Selected topics in scalar–tensor theories and beyond

Classical and Quantum Gravity, 2009

Over the last few decades, astronomers and cosmologists have accumulated vast amounts of data clearly demonstrating that our current theories of fundamental particles and of gravity are inadequate to explain the observed discrepancy between the dynamics and the distribution of the visible matter in the Universe. The Modified Newtonian Dynamics (MOND) proposal aims at solving the problem by postulating that Newton's second law of motion is modified for accelerations smaller than ~10^{-10}m/s^2. This simple amendment, has had tremendous success in explaining galactic rotation curves. However, being non-relativistic, it cannot make firm predictions for cosmology. A relativistic theory called Tensor-Vector-Scalar (TeVeS) has been proposed by Bekenstein building on earlier work of Sanders which has a MOND limit for non-relativistic systems. In this article I give a short introduction to TeVeS theory and focus on its predictions for cosmology as well as some non-cosmological studies.

International Journal of Modern Physics D

In the bibliography, a certain confusion arises in what regards to the classification of the gravitational theories into scalar–tensor theories (STT) and general relativity with a scalar field either minimally or nonminimally coupled to matter. Higher-derivatives Horndeski and beyond Horndeski theories that at first sight do not look like STT only add to the confusion. To further complicate things, the discussion on the physical equivalence of the different conformal frames in which a given scalar–tensor theory may be formulated, makes even harder to achieve a correct classification. In this paper, we propose a specific criterion for an unambiguous identification of STT and discuss its impact on the conformal transformations issue. The present discussion carries not only pedagogical but also scientific interest since an incorrect classification of a given theory as a scalar–tensor theory of gravity may lead to conceptual issues and to the consequent misunderstanding of its physical ...

Gravitation and Cosmology

We study the cosmological implications of scalar-tensor theories compatible with solar-system experiments, binary pulsar dynamics, etc. In particular, homogeneous and isotropic cosmological models and the primordial light element production have are computed. We succeed for the first time in constructing a class of scalar-tensor models which predict correct primordial light element abundances allowing for the Universe closure by only baryons. The reason why such predictions have been possible is that the speed-up factor (the ratio between the present-theory Hubble parameter and that obtained in General Relativity) in this class of theories has a non-monotonic time evolution during the primordial nucleosynthesis. These theories have also important consequences on inflation and on the large-scale structure formation.

Journal of High Energy Physics

Scalar-tensor theory of gravity with non-minimal coupling is a fairly good candidate for dark energy, required to explain late-time cosmic evolution. Here we study the very early stage of evolution of the universe with a modified version of the theory, which includes scalar curvature squared term. One of the key aspects of the present study is that, the quantum dynamics of the action under consideration ends up generically with de-Sitter expansion under semiclassical approximation, rather than power-law. This justifies the analysis of inflationary regime with de-Sitter expansion. The other key aspect is that, while studying gravitational perturbation, the perturbed generalized scalar field equation obtained from the perturbed action, when matched with the perturbed form of the background scalar field equation, relates the coupling parameter and the potential exactly in the same manner as the solution of classical field equations does, assuming de-Sitter expansion. The study also reveals that the quantum theory is well behaved, inflationary parameters fall well within the observational limit and quantum perturbation analysis shows that the power-spectrum does not deviate considerably from the standard one obtained from minimally coupled theory.

2004

In this work, a few models of the Universe which include, in particular, dark energy are presented. In some of them, dark energy is considered to be only a slowly rolling scalar field (quintessence), while in others, its presence is simulated through a negative cosmological constant. The scalar field is minimally coupled to gravity and does not interact with matter, so these models are to be used after decoupling of radiation and matter. However, this ansatz, and a proper normalization, allow to find new general classes of solutions for the cosmological equations. The inclusion of the negative cosmological constant results in the possibility of the future gravitational collapse of the universe; this inclusion solves the horizon problem which prevents the consistent formulation of string theory.

2019

In the present paper we discuss on the issue that arises when one tries to classify the gravitational theories into scalar-tensor theories or general relativity with a scalar field non-minimally coupled to matter. Despite that the issue might seem like a trivial one, some confusion might arise when dealing with higher-derivatives Horndeski theories that at first sight do not look like scalar-tensor theories. To further complicate things, the discussion on the physical equivalence of the different conformal frames in which a given scalar-tensor theory may be formulated, makes even harder to achieve a correct classification.

