Scalar-tensor gravity in an accelerating universe

Abstract

We consider scalar-tensor theories of gravity in an accelerating universe. The equations for the background evolution and the perturbations are given in full generality for any parametrization of the Lagrangian, and we stress that apparent singularities are sometimes artifacts of a pathological choice of variables. Adopting a phenomenological viewpoint, i.e., from the observations back to the theory, we show that the knowledge of the luminosity distance as a function of redshift up to z ∼ (1 − 2), which is expected in the near future, severely constrains the viable subclasses of scalar-tensor theories. This is due to the requirement of positive energy for both the graviton and the scalar partner. Assuming a particular form for the Hubble diagram, consistent with present experimental data, we reconstruct the microscopic Lagrangian for various scalar-tensor models, and find that the most natural ones are obtained if the universe is (marginally) closed.

New constraints on parametrised modified gravity from correlations of the CMB with large scale structure

“…An alternative approach to the phenomenon of cosmic acceleration consists of modifying the laws of gravity on large scales, in order to allow for self-accelerating solutions. Well-known examples of such theories are the f (R) models [2][3][4][5][6], or more general scalar-tensor theories [7][8][9][10], the Dvali-Gabadadze-Porrati (DGP) model [11,12], and its further extensions such as Degravitation [13].…”

Backreaction mechanism in multifluid and extended cosmologies

“…A crucial assumption that we will make is that matter is minimally coupled so that its flow is geodesic, i.e., u µ ∇ µ u α = 0. This is not the case in some extended gravity theories described in certain frames, for example f (R) or general Brans-Dicke theories in the Einstein frame [20,21]. This will be discussed in more detail below.…”

“…The geodesic character can be recovered if congruences are defined with respect to the flux at rest with respect the total energy-momentum tensor. Furthermore, if one departs from the Jordan frame, where the acceleration of a set of observers a µ = u ν ∇ ν u µ is assumed to vanish, i.e., it constitutes a geodesic congruence, and then, performs a conformal transformation (5.3), the 4-acceleration in the Einstein frame becomes 21) where…”

“…Note that the domain of integration can be defined using two hypersurfaces of interest: either with respect to the gravitational frame, which refers to a set of comoving observers defined at every point of the spacetime, or with respect to the rest frame of the fluid [50]. In the latter case, while referring to the rest frame of the matter content, one should be aware that in the Einstein frame there exists a fifth force mediated by the scalar field that will make the matter trajectories non-geodesic [20,21], and ∇ Eµ T µν(m) E = 0. This is natural since in the Einstein frame there is an exchange of energy between the matter and the scalar field.…”

“…This frame possesses the advantage that, in some simple cases, it diagonalises the kinetic terms for the spin-0 (the scalar field) and spin-2 (the graviton) degrees of freedom so that the presence of ghost, Laplacian and tachyonic instabilities can be directly identified. In this frame, the scalar field is coupled to matter [20,21].…”