Can Gravitational Waves Prevent Inflation?

Abstract

To investigate the cosmic no hair conjecture, we analyze numerically 1-dimensional plane symmetrical inhomogeneities due to gravitational waves in vacuum spacetimes with a positive cosmological constant. Assuming periodic gravitational pulse waves initially, we study the time evolution of those waves and the nature of their collisions. As measures of inhomogeneity on each hypersurface, we use the 3-dimensional Riemann invariant ${\cal I}\equiv {}~^{(3)\!}R_{ijkl}~^{(3)\!}R^{ijkl}$ and the electric and magnetic parts of the Weyl tensor. We find a temporal growth of the curvature in the waves' collision region, but the overall expansion of the universe later overcomes this effect. No singularity appears and the result is a ``no hair" de Sitter spacetime. The waves we study have amplitudes between $0.020\Lambda \leq {\cal I}^{1/2} \leq 125.0\Lambda$ and widths between $0.080l_H \leq l \leq 2.5l_H$, where $l_H=(\Lambda/3)^{-1/2}$, the horizon scale of de Sitter spacetime. This supports the cosmic no hair conjecture.Comment: LaTeX, 11 pages, 3 figures are available on request <To [email protected] (Hisa-aki SHINKAI)>, WU-AP/29/9