Cosmological Evolution with \LambdaTerm and Any Linear equation of State
Abstract
Recent observational indications of an accelerating universe enhance the interest in studying models with a cosmological constant. We investigate cosmological expansion (FRW metric) with $\Lambda>0$ for a general linear equation of state $p=w\rho$, $w>1$, so that the interplay between cosmological vacuum and quintessence is allowed, as well. Four closedform solutions (flat universe with any $w$, and $w=1/3$, $1/3, 2/3$) are given, of which the last one appears to be new. For the open universe a simple relation between solutions with different parameters is established: it turns out that a solution with some $w$ and (properly scaled) $\Lambda$ is expressed algebraically via another solution with special different values of these parameters. The expansion becomes exponential at large times, and the amplitude at the exponent depends on the parameters. We study this dependence in detail, deriving various representations for the amplitude in terms of integrals and series. The closedform solutions serve as benchmarks, and the solution transformation property noted above serves as a useful tool. Among the results obtained, one is that for the open universe with relatively small cosmological constant the amplitude is independent of the equation of state. Also, estimates of the cosmic age through the observable ratio $\Omega_\Lambda/\Omega_M$ and parameter $w$ are given; when inverted, they provide an estimate of $w$, i. e., the state equation, through the known age of the universe.
 Publication:

arXiv eprints
 Pub Date:
 October 2001
 arXiv:
 arXiv:grqc/0110062
 Bibcode:
 2001gr.qc....10062S
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 3 figures