Cosmic acceleration with a negative cosmological constant in higher dimensions

Abstract

We study gravitational theories with a cosmological constant and the Gauss-Bonnet curvature squared term and analyze the possibility of de Sitter expanding spacetime with a constant internal space. We find that there are two branches of the de Sitter solutions: Both the curvature of the internal space and the cosmological constant are (1) positive and (2) negative. From the stability analysis, we show that the de Sitter solution of the case (1) is unstable, while that in the case (2) is stable. Namely de Sitter solution in the present system is stable if the cosmological constant is negative. We extend our analysis to the gravitational theories with higher-order Lovelock curvature terms. Although the existence and the stability of the de Sitter solutions are very complicated and highly depend on the coupling constants, there exist stable de Sitter solutions similar to the case (2). We also find de Sitter solutions with Hubble scale much smaller than the scale of a cosmological constant, which may explain a discrepancy between an inflation energy scale and the Planck scale.

21 pages, 18 figures, v2: minor corrections, refs. added and typos corrected

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• Cosmological dynamics in higher-dimensional Einstein-Gauss-Bonnet gravity
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• Constant volume exponential solutions in Einstein-Gauss-Bonnet flat anisotropic cosmology with a perfect fluid
• Cosmological dynamics of spatially flat Einstein-Gauss-Bonnet models in various dimensions: Low-dimensional $\Lambda$-term case
• Stable exponential cosmological solutions with zero variation of $G$ and three different Hubble-like parameters in the Einstein-Gauss-Bonnet model with a $\Lambda$-term
• Mapping Poincaré gauge cosmology to Horndeski theory for emergent dark energy
• Cosmological solutions in Einstein-Gauss-Bonnet gravity with static curved extra dimensions
• A Cosmological Study in Massive Gravity theory
• Stable exponential cosmological solutions with zero variation of G in the Einstein-Gauss-Bonnet model with a Lambda-term
• Exact $(1+3+6)$-dimensional cosmological-type solutions in gravitational model with Yang-Mills field, Gauss-Bonnet term and $\Lambda$-term