Dark energy and inflation invoked in CCGG by locally contorted space-time
Frankfurt Institute for Advanced Studies (FIAS), Ruth-Moufang-Strasse 1, 60438, Frankfurt am Main, Germany
2 Goethe Universität, Max-von-Laue-Strasse 1, 60438, Frankfurt am Main, Germany
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Accepted: 23 April 2020
Published online: 19 May 2020
The cosmological implications of the covariant canonical gauge theory of gravity (CCGG) are investigated. We deduce that, in a metric-compatible geometry, the requirement of covariant conservation of matter invokes torsion of space-time. In the Friedman model, this leads to a scalar field built from contortion and the metric with the property of dark energy, which transforms the cosmological constant to a time-dependent function. Moreover, the quadratic, scale-invariant Riemann–Cartan term in the CCGG Lagrangian endows space-time with kinetic energy, and in the field equations adds a geometrical curvature correction to Einstein gravity. Applying in the Friedman model the standard parameter set, those equations yield a cosmological field depending just on one additional, dimensionless “deformation” parameter of the theory that determines the strength of the quadratic term, viz. the deviation from the Einstein–Hilbert ansatz. Moreover, the apparent curvature of the universe differs from the actual curvature parameter of the metric. The numerical analysis in that parameter space yields three cosmology types: (1) a bounce universe starting off from a finite scale followed by a steady inflation, (2) a singular Big Bang universe undergoing a secondary inflation–deceleration phase and (3) a solution similar to standard cosmology but with a different temporal profile. The common feature of all scenarios is the graceful exit to the current dark energy era. The value of the deformation parameter can be deduced by comparing theoretical calculations with observations, namely with the SNeIa Hubble diagram and the deceleration parameter. That comparison implies a considerable admixture of scale-invariant quadratic gravity to Einstein gravity. This theory also sheds new light on the resolution of the cosmological constant problem and of the Hubble tension.
© The Author(s), 2020