The phase space analysis of modified gravity (MOG)

Abstract

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 $μ(x)$, and one vector field $ϕ_α(x)$. 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 $Λ$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 ($Λ\neq 0$), 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.