Selected topics in scalar–tensor theories and beyond

Abstract

Scalar fields have played an important role in the development of the fundamental theories of physics as well as in other branches of physics such as gravitation and cosmology. For a long time these escaped detection until 2012 year when the Higgs boson was observed for the first time. Since then alternatives to the general theory of relativity like the Brans-Dicke theory, scalar-tensor theories of gravity and their higher derivative generalizations -collectively known as Horndeski theories -have acquired renewed interest. In the present review we discuss on several selected topics regarding these theories, mainly from the theoretical perspective but with due mention of the observational aspect. Among the topics covered in this review we pay special attention to the following: 1) the asymptotic dynamics of cosmological models based in the Brans-Dicke, scalar-tensor and Horndeski theories, 2) inflationary models, extended quintessence and the Galileons, with emphasis in causality and stability issues, 3) the chameleon and Vainshtein screening mechanisms that may allow the elusive scalar field to evade the tight observational constraints implied by the solar system experiments, 4) the conformal frames conundrum with a brief discussion on the disformal transformations and 5) the role of Weyl symmetry and scale invariance in the gravitation theories. The review is aimed at specialists as well as at non-specialists in the subject, including postgraduate students.

An issue with the classification of the scalar–tensor theories of gravity

“…Horndeski theories [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] represent further generalization of scalar-tensor theories to include higher derivatives of the scalar field and also derivative couplings. The history of the re-discovery of the Horndeski theories is quite peculiar.…”

“…Due to the yet unknown nature of the dark components of the cosmic background alternatives to the general theory of relativity like the Brans-Dicke (BD) theory, scalar-tensor theories (STT) of gravity and their higher derivative generalizations -collectively known as Horndeski [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and beyond Horndeski [13,[17][18][19][20][21][22][23] theories -have acquired renewed interest. The use of scalar fields in the gravitational theories has a theoretically-motivated origin in the famous theorem by Lovelock [24].…”

“…Hence, the carriers of the gravitational interactions are the two polarizations of the graviton and the scalar field. Scalar-tensor theories of gravity [12,26] are a generalization of the BD theory where the coupling parameter is a function of the scalar field: ω BD → ω(φ), i. e., it is varying parameter. The need for a generalization of BD theory comes from the tight constraints on ω BD that the solar system experiments have established [27].…”

“…In this paper we shall discuss on these issues on the basis of a unambiguous criterion of what to regard as a scalartensor theory. The issue has been put forward in the review [12] where in subsection 7.1.1 a related brief discussion can be found. However, we feel that the discussion in the mentioned reference was not as exhaustive as required given to the subtlety of the issue.…”

Conservation laws and exact solutions in Brans–Dicke cosmology with a scalar field

“…Scalar fields have been widely used by cosmologists to describe the two major open problems in the cosmological evolution, namely inflation and dark energy [1,2]. Scalar fields are introduced in the Einstein-Hilbert action to provide new degrees of freedom and modify the dynamics of the field equations such that tit provides a mechanism which explains the observable phenomena and the cosmological evolution.…”