General relativity as an attractor for scalar-torsion cosmology

Abstract

We study flat Friedmann-Lemaître-Robertson-Walker cosmological models for a scalar field coupled nonminimally to teleparallel gravity with generic coupling and potential functions. The goal of this paper is to determine the conditions under which cosmological evolution tends to the limit where the variation of the gravitational "constant" ceases and the system evolves close to general relativity. These conditions can be read off from the approximate analytical solutions describing the process in matter and potential domination eras. Only those models where the GR limit exists and is an attractor can be considered viable. We expect the results to hold in the original "pure tetrad" formulation as well as in the recently suggested covariant formulation of the teleparallel theory. In the former case the GR attractor simultaneously provides a mechanism how cosmological evolution suppresses the problematic degrees of freedom stemming from the lack of local Lorentz invariance.PACS numbers: 04.50. Kd, 95.36.+x

Effective Gravitational “Constant” in Scalar-(Curvature)Tensor and Scalar-Torsion Gravities

“…Again, the convergence to the value ϕ is either monotonic or oscillating, depending on the model parameters. In the scalar-torsion cosmology the attractor mechanism works and the approximation solutions can be found also in the radiation domination era [16]. Similarly to the scalar-(curvature)tensor case, the behavior of the gravitational "constant" in cosmological time can be read off from the solutions above.…”

“…Similarly to the scalar-(curvature)tensor case, the behavior of the gravitational "constant" in cosmological time can be read off from the solutions above. So, although scalar-torsion gravity is rather different from scalar-(curvature)tensor gravity, the mechanism to stabilize the gravitational "constant" via cosmological background evolution is also possible here [16].…”

“…and solve them analytically [16]. If the dust matter dominates, ρ U (and U > 0), H = 2 3(t−t s ) , the solutions are…”

“…The action (10) remains invariant under scalar field redefinitions, but not under conformal transformations. For example, we may redefine the scalar field to give the action a similar form to Equation (3) [16],…”

“…However, the TEGR equations of motion are equivalent to general relativity, since torsion and curvature scalars differ by a total divergence only, T = −R − 2∇ µ T λ µλ . Now if a scalar field is introduced with nonminimal coupling to torsion, i.e., scalar-torsion gravity [15,16],…”