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Parity violating Friedmann universes

João Magueijo*

Tom Złośnik†

  • Theoretical Physics Group, The Blackett Laboratory, Imperial College, Prince Consort Rd., London SW7 2BZ, United Kingdom

  • CEICO, Institute of Physics of the Czech Academy of Sciences, Na Slovance 1999/2, 182 21 Prague, Czech Republic

  • *j.magueijo@imperial.ac.uk
  • †zlosnik@fzu.cz
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Phys. Rev. D 100, 084036 – Published 16 October, 2019

DOI: https://doi.org/10.1103/PhysRevD.100.084036

Abstract

We revisit extensions of the Einstein-Cartan theory where the cosmological constant Λ is promoted to a variable, at the cost of allowing for torsion even in the absence of spinors. We remark that some standard notions about Friedmann-Robertson-Walker (FRW) universes collapse in these theories, most notably that spatial homogeneity and isotropy may now coexist with violations of parity invariance. The parity-violating solutions have nonvanishing Weyl curvature even within FRW models. The presence of parity-violating torsion opens up the space of possible such theories with relevant FRW modifications; in particular the Pontryagin term can play an important role even in the absence of spinorial matter. We present a number of parity-violating solutions with and without matter. The former are the non-self-dual vacuum solutions long suspected to exist. The latter lead to tracking and nontracking solutions with a number of observational problems, unless we invoke the Pontryagin term. An examination of the Hamiltonian structure of the theory reveals that the parity-even and the parity-violating solutions belong to two distinct branches of the theory, with different gauge symmetries (constraints) and different numbers of degrees of freedom (d.o.f.). The parity-even branch is nothing but standard relativity with a cosmological constant which has become pure gauge under conformal invariance if matter is absent, or a slave of matter (and so not an independent d.o.f.) if nonconformally invariant matter is present. In contrast, the parity-violating branch contains a genuinely new d.o.f.

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Phys. Rev. D 100, 084036– Published 16 October, 2019
  • Received 16 August 2019
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