General Solutions of Cosmological Equations with Inequalities for Perfect Fluid and Scalar Field

TL;DR

This paper derives general solutions for cosmological equations involving perfect fluids and scalar fields, analyzing inflationary and matter phases, and estimating matter and dark energy proportions based on recent observational data.

Contribution

It provides explicit solutions and inequalities for cosmological models with quintessence and tachyonic scalar fields, including special inflationary and matter expansion cases.

Findings

Derived general solutions for scalar field cosmologies.

Estimated matter and dark energy proportions from observational data.

Identified conditions for positive definiteness of scale factor and derivatives.

Abstract

Spherically symmetric cosmological equations in the usual FLRW coordinates are explored, with different sources. The first couples a perfect fluid with a quintessence scalar field and the second couples a perfect fluid to a tachyonic scalar field. In both cases, in the inflationary regime, the scale factor a(t) and its first two time derivatives are positive definite. Both sources in the matter phase yield a scale factor and its first derivative as positive definite. In both cases and in each phase, the general solutions of the differential equations together with the algebraic and differential inequalities are obtained. As special cases, exponential, hyperbolic, and power law inflation, as well as power law expansion for the matter phase are all derived from the general solutions. With recent data on baryonic matter, Hubble parameter and deceleration parameter, the relative percentages of baryonic matter, daek matter and dark energy are calculated. The quintessence model yields: 4% baryonic matter, 18% dark matter, and 78% dark energy. The tachyonic model gives: 4% baryonic matter, 36% dark matter, and 60% dark energy.