Initial data of axisymmetric gravitational waves with a cosmological constant  pp. 345-352

Initial data of axisymmetric gravitational waves with a cosmological constant

By Ken-Ichi Nakao, Kei-ichi Maeda, Takashi Nakamura and Ken-ichi Oohara

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Abstract. We investigate initial data for localized gravitational waves in space-times with a cosmological constant Λ. By choosing the appropriate extrinsic curvature, we find that the Hamiltonian and momentum constraints turn out to be the same as those of the time-symmetric initial value problem for vacuum space-times without Λ. As initial data, we consider Brill waves and discuss the cosmological apparent horizon. Just as with Brill waves in asymptotically flat space-time, the gravitational “mass” of these waves is positive. Waves with large gravitational mass cause a strong cosmic expansion. Hence, the large amount of gravitational waves do not seem to be an obstacle to the cosmic no-hair conjecture.

INTRODUCTION

The present isotropy and homogeneity of our universe is something of a mystery within the framework of the standard big bang scenario. The inflationary universe scenario, however, is one of the favourable models which may explain the so-called homogeneity problem [1]. In this scenario, when a phase transition of the vacuum occurs due to an inflaton scalar field and supercooling results, the vacuum energy of the scalar field plays the role of a cosmological constant and the space-time behaves like the de Sitter one with a rapid cosmic expansion. This phenomenon is called inflation. As a result, all inhomogeneities go outside the horizon by rapid cosmic expansion. After inflation, the vacuum energy of the scalar field decays into radiation and the standard big bang scenario is recovered. However, there still remains a question in the above scenario.