Abstract
In this paper, we formulate the Mimetic theory of gravity in first-order formalism for differential forms, i.e., the mimetic version of Einstein-Cartan-Sciama-Kibble (ECSK) gravity. We consider different possibilities on how torsion is affected by Weyl transformations and discuss how this translates into the interpolation between two different Weyl transformations of the spin connection, parameterized with a zero-form parameter λ. We prove that regardless of the type of transformation one chooses, in this setting torsion remains as a non-propagating field. We also discuss the conservation of the mimetic stress-energy tensor and show that the trace of the total stress-energy tensor is not null but depends on both, the value of λ and spacetime torsion.
Highlights
JHEP10(2020)150 where Sciama and Kibble rediscovered Cartan’s results [17, 18]
When considering generalized conformal invariance on Riemann-Cartan geometry, the stress-energy tensor’s trace, which usually vanishes for conformally invariant theories of gravity, has a non-zero value depending on torsion and on a parameter which characterizing Weyl transformations for the spin connection
The metric gμν is invariant with respect to Weyl transformations of the auxiliary metric gμν, i.e., it remains unchanged after rescaling gμν → Ω2 (x) gμν
Summary
Mimetic Gravity was first introduced by A. The metric gμν is invariant with respect to Weyl transformations of the auxiliary metric gμν, i.e., it remains unchanged after rescaling gμν → Ω2 (x) gμν It follows from (2.1) that gαβ∂αφ∂βφ = −1. The resultant new degree of freedom associated with the transformation (2.1) represents the longitudinal mode of gravity which is excited even in the absence of any matter field configurations. This last equation is automatically satisfied by the constraint (2.3) even for G = κ4T From this point of view, even in absence of matter, the gravitational field equations have non-trivial solutions for the conformal mode. To understand this extra degree of freedom, let us rewrite eq (2.5) as. Note that the normalization condition for the four velocity uμ and the conservation law for Tμν, are equivalent to (2.3) and (2.6), respectively
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