Unified cosmology with scalar–tensor theory of gravity

Abstract

Unlike the Noether symmetry, a metric independent general conserved current exists for non-minimally coupled scalar-tensor theory of gravity if the trace of the energymomentum tensor vanishes. Thus, in the context of cosmology, a symmetry exists both in the early vacuum and radiation dominated era. For slow roll, symmetry is sacrificed, but at the end of early inflation, such a symmetry leads to a Friedmann-like radiation era. Late-time cosmic acceleration in the matter dominated era is realized in the absence of symmetry, in view of the same decayed and redshifted scalar field. Thus, unification of early inflation with late-time cosmic acceleration with a single scalar field may be realized.

De Sitter and scaling solutions in a higher-order modified teleparallel theory

“…Hence techniques from Classical Mechanics can be applied for the determination of conservation laws and the derivation of solutions. Indeed various approaches have been applied in the literature [61,66,[71][72][73][74].…”

Early universe with modified scalar-tensor theory of gravity

“…Finally, C αβ (x, t) is transverse and trace-free (C β α|β = 0 = C α α ) and corresponds to the tensor-type perturbation. Indices are based on g (3) αβ as the metric and the vertical bar ('|') indicates a covariant derivative. Now, we decompose the energy-momentum tensor along with the scalar field by introducing perturbation as, T a b (x, t) =T a b (t) + δT a b (x, t), φ(x, t) =φ(t) + δφ(x, t), and F =F + δF .…”

“…Although, perturbatively it encounters ghost degrees of freedom, non-perturbatively it is well behaved. Further, although unification of the early inflation with late-time cosmic acceleration with non-minimally coupled scalar field has recently been achieved [3], nevertheless one can't ignore the presence of higher order terms in the early universe, particularly because inflation without phase transition is an essential feature of such higher order term [4,5]. Now, in the homogeneous and isotropic background, R 2 µν and R 2 terms differ only by a total derivative term, and it is therefore sufficient to add scalar curvature squared term to the above action, which therefore reads as…”

“…(where, Σ R = 2 ∂V K √ hd 3 x, Σ R 2 = 4 ∂V RK √ hd 3 x and Σ G = 4 ∂V 2G ij K ij + K 3 √ hd 3 x are the supplementary boundary terms known as the Gibbons-Hawking-York term corresponding to the linear sector, its modified version for curvature squared term and for Gauss-Bonnet-dilatonic coupled sector respectively, α, β, and Λ(φ) are the coupling parameters, V (φ) is the dilatonic potential, while the symbol K stands for K = K 3 − 3KK ij K ij + 2K ij K ik K k j , K being the trace of extrinsic curvature tensor), modified Horowitz' formalism ends up with a different phase-space Hamiltonian, which is not related to the others under canonical transformation [14]. The most important outcome of the work is that, the well-known standard formalisms [6][7][8], for which supplementary boundary terms are not required due to the fact that δh ij = 0 = δK ij at the boundary, don't produce correct classical analogue of the theory under appropriate semi-classical approximation, although modified Horowitz' formalism does [14].…”

Inflation with Scalar-Tensor Theory of Gravity

“…Horndeski' theory [32] presents the most general scalar-tensor theory of gravity ensuring no more than second-order field equations to avoid ghost instability due to Ostrogradski theorem. Recently, in view of a general conserved current, obtained under suitable manipulation of the field Equations [33][34][35][36], a non-minimally coupled scalar-tensor theory of gravity, being a special case of Horndeski' model, has been studied extensively in connection with the cosmological evolution, starting from the very early stage (Inflationary regime) to the late-stage (presently accelerated matter-dominated era) via a radiation dominated era [37]. It has been found that such a theory admits a viable inflationary regime, since the inflationary parameters viz.…”