Modified Saez–Ballester scalar–tensor theory from 5D space-time

Abstract

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.

Kinetic inflation in deformed phase space Brans–Dicke cosmology

“…In this paper, we introduced a dynamical deformation 12 in the phase space associated to the momenta of the spatially flat FLRW scale factor and the BD scalar field. Using the Hamiltonian formalism, after some computations, we have derived the modified equations, such that when the NC parameter vanishes, we recover the equations correspond to the non-deformed case.…”

“…Let us move to the second stage of this section in which we can see the explicit presence of the NC parameter in our dynamical analysis. Taking a constant BD coupling parameter and employing ζ(a) = a n and (18), equation (12) can be rewritten aṡ where…”

“…Concerning the cosmological dynamics, we further show that our NC framework bears close resemblance to the R 2 (Starobinsky) inflationary model. 1 Recently, concerning such an ad hoc scalar potential in scalar tensor theories, it has been shown that the geometry of the higher dimensions can instead naturally yield it; see, for instance, [9,10,11,12]. Moreover, we should note that, in addition to including a scalar potential, there are also other approaches for describing the present day acceleration (which, in turn, suffer from major problems [13]): (i) When the BD coupling parameter is restricted to −2 ≤ ω ≤ −3/2; in this case, the energy condition associated to the BD scalar field is not satisfied.…”

Noncommutativity, Sáez–Ballester Theory and Kinetic Inflation

“…{P φ , h(P a , P φ )} = −θφ 2n+3 ∂h ∂P a , (16) in which h is an arbitrary function of the conjugate momenta.…”

“…To the best of our knowledge, it has not been investigated for which values of W the observational limits can be satisfied. The SB theory and its extended versions, in both the classical and quantum levels, have been widely applied to investigate various cosmological problems in either four or arbitrary dimensions [7][8][9][10][11][12][13][14][15][16][17][18].…”