Regular Article - Theoretical Physics
completion of the Friedmann equations
Institute of Mathematical Sciences, Ewha Woman’s University, 52 Ewhayeodae-gil, Seodaemun-gu, 03760, Seoul, Korea
2 Department of Physics, Sogang University, 35 Baekbeom-ro, Mapo-gu, 04107, Seoul, Korea
3 Department of Physics, McGill University, H3A 2T8, Montreal, QC, Canada
4 Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, 606-8502, Kyoto, Japan
5 Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, 277-8583, Kashiwa, Chiba, Japan
Accepted: 18 August 2020
Published online: 7 September 2020
In string theory the closed-string massless NS-NS sector forms a multiplet of symmetry. This suggests a specific modification to General Relativity in which the entire NS-NS sector is promoted to stringy graviton fields. Imposing off-shell symmetry fixes the correct couplings to other matter fields and the Einstein field equations are enriched to comprise components, dubbed recently as the Einstein Double Field Equations. Here we explore the cosmological implications of this framework. We derive the most general homogeneous and isotropic ansatzes for both stringy graviton fields and the -covariant energy-momentum tensor. Crucially, the former admits space-filling magnetic H-flux. Substituting them into the Einstein Double Field Equations, we obtain the completion of the Friedmann equations along with a generalized continuity equation. We discuss how solutions in this framework may be characterized by two equation-of-state parameters, w and , where the latter characterizes the relative intensities of scalar and tensor forces. When , the dilaton remains constant throughout the cosmological evolution, and one recovers the standard Friedmann equations for generic matter content (i.e. for any w). We further point out that, in contrast to General Relativity, neither an -symmetric cosmological constant nor a scalar field with positive energy density gives rise to a de Sitter solution.
© The Author(s) 2020
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