Phantom Friedmann Cosmologies and Higher-Order Characteristics of Expansion

TL;DR

This paper explores generalized phantom cosmologies with diverse matter content, analyzing their evolution, singularities, and observational signatures, including higher-order characteristics like jerk and kerk, to better understand universe dynamics and potential observational indicators.

Contribution

It introduces a broad class of phantom cosmological models with explicit relations between parameters and higher-order observational characteristics, expanding understanding of universe evolution and singularities.

Findings

Existence of non-singular oscillating (bounce) cosmologies.

Models with both Big-Bang and Big-Rip singularities.

Series expansion formulas for luminosity distance including jerk and kerk.

Abstract

We discuss a more general class of phantom ($p < -\varrho$) cosmologies with various forms of both phantom ($w < -1$), and standard ($w > -1$) matter. We show that many types of evolution which include both Big-Bang and Big-Rip singularities are admitted and give explicit examples. Among some interesting models, there exist non-singular oscillating (or "bounce") cosmologies, which appear due to a competition between positive and negative pressure of variety of matter content. From the point of view of the current observations the most interesting cosmologies are the ones which start with a Big-Bang and terminate at a Big-Rip. A related consequence of having a possibility of two types of singularities is that there exists an unstable static universe approached by the two asymptotic models - one of them reaches Big-Bang, and another reaches Big-Rip. We also give explicit relations between density parameters $\Omega$ and the dynamical characteristics for these generalized phantom models, including higher-order observational characteristics such as jerk and "kerk". Finally, we discuss the observational quantities such as luminosity distance, angular diameter, and source counts, both in series expansion and explicitly, for phantom models. Our series expansion formulas for the luminosity distance and the apparent magnitude go as far as to the fourth-order in redshift $z$ term, which includes explicitly not only the jerk, but also the "kerk" (or "snap") which may serve as an indicator of the curvature of the universe.