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.

Recently, it has been shown that a four-dimensional (4D) Brans-Dicke (BD) theory with an effective matter field and a self interacting potential can be achieved from the vacuum 5D BD field equations, where we refer to as a modified Brans-Dicke theory (MBDT). We investigate a generalized Bianchi type I anisotropic cosmology in 5D BD theory, and by employing the obtained formalism, we derive the induced-matter on any 4D hypersurface in the context of the MBDT. We illustrate that if the usual spatial scale factors are functions of the time while the scale factor of extra dimension is constant, and the scalar field depends on the time and the fifth coordinate, then in general, one will encounter inconsistencies in the field equations. Then, we assume the scale factors and the scalar field depend on the time and the extra coordinate as separated variables in the power-law forms. Hence, we find a few classes of solutions in 5D space-time through which, we probe the one which leads to a generalized Kasner relations among the Kasner parameters. The induced scalar potential is found to be in the power-law or in the logarithmic form, however, for a constant scaler field and even when the scalar field only depends on the fifth coordinate, it vanishes. The conservation law is indeed valid in this MBDT approach for the derived induced energy-momentum tensor (EMT). We proceed our investigations for a few cosmological quantities, where for simplicity we assume the metric and the scalar field are functions of the time. Hence, the EMT satisfies the barotropic equation of state, and the model indicates that constant mean Hubble parameter is not allowed. Thus, by appealing to the variation of Hubble parameter, we assume a fixed deceleration parameter, and set the evolution of the quantities with respect to the fixed deceleration, the BD coupling and the state parameters. The WEC allows a shrinking extra dimension for a decelerating expanding universe that, in the constant scalar field, evolves the same as the flat FRW space-time in GR. The quantities for the stiff fluid and the radiation dominated universe indicate an expanding universe commenced with a big bang. There is a horizon for each of the fluids, and the rate of expansion slows down by the time. The allowed ranges of the deceleration and the BD coupling parameters have been obtained, and the model gives an empty universe when the time goes to infinity.

In this paper, we introduce a noncommutative version of the Brans-Dicke (BD) theory and obtain the Hamiltonian equations of motion for a spatially flat Friedmann-Lemaître-Robertson-Walker universe filled with a perfect fluid. We focus on the case where the scalar potential as well as the ordinary matter sector are absent. Then, we investigate gravity-driven acceleration and kinetic inflation in this noncommutative BD cosmology. In contrast to the commutative case, in which the scale factor and BD scalar field are in a power-law form, in the noncommutative case the power-law scalar factor is multiplied by a dynamical exponential warp factor. This warp factor depends on the noncommutative parameter as well as the momentum conjugate associated to the BD scalar field. We show that the BD scalar field and the scale factor effectively depend on the noncommutative parameter. For very small values of this parameter, we obtain an appropriate inflationary solution, which can overcome problems within BD standard cosmology in a more efficient manner. Furthermore, a graceful exit from an early acceleration epoch towards a decelerating radiation epoch is provided. For late times, due to the presence of the noncommutative parameter, we obtain a zero acceleration epoch, which can be interpreted as the coarse-grained explanation.

We investigate the effects of a special kind of dynamical deformation between the momenta of the scalar field of the Brans-Dicke theory and the scale factor of the FRW metric. This special choice of deformation includes linearly a deformation parameter. We trace the deformation footprints in the cosmological equations of motion when the BD coupling parameter goes to infinity. One class of the solutions gives a constant scale factor in the late time that confirms the previous result obtained via another approach in the literature. This effect can be interpreted as a quantum gravity footprint in the coarse grained explanation. The another class of the solutions removes the big bang singularity, and the accelerating expansion region has an infinite temporal range which overcomes the horizon problem. After this epoch, there is a graceful exiting by which the universe enters in the radiation dominated era.

We study the gravitational collapse of a homogeneous scalar field, minimally coupled to gravity, in the presence of a particular type of dynamical deformation between the canonical momenta of the scale factor and of the scalar field. In the absence of such a deformation, a class of solutions can be found in the literature [R. Goswami and P. S. Joshi, arXiv:gr-qc/0410144], whereby a curvature singularity occurs at the collapse end state, which can be either hidden behind a horizon or be visible to external observers. However, when the phase-space is deformed, as implemented herein this paper, we find that the singularity may be either removed or instead, attained faster. More precisely, for negative values of the deformation parameter, we identify the emergence of a negative pressure term, which slows down the collapse so that the singularity is replaced with a bounce. In this respect, the formation of a dynamical horizon can be avoided depending on the suitable choice of the boundary surface of the star. Whereas for positive values, the pressure that originates from the deformation effects assists the collapse toward the singularity formation. In this case, since the collapse speed is unbounded, the condition on the horizon formation is always satisfied and furthermore the dynamical horizon develops earlier than when the phase-space deformations are absent. These results are obtained by means of a thoroughly numerical discussion.

