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**In the following you could see my recent papers:**

In this paper we derive the post-Newtonian equations of the ideal Magnetohydrodynamics. To do so we use the modern approach to the post-Newtonian theory, where the harmonic gauge is used instead of the standard post-Newtonian gauge, and find the post-Newtonian metric in the presence of the electromagnetic fields. We show that although the electric field does not contribute in the metric (and equivalently in the curvature) of the spacetime, the magnetic field appears in the time-time component of the metric. Appearance of the magnetic field in the time-time component of the metric, in principle, leads to new relativistic contributions to the magnetohydrodynamic governing equations. Therefore, using the post-Newtonian metric, we find the relativistic corrections to the magnetohydrodynamic equations up to the first post-Newtonian order. In addition, as a usage of this derivation, we obtain a complete set of equations by which the behavior of the self-gravitating plasma can be determined in the post-Newtonian gravity.

We find the generalized version of the Toomre’s criterion for the stability of a rotating thin disk in the context of Eddington inspired Born-Infeld (EiBI) gravity which possesses one free parameter χχ. To do so we use the weak field limit of the theory and find the dispersion relation for the propagation of matter density waves on the surface of a self-gravitating and differentially rotating disk. Finally we find a new version of Toomre’s stability criterion for thin disks. We show that EiBI gravity with negative χχ destabilizes all the rotating thin disks. On the other hand EiBI with positive χχ substantially can suppress the local fragmentation, and has stabilizing effects against axi-symmetric perturbations. More specifically, we show that only an annulus remains unstable on the surface of the disk. The width of the annulus directly depends on the magnitude of χχ.

A simple generalization to Einstein’s general relativity (GR) was recently proposed which allows a correction term TαβTαβ in the action functional of the theory. This theory is called energy-momentum squared gravity (EMSG) and introduces a new coupling parameter η. EMSG resolves the big bang singularity and has a viable sequence of cosmological epochs in its thermal history. Interestingly, in the vacuum EMSG is equivalent to GR, and its effects appear only inside the matter-energy distribution. More specifically, its consequences appear in high curvature regime. Therefore it is natural to expect deviations form GR inside compact stars. In order to study spherically symmetric compact stars in EMSG, we find the relativistic governing equations. More specifically, we find the generalized version of the Tolman-Oppenheimer-Volkov equation in EMSG. Finally we present two analytical solutions, and two numerical solutions for the field equations. For obtaining the numerical solutions we use polytropic equation of state which is widely used to understand the internal structure of neutron stars in the literature. Eventually we find a mass-radius relation for neutron stars. Also, we found that EMSG, depending on the central pressure of the star and the magnitude of free parameter η, can lead to larger or smaller masses for neutron stars compared with GR. Existence of high-mass neutron stars with ordinary polytropic equation of state in EMSG is important in the sense that these stars exist in GR when equation of state is more complicated.

We study the stellar bar growth in high-resolution numerical galaxy models with and without dark matter halos. In all models, the galactic disk is exponential, and the halos are rigid or live Plummer spheres. More specifically, when there is no dark matter halo, we modify the gravitational force between point particles. To do so, we use the weak field limit of an alternative theory of dark matter known as MOG in the literature. The galaxy model in MOG has the same initial conditions as galaxy models with a dark matter halo. On the other hand, the initial random velocities and Toomre’s local stability parameter are the same for all of the models. We show that the evolution and growth of the bar in MOG is substantially different from the standard cases including dark matter halo. More importantly, we find that the bar growth rate and its final magnitude are smaller in MOG. On the other hand, the maximum value of the bar in MOG is smaller than that in the Newtonian models. It is shown that although the live dark matter halo may support bar instability, MOG has stabilizing effects. Furthermore, we show that MOG supports fast pattern speeds, and unlike in the dark matter halo models, the pattern speed does not decrease with time. These differences, combined with the relevant observations, may help to distinguish between dark matter and modified gravity in galactic scales.

https://doi.org/10.1093/mnras/stx3353

Recent observations of the filamentary molecular clouds show that their properties deviate from the isothermal equation of state. Theoretical investigations proposed that the logatropic and the polytropic equations of state with negative indexes can provide a better description for these filamentary structures. Here, we aim to compare the effects of these softer non-isothermal equation of states with their isothermal counterpart on the global gravitational instability of a filamentary molecular cloud. By incorporating the ambipolar diffusion, we use the non-ideal magnetohydrodynamics framework for a filament that is threaded by a uniform axial magnetic field. We perturb the fluid and obtain the dispersion relation both for the logatropic and polytropic equations of state by taking the effects of magnetic field and ambipolar diffusion into account. Our results suggest that, in absence of the magnetic field, a softer equation of state makes the system more prone to gravitational instability. We also observed that a moderate magnetic field is able to enhance the stability of the filament in a way that is sensitive to the equation of state in general. However, when the magnetic field is strong, this effect is suppressed and all the equations of state have almost the same stability properties. Moreover, we find that for all the considered equations of state, the ambipolar diffusion has destabilizing effects on the filament.

