Odintsov, Sergei D.; Sáez-Gómez, Diego \(f(R, T, R_{\mu \nu} T^{\mu \nu})\) gravity phenomenology and \(\lambda\)CDM universe. (English) Zbl 1364.83039 Phys. Lett., B 725, No. 4-5, 437-444 (2013). Summary: We propose general \(f(R, T, R_{\mu \nu} T^{\mu \nu})\) theory as generalization of covariant Hořava-like gravity with dynamical Lorentz symmetry breaking. FRLW cosmological dynamics for several versions of such theory is considered. The reconstruction of the above action is explicitly done, including the numerical reconstruction for the occurrence of \(\Lambda\)CDM universe. De Sitter universe solutions in the presence of non-constant fluid are also presented. The problem of matter instability in \(f(R, T, R_{\mu \nu} T^{\mu \nu})\) gravity is discussed. Cited in 30 Documents MSC: 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories 83F05 Relativistic cosmology PDFBibTeX XMLCite \textit{S. D. Odintsov} and \textit{D. Sáez-Gómez}, Phys. Lett., B 725, No. 4--5, 437--444 (2013; Zbl 1364.83039) Full Text: DOI arXiv References: [1] Myrzakulov, R.; Sebastiani, L.; Zerbini, S. [2] Elizalde, E.; Sáez-Gómez, D., Phys. Rev. D, 80, 044030 (2009) [3] Dunsby, P. K.S.; Elizalde, E.; Goswami, R.; Odintsov, S.; Sáez-Gómez, D., Phys. Rev. D, 82, 023519 (2010) [4] Nojiri, S.; Odintsov, S. D., Phys. Rev. D, 68, 123512 (2003) [5] Bamba, K.; Geng, C.-Q.; Lee, C.-C., JCAP, 1011, 001 (2010) [6] Faraoni, V., Phys. Rev. D, 74, 104017 (2006) [7] Appleby, S. A.; Battye, R. A.; Starobinsky, A. A., JCAP, 1006, 005 (2010) [8] Sáez-Gómez, D., Class. Quantum Grav., 30, 095008 (2013) · Zbl 1269.83072 [9] de la Cruz-Dombriz, A.; Sáez-Gómez, D., Class. Quant. Grav., 29, 245014 (2012) · Zbl 1260.83026 [10] Harko, T.; Lobo, F. S.N.; Nojiri, S.; Odintsov, S. D., Phys. Rev. D, 84, 024020 (2011) [11] Shabani, H.; Farhoudi, M. [12] Alvarenga, F. G.; de la Cruz-Dombriz, A.; Houndjo, M. J.S.; Rodrigues, M. E.; Sáez-Gómez, D. [13] Haghani, Z.; Harko, T.; Lobo, F. S.N.; Sepangi, H. R.; Shahidi, S. [14] Nojiri, S.; Odintsov, S. D., Phys. Rev. D, 83, 023001 (2011) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.