In this paper we consider the equation of motion for

\r\nthe F (R, T) gravity on their property of conformal invariance. It

\r\nis shown that in the general case, such a theory is not conformal

\r\ninvariant. Studied special cases for the functions v and u in which

\r\ncan appear properties of the theory. Also we consider cosmological

\r\naspects F (R, T) theory of gravity, having considered particular case

\r\nF (R, T) = μR+νT^2. Showed that in this case there is a nonlinear

\r\ndependence of the parameter equation of state from time to time,

\r\nwhich affects its evolution.<\/p>\r\n","references":"[1] Perlmuter S. et al. Measurements of \u03a9 and \u039b from 42 High-Redshift\r\nSupernovae. The Astrophysical Journal, 1999, 57(2), p. 565.\r\n[2] Riess A. G. et al. Supernova Search Team Collaboration: Observational\r\nEvidence from Supernovae for an Accelerating Universe and a Cosmological\r\nConstant. The Astronomical Journal, 1998, 116(3), p.1009.\r\n[3] Tegmark M. et al. Cosmological parameters from SDSS and WMAP.\r\nPhysical Review D, 2004, 69, 103501.\r\n[4] Eisenstein D. J. et. al. Detection of the Baryon Acoustic Peak in the\r\nLarge-Scale Correlation Function of SDSS Luminous Red Galaxies. The\r\nAstrophysics Journal, 2005, 633(2), p.560.\r\n[5] Komatsu E. et. al. Seven-Year Wilkinson Microwave Anisotropy\r\nProbe (WMAP) Observations: Cosmological Interpretation. Astrophysical\r\nJournal Supplement Series, 2011, 192(2), 47 pp.\r\n[6] Jain B., Taylor A. Cross-correlation Tomography: Measuring Dark\r\nEnergy Evolution with Weak Lensing. Physical Review Letters, 2003,\r\n91, 141302.\r\n[7] Armendariz-Picon C., Damour T., Mukhanov V. k-Inflation. Physics\r\nLetters B, 458(2\u20133), p.209. [8] Starobinsky A.A. A new type of isotropic cosmological models without\r\nsingularity. Physics Letters B, 91(1), p.99.\r\n[9] Myrzakulov R. Reconstruction of f(T) and f(R) gravity according\r\nto (m, n)-type holographic dark energy. Canadian Journal of Physics,\r\n91(9), p.703.\r\n[10] Maldacena J.M. Gravity, Particle Physics and Their Unification. International\r\nJournal of Modern Physics A, 15(1b), p. 840.\r\n[11] Bamba K., Odintsov S.D., Saez-Gomez D. Conformal symmetry and\r\naccelerating cosmology in teleparallel gravity. Physical Review D, 88,\r\n084042.\r\n[12] Duff M.J. Twenty years of the Weyl anomaly. Classical and quantum\r\ngravity, 11(6), p.1387.\r\n[13] Bars I., Steinhard P.J., Turok N. Cyclic Cosmology, Conformal Symmetry\r\nand the Metastability of the Higgs. arxiv: 1307.8106.\r\n[14] Myrzakulov R. FRW cosmology in F (R, T) gravity. The European\r\nPhysical Journal C, 72, p.2203.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 98, 2015"}