**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32870

##### Conformal Invariance in F (R, T) Gravity

**Authors:**
Pyotr Tsyba,
Olga Razina,
Ertan Güdekli,
Ratbay Myrzakulov

**Abstract:**

In this paper we consider the equation of motion for the F (R, T) gravity on their property of conformal invariance. It is shown that in the general case, such a theory is not conformal invariant. Studied special cases for the functions v and u in which can appear properties of the theory. Also we consider cosmological aspects F (R, T) theory of gravity, having considered particular case F (R, T) = μR+νT^2. Showed that in this case there is a nonlinear dependence of the parameter equation of state from time to time, which affects its evolution.

**Keywords:**
Conformally invariance,
F (R,
T) gravity,
metric
FRW,
equation of motion,
dark energy.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1338214

**References:**

[1] Perlmuter S. et al. Measurements of Ω and Λ from 42 High-Redshift Supernovae. The Astrophysical Journal, 1999, 57(2), p. 565.

[2] Riess A. G. et al. Supernova Search Team Collaboration: Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant. The Astronomical Journal, 1998, 116(3), p.1009.

[3] Tegmark M. et al. Cosmological parameters from SDSS and WMAP. Physical Review D, 2004, 69, 103501.

[4] Eisenstein D. J. et. al. Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies. The Astrophysics Journal, 2005, 633(2), p.560.

[5] Komatsu E. et. al. Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation. Astrophysical Journal Supplement Series, 2011, 192(2), 47 pp.

[6] Jain B., Taylor A. Cross-correlation Tomography: Measuring Dark Energy Evolution with Weak Lensing. Physical Review Letters, 2003, 91, 141302.

[7] Armendariz-Picon C., Damour T., Mukhanov V. k-Inflation. Physics Letters B, 458(2–3), p.209.

[8] Starobinsky A.A. A new type of isotropic cosmological models without singularity. Physics Letters B, 91(1), p.99.

[9] Myrzakulov R. Reconstruction of f(T) and f(R) gravity according to (m, n)-type holographic dark energy. Canadian Journal of Physics, 91(9), p.703.

[10] Maldacena J.M. Gravity, Particle Physics and Their Unification. International Journal of Modern Physics A, 15(1b), p. 840.

[11] Bamba K., Odintsov S.D., Saez-Gomez D. Conformal symmetry and accelerating cosmology in teleparallel gravity. Physical Review D, 88, 084042.

[12] Duff M.J. Twenty years of the Weyl anomaly. Classical and quantum gravity, 11(6), p.1387.

[13] Bars I., Steinhard P.J., Turok N. Cyclic Cosmology, Conformal Symmetry and the Metastability of the Higgs. arxiv: 1307.8106.

[14] Myrzakulov R. FRW cosmology in F (R, T) gravity. The European Physical Journal C, 72, p.2203.