Exact cosmological solutions for MOG

We find some new exact cosmological solutions for the covariant scalar-tensor-vector gravity theory, the so-called MOdified Gravity (MOG). The exact solution of the vacuum field equations has been derived. Also, for non vacuum cases we have found some exact solutions with the aid of the Noether symmetry approach. More specifically, the symmetry vector and also the Noether conserved quantity associated to the point-like Lagrangian of the theory have been found. Also we find the exact form of the generic vector field potential of this theory by considering the behavior of the relevant point-like Lagrangian under the infinitesimal generator of the Noether symmetry. Finally, we discuss the cosmological implications of the solutions.Comment: 8 pages, to appear in European Physical Journal

Jeans analysis in modified gravity

MOdified Gravity (MOG) is a covariant modification of Einstein's general relativity. This theory is one of the current alternatives to dark matter models. We describe dynamics of collisionless self-gravitating systems in the context of MOG. By studying the weak field approximation of this theory, we derive the equations governing the dynamics of the self-gravitating systems. More specifically, we consider the Jeans instability for self-gravitating fluid and stellar systems, and derive new Jeans mass limit $\tilde{M}_J$ and wave-number $\tilde{k}_J$. Furthermore, considering the gravitational instability in star forming regions, we show that MOG has not a significant difference with general relativity on this astrophysical scale. However, at larger scales such as intergalactic space MOG may lead to different galaxy and structure formation processes

The phase space analysis of modified gravity (MOG)

We investigate the cosmological consequences of a scalar-vector-tensor theory of gravity known as MOG. In MOG, in addition to metric tensor, there are two scalar fields $G(x)$ and $\mu(x)$, and one vector field $\phi_{\alpha}(x)$. Using the phase space analysis, we explore the cosmological consequences of a model of MOG and find some new interesting features which are absent in $\Lambda$CDM model. More specifically we study the possibility that if the extra fields of this theory behave like dark energy to explain the cosmic speedup. More interestingly, with or without cosmological constant, strongly phantom crossing happens. Also we find that this theory in its original form ($\Lambda\neq 0$), possesses a true sequence of cosmological epochs. Albeit we show that, surprisingly, there are two radiation dominated epochs $f_5$ and $f_6$, two matter dominated phases $f_3$ and $f_4$, and two late time accelerated eras $f_{12}$ and $f_{7}$. Depending on the initial conditions the universe will realize only three of these six eras. However, the matter dominated phases are dramatically different from the standard matter dominated epoch. In these phases the cosmic scale factor grows as $a(t)\sim t^{0.46}$ and $t^{0.52}$, respectively, which are slower than the standard case, i.e. $a(t)\sim t^{2/3}$. Considering these results we discuss the cosmological viability of MOG.Comment: To appear in EPJ

Exact cosmological solutions from Hojman conservation quantities

We present a new approach to find exact solutions for cosmological models. By requiring the existence of a symmetry transformation vector for the equations of motion of the given cosmological model (without using either Lagrangian or Hamiltonian), one can find corresponding Hojman conserved quantities. With the help of these conserved quantities, the analysis of the cosmological model can be simplified. In the case of quintessence scalar-tensor models, we show that the Hojman conserved quantities exist for a wide range of V(\phi)-potentials and allow to find exact solutions for the cosmic scale factor and the scalar field. Finally, we investigate the general cosmological behavior of solutions by adopting a phase-space view.Comment: 11 pages, 13 figures, accepted for publication in Phys. Lett.