**Abstract **(arXiv)

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 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. θs, in MOG. We find that 8× 10−3rad<θs<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 unless one adds a cosmological constant, and more importantly, the matter dominated era is still slightly different from the standard case.

https://doi.org/10.1093/mnras/stw2820

The gravitational instability of a filamentary molecular cloud in non-ideal magnetohydrodynamics is investigated. The filament is assumed to be in hydrostatic equilibrium. We add the effect of ambipolar diffusion to the filament which is threaded by an initial uniform axial magnetic field along its axis. We write down the fluid equations in cylindrical coordinates and perform linear perturbation analysis. We integrate the resultant differential equations and then derive the numerical dispersion relation. We find that, a more efficient ambipolar diffusion leads to an enhancement of the growth of the most unstable mode, and to increase of the fragmentation scale of the filament.

**Abstract **(IOP)

The Jeans analysis is studied in the first post-Newtonian limit. In other words, the relativistic effects on local gravitational instability are considered for systems whose characteristic velocities and corresponding gravitational fields are higher than those permitted in the Newtonian limit. The dispersion relation for the propagation of small perturbations is found in the post-Newtonian approximation using two different techniques. A new Jeans mass is derived and compared to the standard Jeans mass. In this limit, the relativistic effects make the new Jeans mass smaller than the Newtonian Jeans mass. Furthermore, the fractional difference between these two masses increases when the temperature/pressure of the system increases. Interestingly, in this limit, pressure can enhance gravitational instability instead of preventing it. Finally, the results are applied to high-temperature astrophysical systems, and the possibility of local fragmentation in some relativistic systems is investigated.

Mon.Not.Roy.Astron.Soc. 468 (2017) no.4, 4450-4464

**Abstract **(Oxford University Press)

Using N-body simulations, we study the global stability of a self-gravitating disc in the context of modified gravity (MOG). This theory is a relativistic scalar–tensor–vector theory of gravity and it is presented to address the dark matter problem. In the weak field limit, MOG possesses two free parameters α and μ_0, which have already been determined using the rotation curve data of spiral galaxies. The evolution of a stellar self-gravitating disc and, more specifically, the bar instability in MOG are investigated and compared to a Newtonian case. Our models have exponential and Mestel-like surface densities as Σ ∝ exp (−r/h) and Σ ∝ 1/r. It is found that, surprisingly, the discs are more stable against the bar mode in MOG than in Newtonian gravity. In other words, the bar growth rate is effectively slower than the Newtonian discs. Also, we show that both free parameters (i.e. α and μ_0) have stabilizing effects. In other words, an increase in these parameters will decrease the bar growth rate.

**Abstract **(IOP)

We study the global gravitational stability of a gaseous self-gravitating Maclaurin disk in the absence of a halo. Further, we replace Newtonian gravity with the specific modified gravity theory known as MOG in the relevant literature. MOG is an alternative theory for addressing the dark matter problem without invoking exotic dark matter particles, and it possesses two free parameters α and μ (0) in the weak field limit. We derive the equilibrium gravitational potential of the Maclaurin disk in MOG and develop a semianalytic method for studying the response of the disk to linear nonaxisymmetric perturbations. The eigenvalue spectrum of the normal modes of the disk is obtained, and its physical meaning has been explored. We show that Maclaurin disks are less stable in MOG than in Newtonian gravity. In fact, both parameters (α, μ (0)) have destabilizing effects on the disk. Interestingly, μ (0) excites only the bar mode m = 2, while α affects all of the modes. More specifically, when α > 1, the bar mode is strongly unstable and unlike in Newtonian gravity cannot be avoided, at least in the weak field limit, with increasing the pressure support of the disk.

**Abstract **(Springer)

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)μ(x) , and one vector field ϕα(x)ϕα(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 ΛΛ 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 ( Λ≠0Λ≠0 ) possesses a true sequence of cosmological epochs. However, we show that, surprisingly, there are two radiation-dominated epochs, f5f5 and f6f6 , two matter-dominated phases, f3f3 and f4f4 , and two late time accelerated eras, f12f12 and f7f7 . 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)∼t0.46a(t)∼t0.46 and t0.52t0.52 , respectively, which are slower than the standard case, i.e. a(t)∼t2/3a(t)∼t2/3 . Considering these results we discuss the cosmological viability of MOG.

