2017 **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 a…

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“…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.…”

confidence: 99%

“…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.…”

confidence: 99%

“…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…”

confidence: 99%

“…{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.…”

confidence: 99%

“…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].…”

confidence: 99%