Physical Review D, 1981

The cosmological consequences of a simple scalar field model for the generation of Newton's constant through the spontaneous breaking of scale invariance in a curved space are presented and discussed.

\ The cosmological consequences of a simple scalar field model for the generation of Newton's constant through the spontaneous breaking of scale invariance in a curved space are presented and discussed. Considerable interest has been dedicated recently to the derivation of Einstein gravity as a symmetry-breaking effect. In particular, so as to maintain re-normalizability, the introduction of masses and dimensional parameters in the Lagrangian density is avoided and they are expected to arise through the spontaneous breaking of scale invariance introduced by scalar" or gauge fields. " The purpose of this note is to examine the cosmo-logical consequences of the following globally scale-invariant Lagrangian density for a scalar field o-in a curved space-time': in our case, has a mass of the order of the Planck mass (-10' GeV). %e therefore expect that the approach suggested by the Lagrangian density Eq. (1) will lead to cosmo-logical predictions differing from Einstein gravity less than the Brans-Dicke theory (because of the stabilizing potential term) but more than other approaches involving massive scalar fields (or very deep potential wells) and the purpose of this note is to exhibit the results obtained. Let us consider a Robertson-Walker universe with line element given by L, =-g&"Q o. l) o-o +~a R +L~, (1) V 4 where y and A. are dimensionless positive constants, R is the curvature scalar, and L is the matter Lagrangian density which we assume does not contain o-. In flat space the above Lagrangian density has been shown to allow for spontaneous symmetry breaking, ' therefore let us consider the vacuum a condensate of scalar particles and treat the presence of matter as a perturbation about a suitable ground-state (vacuum) solution to Eq. (1). Such an approach has been shown to lead, in the weak-field limit, to essentially the same equations (up to a rede-finition of the fields) as are obtained from the Brans-Dicke theory. In contrast to that case, however , here one has a background solution (prior geometry) associated with a small, but nonzero, positive cosmological constant. This work further differs from other approaches for the generation of Einstein gravity through the use of scalar fields and spontaneous symmetry breaking, ' in that in the latter approach the scalar field rather than being massless, as tts~= ttt'+g (t)-, +r'ttt)' +r' i st y tg(2) df 1-kr t p = 3 (p+p)-S S '2~2 S k p 1 o. S a-l + = +-2-+ Xrr, (5) S S 3yg 6y p-So-12' (~~g 3) P P S3 dt 6y+1 (6) where the dot denotes differentiation with respect to the time t. In the absence of matter (p = p =0) we have the and matter behaving like an isentropic perfect fiuid having energy-momentum tensor T s=pg a+(p+p)u ua, where p(t), p(t), and u are the energy density, pressure, and velocity four-vector, respectively. The Einstein equations obtained from Eq. (I) will become 24 3338

arXiv (Cornell University), 2016

Classical and Quantum Gravity, 2008

We establish the dynamical attractor behavior in scalar-tensor theories of dark energy, providing a powerful framework to analyze classes of theories, predicting common evolutionary characteristics that can be compared against cosmological constraints. In the Jordan frame the theories are viewed as a coupling between a scalar field, Φ, and the Ricci scalar, R, F (Φ)R. The Jordan frame evolution is described in terms of dynamical variables m ≡ d ln F/d ln Φ and r ≡ −ΦF/f , where F (Φ) = df (Φ)/dΦ. The evolution can be alternatively viewed in the Einstein frame as a general coupling between scalar dark energy and matter, β. We present a complete, consistent picture of evolution in the Einstein and Jordan frames and consider the conditions on the form of the coupling F and β required to give the observed cold dark matter (CDM) dominated era that transitions into a late time accelerative phase, including transitory accelerative eras that have not previously been investigated. We find five classes of evolutionary behavior of which four are qualitatively similar to those for f (R) theories (which have β = 1/2). The fifth class exists only for |β| < √ 3/4, i.e. not for f (R) theories. In models giving transitory late time acceleration, we find a viable accelerative region of the (r, m) plane accessible to scalar-tensor theories with any coupling, β (at least in the range |β| ≤ 1/2, which we study in detail), and an additional region open only to theories with |β| < √ 3/4.