**Abstract **(APS)

A new covariant generalization of Einstein’s general relativity is developed which allows the existence of a term proportional to TαβTαβ in the action functional of the theory (Tαβ is the energy-momentum tensor). Consequently, the relevant field equations are different from general relativity only in the presence of matter sources. In the case of a charged black hole, we find exact solutions for the field equations. Applying this theory to a homogeneous and isotropic spacetime, we find that there is a maximum energy density ρmax, and correspondingly a minimum length amin, at the early Universe. This means that there is a bounce at early times, and this theory avoids the existence of an early-time singularity. Moreover, we show that this theory possesses a true sequence of cosmological eras. We also argue that, although in the context of the standard cosmological model the cosmological constant Λ does not play any important role in the early times and becomes important only after the matter-dominated era, in this theory the “repulsive” nature of the cosmological constant plays a crucial role at early times in resolving the singularity.

**Abstract **(Springer)

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.

Astrophys.Space Sci. 358 (2015) no.1, 11

**Abstract **(Springer)

In the framework of metric f(R)f(R) gravity, we find the dispersion relation for the propagation of tightly wound spiral density waves in the surface of rotating, self-gravitating disks. Also, new Toomre-like stability criteria for differentially rotating disks has been derived for both fluid and stellar disks.

**Abstract **(IOP)

We find the dispersion relation for tightly wound spiral density waves in the surface of rotating, self-gravitating disks in the framework of Modified Gravity (MOG). Also, the Toomre-like stability criterion for differentially rotating disks has been derived for both fluid and stellar disks. More specifically, the stability criterion can be expressed in terms of a matter density threshold over which the instability occurs. In other words the local stability criterion can be written as Σ0<Σcrit(vs,κ,α,μ0)Σ0<Σcrit(vs,κ,α,μ0), where ΣcritΣcrit is a function of vs (sound speed), κ (epicycle frequency) and α and μ0μ0 are the free parameters of the theory. In the case of a stellar disk the radial velocity dispersion σrσr appears in ΣcritΣcrit instead of vs. We find the exact form of the function ΣcritΣcrit for both stellar and fluid self-gravitating disks. Also, we use a sub-sample of THINGS catalog of spiral galaxies in order to compare the local stability criteria. In this perspective, we have compared MOG with Newtonian gravity and investigated the possible and detectable differences between these theories.

**Abstract **(APS)

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 the 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 M˜J and wave-number 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.

**Abstract **(arXiv)

We study local stability of self-gravitating fluid and stellar disk in the context of modified gravity theories which predict a Yukawa-like term in the gravitational potential of a point mass. We investigate the effect of such a Yukawa-like term on the dynamics of self-gravitating disks. More specifically, we investigate the consequences of the presence of this term for the local stability of the self-gravitating disks. In fact, we derive a generalized version of Toomre’s local stability criterion for diferentially rotating disks. This criterion is complicated than the original one in the sense that it depends on the physical properties of the disk. In the case of MOdified Gravity theory (MOG), we use the current confirmed values for the free parameters of this theory, to write the generalized Toomre’s criterion in a more familiar way comparable with the Toomre’s criterion. This generalized Toomre’s criterion may be used to study the global stability of stellar and fluid disks using computer simulations.

**Abstract **(Elsevier)

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(ϕ) -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.

Conference: C12-07-01.1, p.963-966 Proceedings

**Abstract **(World Scientific)

We estimate virial masses of galaxy clusters using the parametrized post-Newtonian (PPN) virial theorem. Also, we show explicitly that post-Newtonian corrections can not address the mass discrepancy in the galaxy clusters.

**Abstract **(arXiv)

**Abstract **(arXiv)

We consider the Post-Newtonian limit of massive Brans-Dicke theory and we make some notes about the Post-Newtonian limit of the case ω=0ω=0. This case is dynamically equivalent to the metric f(R)f(R) theory. It is known that this theory can be compatible with the solar system tests if Chameleon mechanism occurs. Also, it is known that this mechanism is because of the non-linearity in the field equations produced by the largeness of the local curvature relative to the background curvature. Thus, the linearization of the field equations breaks down. On the other hand we know that Chameleon mechanism exists when a coupling between the matter and the scalar field exists. In the Jordan frame of Brans-Dicke theory, we have not such a coupling. But in the Einstein frame this theory behaves like a Chameleon scalar field. By confining ourselves to the case ω=0ω=0, we show that ‘Chameleon-like’ behavior can exist also in the Jordan frame but it has an important difference compared with the Chameleon mechanism. Also we show that the conditions which lead to the existence of ‘Chameleon-like’ mechanism are consistent with the conditions in the Post-Newtonian limit which correspond to a heavy scalar filed at the cosmological scale and a small effective cosmological constant. Thus, one can linearize field equations to the Post-Newtonian order and this linearization has not any contradiction with the existence of ‘Chameleon-like’ behavior.

