Exact Cosmological Solutions of f(R)f(R) Theories via Hojman Symmetry

Nowadays, $f(R)$ theory has been one of the leading modified gravity theories to explain the current accelerated expansion of the universe, without invoking dark energy. It is of interest to find the exact cosmological solutions of $f(R)$ theories. Besides other methods, symmetry has been proved as a powerful tool to find exact solutions. On the other hand, symmetry might hint the deep physical structure of a theory, and hence considering symmetry is also well motivated. As is well known, Noether symmetry has been extensively used in physics. Recently, the so-called Hojman symmetry was also considered in the literature. Hojman symmetry directly deals with the equations of motion, rather than Lagrangian or Hamiltonian, unlike Noether symmetry. In this work, we consider Hojman symmetry in $f(R)$ theories in both the metric and Palatini formalisms, and find the corresponding exact cosmological solutions of $f(R)$ theories via Hojman symmetry. There exist some new solutions significantly different from the ones obtained by using Noether symmetry in $f(R)$ theories. To our knowledge, they also have not been found previously in the literature. This work confirms that Hojman symmetry can bring new features to cosmology and gravity theories.Comment: 16 pages, revtex4; v2: discussions added, Nucl. Phys. B in press; v3: published version. arXiv admin note: text overlap with arXiv:1505.0754

Reentrant phase transitions and triple points of topological AdS black holes in Born-Infeld-massive gravity

Motivated by recent developments of black hole thermodynamics in de Rham, Gabadadze and Tolley(dRGT) massive gravity, we study the critical behaviors of four-dimensional topological Anti-de Sitter(AdS) black holes in the presence of Born-Infeld nonlinear electrodynamics by treating the cosmological constant as pressure and the corresponding conjugate quantity is interpreted as thermodynamic volume. It shows that besides the Van der Waals-like SBH/LBH phase transitions appears, the so-called reentrant phase transitions (RPTs) are also observed when the coupling coefficients $c_i m^2$ of massive potential and Born-Infeld parameter $b$ satisfy some certain conditions.Comment: arXiv admin note: text overlap with arXiv:1612.08056; text overlap with arXiv:1402.2837, arXiv:1306.5756 by other autho