Abstract
We study how massive ghost-free gravity \(f(R)\)-modified theories, MGFTs, can be encoded into generic off-diagonal Einstein spaces. Using “auxiliary” connections completely defined by the metric fields and adapted to nonholonomic frames with associated nonlinear connection structure, we decouple and integrate in certain general forms the field equations in MGFT. Imposing additional nonholonomic constraints, we can generate Levi-Civita, LC, configurations and mimic MGFT effects via off-diagonal interactions of effective Einstein and/or Einstein–Cartan gravity with nonholonomically induced torsion. We show that imposing nonholonomic constraints it is possible reproduce very specific models of massive \(f(R)\) gravity studied in Cai et al. (arXiv:1307.7150, 2013), Klusoňet al. (Phys Lett B 726:918, 2013), Nojiri and Odintov (Phys Lett B 716:377, 2012) and Nojiri et al. (JCAP 1305:020, 2013). The cosmological evolution of ghost-free off-diagonal Einstein spaces is investigated. Certain compatibility of MGFT cosmology to small off-diagonal deformations of \(\Lambda \)CDM models is established.
Highlights
In [1–4], two models of nonlinear massive gravitational theories including f (R) modifications were elaborated
We study how massive ghost-free gravity f (R)modified theories, MGFTs, can be encoded into generic off-diagonal Einstein spaces
Using “auxiliary” connections completely defined by the metric fields and adapted to nonholonomic frames with associated nonlinear connection structure, we decouple and integrate in certain general forms the field equations in MGFT
Summary
In [1–4], two models of nonlinear massive gravitational theories including f (R) modifications were elaborated. Such theories contain the benefits of the dRGT model [5,6] and are free of ghost modes [7–10]. It is the point of this paper to apply in MGFT the so-called anholonomic frame deformation method, AFDM, [28–34] for constructing generic off-diagonal exact solutions. Such a method provides geometric techniques, which allows us to integrate systems of partial differential equations, PDEs, with functional and parametric dependencies for the Levi-Civita (zero torsion) and nontrivial torsion configurations
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