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.
