitrarily large. Hence, the time lapse from the initial singularity can be as long as desired, even infinity, depending on the linear momentum of the observer. This conclusion applies to similar inflationary models. Due to the interest of these models, we address here the properties of such singularities.