Models of universe with a polytropic equation of state: III. The phantom universe

2012/08/06 by Pierre-Henri Chavanis, Chavanis, Pierre-Henri
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #Relativity and Gravitational Theory

paper · pdf · doi:10.48550/arxiv.1208.1185

openalex publication_date 2012/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct models of universe with a generalized equation of state p=(αρ+kρ^1+1/n)c² having a linear component and a polytropic component. The linear equation of state p=αρc² with -1≤ α≤ 1 describes radiation (α=1/3), pressureless matter (α=0), stiff matter (α=1), and vacuum energy (α=-1). The polytropic equation of state p=kρ^1+1/n c² may be due to Bose-Einstein condensates with repulsive (k>0) or attractive (k<0) self-interaction, or have another origin. In this paper, we consider the case where the density increases as the universe expands. This corresponds to a "phantom universe" for which w=p/ρc²-1 there is no Big Rip singularity although w≤ -1. For n=-1, we provide an analytical model of phantom bouncing universe "disappearing" at t=0. We also determine the potential of the phantom scalar field and phantom tachyon field corresponding to the generalized equation of state p=(αρ+kρ^1+1/n)c².

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