We investigate the cosmological solutions of f (R, T ) modified theories of gravity for a perfect fluid in a spatially FLRW metric through the phase space analysis, where R is the Ricci scalar and T denotes the trace of the energy-momentum tensor of the matter content. We explore and analyze the three general theories with the Lagrangians of minimal g(R) + h(T ), pure non-minimal g(R)h(T ) and non-minimal g(R) (1 + h(T )) couplings through the dynamical systems approach. We introduce a few variables and dimensionless parameters to simplify the equations in more concise forms. The conservation of the energy-momentum tensor leads to a constraint equation that, in the minimal gravity, confines the functionality of h(T ) to a particular form, hence, relates the dynamical variables. In this case, the acceptable cosmological solutions that contain a long enough matter dominated era followed by a late-time accelerated expansion are found. To support the theoretical results, we also obtain the numerical solutions for a few functions of g(R), and the results of the corresponding models confirm the predictions. We classify the solutions into six classes which demonstrate more acceptable solutions and there is more freedom to have the matter dominated era than in the f (R) gravity. In particular, there is a new fixed point which can represent the late-time acceleration. We draw different diagrams of the matter densities (consistent with the present values), the related scale factors and the effective equation of state. The corresponding diagrams of the parameters illustrate that there is a saddle acceleration era which is a middle era before the final stable acceleration de Sitter era for some models. All presented diagrams determine radiation, matter and late-time acceleration eras very well. The pure non-minimal theory suffers from the absence of a standard matter era, though we illustrate that the non-minimal theory can have acceptable cosmological solutions.2 development of a general phenomenological framework, i.e. the PPN-formalism, determine that it is the best known metric theory of gravity [46].Among the extended theories of gravity, there are at least two main motivations 3 for employing the higher-order gravities, i.e., those in which the Einstein-Hilbert action is modified by higher-order curvature invariants with respect to the Ricci scalar. The first motivation has a theoretical background and is related to the non-renormalizability of GR [49,50] and to the fact that GR cannot be quantized conventionally. Regarding this issue, some authors have shown that the inclusion of higher-order terms can solve this problem [51,52]. The other motivation is related to the recently achieved data in astrophysics and cosmology. Two contemporary evidences, which are referred to as dark matter and dark energy, have challenged our knowledge about the universe and have accounted for the first signals of GR breakdown. It is also worth mentioning that the concordance or ΛCDM model [53], the simplest model which adequately fits the...

To find more deliberate f (R, T ) cosmological solutions, we proceed our previous paper further by studying some new aspects of the considered models via investigation of some new cosmological parameters/quantities to attain the most acceptable cosmological results. Our investigations are performed by applying the dynamical system approach. We obtain the cosmological parameters/quantities in terms of some defined dimensionless parameters that are used in constructing the dynamical equations of motion. The investigated parameters/quantities are the evolution of the Hubble parameter and its inverse, the "weight function", the ratio of the matter density to the dark energy density and its time variation, the deceleration, the jerk and the snap parameters, and the equation-of-state parameter of the dark energy. We numerically examine these quantities for two general models R + αR −n + √ −T and R log [αR] q + √ −T . All considered models have some inconsistent quantities (with respect to the available observational data), except the model with n = −0.9 which has more consistent quantities than the other ones. By considering the ratio of the matter density to the dark energy density, we find that the coincidence problem does not refer to a unique cosmological event, rather, this coincidence also occurred in the early universe. We also present the cosmological solutions for an interesting model R+c1 √ −T in the non-flat FLRW metric. We show that this model has an attractor solution for the late times, though with w (DE) = −1/2. This model indicates that the spatial curvature density parameter gets negligible values until the present era, in which it acquires the values of the order 10 −4 or 10 −3 . As the second part of this work, we consider the weak-field limit of f (R, T ) gravity models outside a spherical mass immersed in the cosmological fluid. We have found that the corresponding field equations depend on the both background values of the Ricci scalar and the background cosmological fluid density. As a result, we attain the parametrized post-Newtonian (PPN) parameter for f (R, T ) gravity and show that this theory can admit the experimentally acceptable values of this parameter. As a sample, we present the PPN gamma parameter for general minimal power law models, in particular, the model R + c1 √ −T .

We consider f (R, T ) modified theory of gravity, in which the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the energy-momentum tensor of the matter, in order to investigate the dark-matter effects on the galaxy scale. We obtain the metric components for a spherically symmetric and static spacetime in the vicinity of general relativity solutions. However, we concentrate on a specific model of the theory where the matter is minimally coupled to the geometry, and derive the metric components in the galactic halo. Then, we fix the components by the rotational velocities of the galaxies for the model, and show that the mass corresponding to the interaction term (which appears in the Einstein modified field equation) leads to a flat rotation curve in the halo of galaxies. In addition, for the proposed model, the light-deflection angle has been derived and drawn using some observed data.PACS numbers: 04.50. Kd; 95.35.+d; 98.35.Gi;

Within an algebraic framework, used to construct the induced-matter-theory (IMT) setting, in (D + 1)-dimensional Brans-Dicke (BD) scenario, we obtain a modified BD theory (MBDT) in D dimensions. Being more specific, from the (D + 1)-dimensional field equations, a D-dimensional BD theory, bearing new features, is extracted by means of a suitable dimensional reduction onto a hypersurface orthogonal to the extra dimension. In particular, the BD scalar field in such Ddimensional theory has a self-interacting potential, which can be suitably interpreted as produced by the extra dimension. Subsequently, as an application to cosmology, we consider an extended spatially flat FLRW geometry in a (D + 1)-dimensional space-time. After obtaining the power-law solutions in the bulk, we proceed to construct the corresponding physics, by means of the induced MBDT procedure, on the D-dimensional hypersurface. We then contrast the resulted solutions (for different phases of the universe) with those usually extracted from the conventional GR and BD theories in view of current ranges for cosmological parameters. We show that the induced perfect fluid background and the induced scalar potential can be employed, within some limits, for describing different epochs of the universe. Finally, we comment on the observational viability of such a model.

An almost brief, though lengthy, review introduction about the long history of higher order gravities and their applications, as employed in the literature, is provided. We review the analogous procedure between higher order gravities and GR, as described in our previous works, in order to highlight its important achievements. Amongst which are presentation of an easy classification of higher order Lagrangians and its employment as a criteria in order to distinguish correct metric theories of gravity. For example, it does not permit the inclusion of only one of the second order Lagrangians in isolation. But, it does allow the inclusion of the cosmological term. We also discuss on the compatibility of our procedure and the Mach idea. We derive a dimensional dependent version of Duff's trace anomaly relation, which in four -dimension is the same as the usual Duff relation. The Lanczos Lagrangian satisfies this new constraint in any dimension. The square of the Weyl tensor identically satisfies it independent of dimension, however, this Lagrangian satisfies the previous relation only in three and four dimensions.