Dark Energy, Hyperbolic Cosecant Cardassian and Virial Collapse for Power-style Cardassian

TL;DR

This paper introduces a new hyperbolic cosecant Cardassian model within the GF fluid framework, analyzing its dynamical behavior, phase space, and virial collapse, demonstrating its stability and ability to facilitate virialization without singularities.

Contribution

It develops a novel hyperbolic cosecant Cardassian model with detailed dynamical analysis and explores virial collapse processes, highlighting stability and parameter effects.

Findings

Critical points exhibit self-consistency and auto-normalization.

Virial collapse of matter alone is forbidden, but possible with Cardassian effects.

No singularities are generated in the collapse process.

Abstract

New work gathers in Chapter 6 and Chapter 7. Tthe Cardassian dynamical equations are introduced generally and logically under GF fluid scenario, together with the flowing process of constructing phase space and differential dynamical systems from Friedmann equation. Hyperbolic cosecant Cardassian term is employed for concrete computing. The analysis proceeds in two cases, namely a unified description of matter and radiation energy density (case 1) and a separate description of matter and radiation terms (case 2).Formalism of case 2 is more exact at the expense of more complicatedness, and due to the mathematical symmetry of matter term and radiation term in hyperbolic cosecant function, the differential dynamical equations are considerably simplified. Phase space and dynamical systems for both cases are achieved. When we calculate the critical points for case 2, amazingly interesting behaviors of self-consistency and auto-normalization are exhibited, which is a strong support for the new model,along with a forever positive sound speed. The process of virial collapse in Cardassian cosmos is analyzed. Power-style Cardassian term is employed for its simplicity.Calculation declares that virial collapse of matter alone isforbidden. Yet Cardassian has excellent ability for virial collapse,after the virial collapse ending up with a stable sphere, the ratio of the ultimate radius to the original radius depends on the adjustable parameters in Cardassian term. And, the mixture of GF fluid and matter could conduct virial collapse, the ratio of the ultimate radius to the original radius depends on the adjustable parameters in Cardassian term, too. No singularity is generated.