Abstract. We consider the cosmological consequences of a special scalar-tensor-vector theory of gravity, known as MOG (for MOdified Gravity), proposed to address the dark matter problem. This theory introduces two scalar fields G(x) and µ(x), and one vector field φ α (x), in addition to the metric tensor. We set the corresponding self-interaction potentials to zero, as in the standard form of MOG. Then using the phase space analysis in the flat Friedmann-Robertson-Walker background, we show that the theory possesses a viable sequence of cosmological epochs with acceptable time dependency for the cosmic scale factor. We also investigate MOG's potential as a dark energy model and show that extra fields in MOG cannot provide a late time accelerated expansion. Furthermore, using a dynamical system approach to solve the non-linear field equations numerically, we calculate the angular size of the sound horizon, i.e. θ s , in MOG. We find that 8 × 10 −3 rad < θ s < 8.2 × 10 −3 rad which is way outside the current observational bounds. Finally, we generalize MOG to a modified form called mMOG, and we find that mMOG passes the sound-horizon constraint. However, mMOG also cannot be considered as a dark energy model un;ess one adds a cosmological constant, and more importantly, the matter dominated era is still slightly different from the standard case.

We investigate the cosmological consequences of a scalar-vector-tensor theory of gravity known as modified gravity (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 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, a strongly phantom crossing occurs. Also we find that this theory in its original form ( = 0) possesses a true sequence of cosmological epochs. However, 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) ∼ t 0.46 and t 0.52 , respectively, which are slower than the standard case, i.e. a(t) ∼ t 2/3 . Considering these results we discuss the cosmological viability of MOG.

We investigate the impacts of interaction between dark matter and dark energy in the context of two dark energy models, holographic and ghost dark energy. In fact, using the dynamical system analysis, we obtain the cosmological consequence of several interactions, considering all relevant component of universe, i.e. matter (Dark and luminous), radiation and dark energy. Studying the phase space for all interactions in detail, we show the existence of unstable matter dominated and stable dark energy dominated phases. We also show that linear interactions suffer from the absence of standard radiation dominated epoch. Interestingly, this failure resolved by adding the non-linear interactions to the models. We find an upper bound for the value of the coupling constant of the interaction between dark matter and dark energy as b < 0.57 in the case of holographic model, and b < 0.61 in the case of ghost dark energy model, to result in a cosmological viable matter dominated epoch. More specifically, this bound is vital to satisfy instability and deceleration of matter dominated epoch.

We investigate the cosmological perturbations in the context of a Scalar-Tensor-Vector theory of Gravity known as MOG in the literature. Although MOG is plagued by ghosts, it does not suffer from tachyonic instability. Therefore it can be considered as a valid theory, at least in the classical limit. In the weak field limit, MOG increases the strength of gravity, and consequently addresses some astrophysical tests, without invoking dark matter particles. Recent investigations show that MOG reproduces a viable background cosmological evolution comparable to ΛCDM. However, the matter dominated era is slightly faster in MOG compared to ΛCDM. In this paper, in order to clarify whether this evolution is compatible with observations, we study the linear matter perturbations and estimate the relevant modified gravity parameters. In contrast to some current claims in the relevant literature, we show that MOG reduces the growth rate of the perturbations. We then compare MOG to the redshift space distortion (RSD) data. We find that MOG yields a much higher value than ΛCDM for the power spectrum parameter σ 8 . Although MOG cannot yet be ruled out by RSD data alone, the low growth and high σ 8 constitute a powerful challenge to the cosmological viability of MOG.