Scalar field vs hydrodynamic models in the homogeneous isotropic cosmology

TL;DR

This paper investigates the conditions under which scalar field and hydrodynamic models of dark energy produce equivalent cosmological evolutions, providing explicit potentials and criteria for their approximate and exact equivalence.

Contribution

It derives differential equations and conditions that ensure scalar field and hydrodynamic models of dark energy are equivalent or approximately equivalent in homogeneous isotropic cosmology.

Findings

Derived a differential equation for scalar field potential ensuring model equivalence.

Established conditions for approximate equivalence based on energy-momentum tensor differences.

Explicitly found scalar field potentials for linear equations of state and provided complex examples.

Abstract

We study relations between hydrodynamical (H) and scalar field (SF) models of the dark energy in the early Universe. Main attention is paid to SF described by the canonical Lagrangian within the homogeneous isotropic spatially flat cosmology. We analyze requirements that guarantee the same cosmological history for the SF and H-models at least for solutions with specially chosen initial conditions and we present a differential equation for the SF potential that ensures such a restricted equivalence of the SF and H-models. Also, we derived a condition that guarantees an approximate equivalence when there is a small difference between energy momentum tensors of the models. The "equivalent" scalar field potentials for linear equations of state (EOS) are found in an explicit form, we also present an examples with more complicated EOS.