• Open Access

Constraints and horizons for de Sitter with extra dimensions

Saurya Das, S. Shajidul Haque, and Bret Underwood
Phys. Rev. D 100, 046013 – Published 22 August 2019

Abstract

In order for spacetimes with static extra dimensions to have four-dimensional de Sitter expansion they must have at least positive curvature, warping sourced by the four-dimensional expansion, or violate the null energy condition everywhere in the extra dimensions. We show how this constraint arises from the null Raychaudhuri equation, and that it is independent of the matter content, the Einstein equations, and is true point by point in the extra dimensions (not integrated), setting it apart from other no-go theorems in the literature. We present two previously known examples—a Freund-Rubin compactification with bulk cosmological constant, and a Randall-Sundrum model where the mismatch between the brane and bulk cosmological constants sources nontrivial warping—which evade the constraint and discuss the implications for flux compactifications. We also show that any spacetime with static compact extra dimensions and four-dimensional de Sitter expansion has an apparent horizon and antitrapped region in the extra dimensions, which may have interesting implications for the dynamics of bulk fields in cosmology.

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  • Received 31 May 2019

DOI:https://doi.org/10.1103/PhysRevD.100.046013

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

Saurya Das*

  • Theoretical Physics Group, Department of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta T1K 3M4, Canada

S. Shajidul Haque

  • Department of Physics, University of Windsor, Windsor, Ontario N9A 0C5, Canada

Bret Underwood

  • Department of Physics, Pacific Lutheran University, Tacoma, Washington, DC 98447, USA

  • *saurya.das@uleth.ca
  • shajid.haque@uwindsor.ca
  • bret.underwood@plu.edu

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Vol. 100, Iss. 4 — 15 August 2019

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