Scale-invariant power spectra from a Weyl-invariant scalar–tensor theory

Abstract

We obtain scale-invariant scalar and tensor power spectra from a Weyl-invariant scalar-tensor theory in de Sitter spacetime. This implies that the Weyl invariance guarantees the implementation of the scale invariance of the power spectrum in de Sitter spacetime. We establish a deep connection between the Weyl invariance of the action and the scale invariance of the power spectrum in de Sitter spacetime.

Einstein-singleton theory and its power spectra in de Sitter inflation

“…with two complex coefficientsc 1 andc 2 . This is one of our main results which states that the solution (23) is an exact solution to the fourth-order equation (16). The c.c.…”

“…Its two asymptotic behaviors are quite different from those [(52) and (55)] of a massless scalar. In the subhorizon limit z → ∞, the power spectrum (51) of a singleton is a negatively scale-invariant one which is opposite to (52) of scale-invariant scalar-tensor theory [16], while it blows up (negatively divergent) in the superhorizon limit of z → 0 as is shown in (54).…”

“…because Re[f (z)] → − 5 4 in this limit. We note that the power spectrum of the scaleinvariant scalar tensor theory is given by [16] P SIST = 1 2(2π) 2 .…”

“…In order to compute the complete power spectrum, we have to know the solution to singleton equations (15) and (16) in the whole range of η ∈ [−∞, − 0]. For this purpose, two scalars…”

Charged and Non-Charged Black Hole Solutions in Mimetic Gravitational Theory

“…Among these trails f (R) gravity [8][9][10][11][12][13][14][15][16][17][18][19][20] and the torsion-based f (T) gravity [21][22][23][24][25][26]. In this study, we use another trial which is the conformal invariant gravitational theories [27][28][29][30][31][32][33][34][35]. It is well known that Einstein's GR is invariant under general diffeomorphisms however, it is not invariant under the conformal transformation.…”