Cosmology with a stiff matter era

TL;DR

This paper derives analytical solutions for cosmological models incorporating stiff matter, dust, and dark energy, revealing conditions for singular, non-singular, and cyclic universe evolutions based on the properties of stiff matter and the cosmological constant.

Contribution

It provides a comprehensive analytical framework for understanding how stiff matter and dark energy influence universe dynamics, including singular and non-singular scenarios.

Findings

Positive stiff matter leads to singular primordial universe.

Negative stiff matter results in non-singular universe starting from finite scale factor.

Positive cosmological constant yields an accelerating de Sitter universe.

Abstract

We provide a simple analytical solution of the Friedmann equations for a universe made of stiff matter, dust matter, and dark energy. A stiff matter era is present in the cosmological model of Zel'dovich (1972) where the primordial universe is assumed to be made of a cold gas of baryons. It also occurs in certain cosmological models where dark matter is made of relativistic self-gravitating Bose-Einstein condensates (BECs). When the energy density of the stiff matter is positive, the primordial universe is singular. It starts from a state with a vanishing scale factor and an infinite density. We consider the possibility that the energy density of the stiff matter is negative (anti-stiff matter). This happens, for example, when the BECs have an attractive self-interaction. In that case, the primordial universe is non-singular. It starts from a state in which the scale factor is finite and the energy density is equal to zero. For the sake of generality, we consider a cosmological constant of arbitrary sign. When the cosmological constant is positive, the universe asymptotically reaches a de Sitter phase where the scale factor increases exponentially rapidly. This can account for the accelerating expansion of the universe that we observe at present. When the cosmological constant is negative (anti-de Sitter), the evolution of the universe is cyclic. Therefore, depending on the sign of the energy density of the stiff matter and of the dark energy, we obtain singular and non-singular expanding or cyclic universes.