We establish an extended version of the modified Sáez-Ballester (SB) scalar-tensor theory in arbitrary dimensions whose energy momentum tensor as well as potential are pure geometrical quantities. This scenario emerges by means of two scalar fields (one is present in the SB theory and the other is associated with the extra dimension) which widens the scope of the induced-matter theory. Moreover, it bears a close resemblance to the standard Sáez-Ballester scalar-tensor theory, as well as other alternative theories to general relativity, whose construction includes either a minimally or a non-minimally coupled scalar field. However, contrary to those theories, in our framework the energy momentum tensor and the scalar potential are not added by hand, but instead are dictated from the geometry. Concerning cosmological applications, our herein contribution brings a new perspective. We firstly show that the dark energy sector can be naturally retrieved within a strictly geometric perspective, and we subsequently analyze it. Moreover, our framework may provide a hint to understand the physics of lower gravity theories.

In this paper, we bring together the five-dimensional Saez-Ballester (SB) scalar-tensor theory [1] and the induced-matter-theory (IMT) setting [2], to obtain a modified SB theory (MSBT) in four dimensions. Specifically, by using an intrinsic dimensional reduction procedure into the SB field equations in five-dimensions, a MSBT is obtained onto a hypersurface orthogonal to the extra dimension. This four-dimensional MSBT is shown to bear distinctive new features in contrast to the usual corresponding SB theory as well as to IMT and the Modified Brans-Dicke Theory (MBDT) [3]. In more detail, besides usual induced matter terms retrieved through the IMT, the MSBT scalar field is provided with additional physically distinct (namely, SB induced) terms as well as an intrinsic self-interacting potential (interpreted as consequence of the IMT process and the concrete geometry associated to the extra dimension). Moreover, our MSBT has four sets of field equations, with two sets having no analog in the standard SB scalar-tensor theory. It should be emphasized that the herein appealing solutions can emerge solely from the geometrical reductional process, from presence also of extra dimension(s) and not from any ad-hoc matter either in the bulk or on the hypersurface. Subsequently, we apply the herein MSBT to cosmology and consider an extended spatially flat FLRW geometry in a five-dimensional vacuum space-time. After obtaining the exact solutions in the bulk, we proceed to construct, by means of the MSBT setting, the corresponding dynamic, on the four-dimensional hypersurface. More precisely, we obtain the (SB) components of the induced matter, including the induced scalar potential terms. We retrieve two different classes of solutions. Concerning the first class, we show that the MSBT yields a barotropic equation of state for the induced perfect fluid. We then investigate vacuum, dust, radiation, stiff fluid and false vacuum cosmologies for this scenario and contrast the results with those obtained in the standard SB theory, IMT and BD theory. Regarding the second class solutions, we show that the scale factor behaves similar to a de Sitter (DeS) model. However, in our MSBT setting, this behavior is assisted by non-vanishing induced matter instead, without any a priori cosmological constat. Moreover, for all these solutions, we show that the extra dimension contracts with the cosmic time.

We consider a noncommutative (NC) inflationary model with a homogeneous scalar field minimally coupled to gravity. The particular NC inflationary setting herein proposed, produces entirely new consequences as summarized in what follows. We first analyze the free field case and subsequently examine the situation where the scalar field is subjected to a polynomial and exponential potentials. We propose to use a canonical deformation between momenta, in a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe, and while the Friedmann equation (Hamiltonian constraint) remains unaffected the Friedmann acceleration equation (and thus the Klein-Gordon equation) is modified by an extra term linear in the NC parameter. This concrete noncommutativity on the momenta allows interesting dynamics that other NC models seem not to allow. Let us be more precise. This extra term behaves as the sole explicit pressure that under the right circumstances implies a period of accelerated expansion of the universe. We find that in the absence of the scalar field potential, and in contrast with the commutative case, in which the scale factor always decelerates, we obtain an inflationary phase for small negative values of the NC parameter. Subsequently, the period of accelerated expansion is smoothly replaced by an appropriate deceleration phase providing an interesting model regarding the graceful exit problem in inflationary models. This last property is present either in the free field case or under the influence of the scalar field potentials considered here. Moreover, in the case of the free scalar field, we show that not only the horizon problem is solved but also there is some resemblance between the evolution equation of the scale factor associated to our model and that for the R 2 (Starobinsky) inflationary model. Therefore, our herein NC model not only can be taken as an appropriate scenario to get a successful kinetic inflation, but also is a convenient setting to obtain inflationary universe possessing the graceful exit when scalar field potentials are present.