The Scalar-Tensor Theory of Gravitation

Abstract

The scalar-tensor theory of gravitation is one of the most popular alternatives to Einstein's theory of gravitation. This book provides a clear and concise introduction to the theoretical ideas and developments, exploring scalar fields and placing them in context with a discussion of Brans-Dicke theory. Topics covered include the cosmological constant problem, time variability of coupling constants, higher dimensional space-time, branes and conformal transformations. The authors emphasize the physical applications of the scalar-tensor theory and thus provide a pedagogical overview of the subject, keeping more mathematically detailed sections for the appendices. This book is suitable for graduate courses in cosmology, gravitation and relativity. It will also provide a valuable reference for researchers.

Effective gravitational couplings for cosmological perturbations in the most general scalar–tensor theories with second-order field equations

“…In the limit that M 2 → 0 we have G eff ≃ (M pl /φ)(4+2ω BD )/(3+2ω BD )G and η ≃ (1+ω BD )/(2+ω BD ) [29,31]. The effective gravitational coupling in the latter case also agrees with the one corresponding to the gravitational force between two test particles [52].…”

Gauge invariant perturbations of scalar-tensor cosmologies: The vacuum case

“…where the last equality in (16) follows on using the Klein -Gordon equation (7). We can see from (18) that ψ is an acceleration potential for the fluid flow [10].…”

“…The idea that gravity might work differently on different scales is suggested by many fundamental schemes such as quantum field theory in curved spacetime [5], as well as the compactification of internal spaces in multidimensional gravity [6,7], the low energy limit of string theory [8] and some braneworld models [9]. Furthermore, GR has only been well tested on small scales and at low energies, so currently we lack strong constraints in the other regimes.…”

Conical singularities and the Vainshtein screening in full GLPV theories

“…An alternative approach to explaining the Universe acceleration (for both dark energy and inflation) is to introduce a scalar field φ beyond the standard model of particle physics [7]. Such a scalar field can be generally coupled to gravity [8,9] through interactions like G 4 (φ, X)R and G 5 (φ, X)G µν ∇ µ ∇ ν φ, where G 4,5 (φ, X) are functions of φ and X = ∇ µ φ∇ µ φ (∇ µ is the covariant derivative operator), R is the Ricci scalar, and G µν is the Einstein tensor.…”