An exposition on Friedmann Cosmology with Negative Energy Densities

Abstract

How would negative energy density affect a classic Friedmann cosmology? Although never measured and possibly unphysical, certain realizations of quantum field theories leaves the door open for such a possibility. In this paper we analyze the evolution of a universe comprising varying amounts of negative energy forms. Negative energy components have negative normalized energy densities, $\Omega <0$. They include negative phantom energy with an equation of state parameter $w<-1$, negative cosmological constant: $w=-1$, negative domain walls: $w=-2/3$, negative cosmic strings: $w=-1/3$, negative mass: $w=0$, negative radiation: $w=1/3$ and negative ultralight: $w>1/3$. Assuming that such energy forms generate pressure like perfect fluids, the attractive or repulsive nature of negative energy components are reviewed. The Friedmann equation is satisfied only when negative energy forms are coupled to a greater magnitude of positive energy forms or positive curvature. We show that the solutions exhibit cyclic evolution with bounces and turnovers.The future and fate of such universes in terms of curvature, temperature, acceleration, and energy density are reviewed. The end states are dubbed Big Crunch, Big Void, or Big Rip and further qualified as "Warped", "Curved", or "Flat", "Hot" versus "Cold", "Accelerating" versus "Decelerating" versus "Coasting". A universe that ends by contracting to zero energy density is termed "Big Poof." Which contracting universes "bounce" in expansion and which expanding universes "turnover" into contraction are also reviewed.

Abridged version with minor corrections

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