**Abstract **(arXiv)

We consider the Post-Newtonian limit of massive Brans-Dicke theory and we make some notes about the Post-Newtonian limit of the case ω=0ω=0. This case is dynamically equivalent to the metric f(R)f(R) theory. It is known that this theory can be compatible with the solar system tests if Chameleon mechanism occurs. Also, it is known that this mechanism is because of the non-linearity in the field equations produced by the largeness of the local curvature relative to the background curvature. Thus, the linearization of the field equations breaks down. On the other hand we know that Chameleon mechanism exists when a coupling between the matter and the scalar field exists. In the Jordan frame of Brans-Dicke theory, we have not such a coupling. But in the Einstein frame this theory behaves like a Chameleon scalar field. By confining ourselves to the case ω=0ω=0, we show that ‘Chameleon-like’ behavior can exist also in the Jordan frame but it has an important difference compared with the Chameleon mechanism. Also we show that the conditions which lead to the existence of ‘Chameleon-like’ mechanism are consistent with the conditions in the Post-Newtonian limit which correspond to a heavy scalar filed at the cosmological scale and a small effective cosmological constant. Thus, one can linearize field equations to the Post-Newtonian order and this linearization has not any contradiction with the existence of ‘Chameleon-like’ behavior.

**Abstract **(arXiv)

We consider Brans-Dicke (BD) scalar tensor theory in the conformally transformed Einstein frame. In this frame BD theory behaves like an interacting quintessence model. We find the necessary conditions on the form of the potential V(φ)V(φ) in order to have thawing behavior. Finally, by setting the BD coupling constant ω=0ω=0, the metric f(R)f(R) gravity has been considered in the Einstein frame. Assuming the existence of thawing solution, some necessary conditions for f(R)f(R) gravity models have been derived.

**Abstract **(arXiv)

Metric f(R)f(R) gravity theories are conformally equivalent to models of quintessence in which matter is coupled to dark energy. We derive a condition for stable tracker solution for metric f(R)f(R) gravity in the Einstein frame. We find that tracker solutions with −0.361<ωφ<1−0.361<ωφ<1 exist if 0<Γ<0.2170<Γ<0.217 and ddtlnf′(R~)>0ddtlnf′(R~)>0, where Γ=VφφVV2φΓ=VφφVVφ2 is dimensionless function, ωφωφ is the equation of state parameter of the scalar field and R~R~ refers to Jordan frame’s curvature scalar. Also, we show that there exists f(R~)f(R~) gravity models which have tracking behavior in the Einstein frame and so the curvature of space time is decreasing with time while they lead to the solutions in the Jordan frame that the curvature of space time can be increasing with time.

**Abstract **(Elsevier)

We consider scalar–tensor theory for describing varying speed of light in a spatially flat FRW space–time. We find some exact solutions in the metric and Palatini formalisms. Also we examine the dynamics of this theory by dynamical system method assuming a ΛCDM background and we find some exact solutions by considering the character of critical points of the theory in both formalisms. We show that for any attractor the form of non-minimal coupling coefficient is quadratic in terms of the scalar field Ψ . Also we show that only attractors of the de Sitter era satisfy the horizon criteria

**Abstract **(Elsevier)

We study Palatini f(R) cosmology using Noether symmetry approach for the matter-dominated universe. In order to construct a point-like Lagrangian in the flat FRW space–time, we use the dynamical equivalence between f(R) gravity and scalar–tensor theories. The existence of Noether symmetry of the cosmological f(R) Lagrangian helps us to find out the form of f(R) and the exact solutions for cosmic scale factor. We show that this symmetry always exist for f(R)∼Rn and the Noether constant is a function of the Newton’s gravitational constant and the current matter content of the universe.

Phys.Lett. B666 (2008) 10-15

**Abstract **(Elsevier)

We discuss scalar–tensor cosmology with an extra R−1 correction by the Noether symmetry approach. The existence of such a symmetry selects the forms of the coupling ω(φ) , of the potential V(φ) and allows to obtain physically interesting exact cosmological solutions.

**Abstract **(APS)

We derive the equations of motion of an electrically neutral test particle for modified gravity theories for which the covariant divergence of the ordinary matter energy-momentum tensor does not vanish (i.e., ∇μTμν≠0). In fact, we generalize the Mathisson-Papapetrou equations by deriving a general form for the equations of motion of a test particle. Furthermore, using the generalized Mathisson-Papapetrou equations, we investigate the equations of motion of a pole-dipole (spinning) particle in the context of modified gravity.