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Effective Einstein cosmological spaces for non-minimal modified gravity

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Abstract

Certain off-diagonal vacuum and nonvacuum configurations in Einstein gravity can mimic physical effects of modified gravitational theories of \( f(R,T,R_{\mu \nu }T^{\mu \nu })\) type. We prove this statement by constructing exact and approximate solutions which encode certain models of covariant Hořava type gravity with dynamical Lorentz symmetry breaking. Off-diagonal generalizations of de Sitter and nonholonomic \(\Lambda \)CDM universes are constructed which are generated through nonlinear gravitational polarization of fundamental physical constants and which model interactions with non-constant exotic fluids and effective matter. The problem of possible matter instability for such off-diagonal deformations in (modified) gravity theories is discussed.

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Notes

  1. We have to introduce a system of notations which is different from that in standard cosmology. This will be convenient for constructing cosmological models with generic off-diagonal metrics.

  2. Which cannot be diagonalized by coordinate transformations.

  3. The Einstein rule on index summation will be applied if the contrary is not stated. Boldface letters are used in order to emphasize that an N-connection spitting is considered on a spacetime manifold \(\mathbf {V=(}V,\mathbf {N).}\)

  4. see details in Sects. 3.1.2 and 3.2.

  5. The method can be extended to account for \(y^{3}\) dependence and non-Killing configurations (see [23–29]). In this paper the local coordinates and ansätze for d-metrics are parameterized in different forms than in previous works, what is more convenient for the study of cosmological models.

  6. In section III A of that work, a model with \(G(T)=0\) was investigated in detail. The conclusion was that in order to elaborate a realistic evolution it is necessary to consider nontrivial values for \(G(T)\). In nonholonomic variables, such term \(\widehat{\mathbf {G}}(\widehat{\mathbf {T}})\) allows to encode \(f(R)\) modified theories and related into certain off-diagonal configurations in GR, which simplifies the solution of the problem of matter instability (see Sect. 4.3).

  7. We use a system of notations different from that article; here, e.g., \(N\) in used for the N-connection and we work with nonholonomic geometric objects.

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Acknowledgments

This work has been partially supported by the Program IDEI, PN-II-ID-PCE-2011-3-0256, by an associated visiting research position at CERN, by MINECO (Spain), Grants PR2011-0128 and FIS2013-44881-P, by the CPAN Consolider Ingenio Project, and by AGAUR (Generalitat de Catalunya), contract 2009SGR-994. We thank S. Capozziello, S. D. Odintsov, S. Rajpoot, E. Saridakis, D. Singleton, and P. Stavrinos for important discussions and support.

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Authors and Affiliations

  1. Instituto de Ciencias del Espacio, Consejo Superior de Investigaciones Científicas, ICE-CSIC and IEEC, Campus UAB, Facultat de Ciències, Torre C5-Parell-2a planta, 08193, Bellaterra, Barcelona, Spain

    Emilio Elizalde

  2. Theory Division, CERN, 1211, Geneva 23, Switzerland

    Sergiu I. Vacaru

  3. Rector’s Department, Alexandru Ioan Cuza University, Alexandru Lapuşneanu Street, nr. 14, UAIC - Corpus R, Office 323, 700057, Iasi, Romania

    Sergiu I. Vacaru

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  1. Emilio Elizalde
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Correspondence to Sergiu I. Vacaru.

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Elizalde, E., Vacaru, S.I. Effective Einstein cosmological spaces for non-minimal modified gravity. Gen Relativ Gravit 47, 64 (2015). https://doi.org/10.1007/s10714-015-1905-5

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