Warped de Sitter compactifications in the scalar–tensor theory

Abstract

We present new solutions of warped compactifications in the higher-dimensional gravity coupled to the scalar and the form field strengths. These solutions are constructed in the D-dimensional spacetime with matter fields, with the internal space that has a finite volume. Our solutions give explicit examples where the cosmological constant or 0-form field strength leads to a de Sitter spacetime in arbitrary dimensions.PACS numbers: 11.25.Mj We present exact solutions of warped de Sitter compactifications in the scalar-tensor theory coupled to the form field strength. We show that certain coupling constants and the warped structure [1-6] allow accelerating expansion of our Universe [7-10] in arbitrary dimensions. In the higher-dimensional gravity theory, timedependence of the hyperbolic compact internal space yields an accelerating universe in the four-dimensional Einstein frame without the warped structure [11]. Then, more general accelerating solutions without warping in the context of higher-dimensional theory have been studied extensively in [11][12][13][14][15][16]. A (warped) compactification to de Sitter or accelerating universe has also been invoked as models not only in higher-dimensional gravity but also in supergravity and string theory [2,[17][18][19][20][21][22][23][24]. In many of these applications the solutions of the de Sitter spacetime with a warped compactification are evaluated at appropriate values of their parameters. At present several warped solutions which give the four-dimensional de Sitter spacetime have been reported recently in [3,6] where one of the internal dimensions is noncompact, but de Sitter compactification with a compact internal space has been explored much less extensively (see e.g., [1] for the arguments on general properties of the warped de Sitter compactification). The main purpose of the present work is to present an explicit example of such warped de Sitter compactification just as the starting point for the research in this direction, though the solution presented in this Letter still may not be suitable for the realistic cosmological models.Without relying on an infinite volume of extra dimensions, we can directly deduce a known construction of the de Sitter compactification in the framework of the higher-dimensional gravity theory. The strategy to find solutions basically follows one used in [6].We also assume the same metric ansatz in [6], except for the replacement of the noncompact direction with that of S 1 . As we will see, our relatively simple ansatz, however, will give us much information to reveal the essential properties of the warped de Sitter compactification.In the following, we construct the de Sitter compacti-fications in the D-dimensional theory. Our construction is analogous to a previous approach to warped compactifications [4,6]. The starting point of the construction is that the internal space can be expressed as a compact manifold. In the first model, we introduce the cosmological constant and matter fields such as the scalar and gauge fields...