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

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 implications.

Weyl transformation: A dynamical degree of freedom in the light of Dirac’s Large Number hypothesis

In Einstein’s Field Equation (EFE), the geometry of the spacetime is connected with the matter distribution. The geometry or the gravitational sector deals with classical macroscopic objects involving gravitational units while the matter sector can be better described by quantum theory involving atomic units. It has been argued by Bisabr [ arXiv:gr-qc/1904.09336 ] that there exists an epoch-dependent conversion factor between these two unit systems present in two different conformal frames, i.e. the conformal factor is epoch-dependent. We argue that the conformal transformation (CT) is a dynamical degree of freedom describing it’s possible relevance in inflation in context to the graceful exit problem, dynamics of the cosmological constant [Formula: see text] and justify the argument in the light of consequences of Dirac’s Large Number hypothesis (LNH).

Are there really conformal frames? Uniqueness of affine inflation

Here, we concisely review the nonminimal coupling dynamics of a single scalar field in the context of purely affine gravity and extend the study to multifield dynamics. The coupling is performed via an affine connection and its associated curvature without referring to any metric tensor. The latter arises a posteriori and it may gain an emergent character like the scale of gravity. What is remarkable in affine gravity is the transition from nonminimal to minimal couplings which is realized by only field redefinition of the scalar fields. Consequently, the inflationary models gain a unique description in this context where the observed parameters, like the scalar tilt and the tensor-to-scalar ratio, are invariant under field reparametrization. Overall, gravity in its affine approach is expected to reveal interesting and rich phenomenology in cosmology and astroparticle physics.

Conformal frames in cosmology

From higher dimensional theories, e.g. string theory, one expects the presence of nonminimally coupled scalar fields. We review the notion of conformal frames in cosmology and emphasize their physical equivalence, which holds at least at a classical level. Furthermore, if there is a field, or fields, which dominates the universe, as it is often the case in cosmology, we can use such notion of frames to treat our system, matter and gravity, as two different sectors. On one hand, the gravity sector which describes the dynamics of the geometry and on the other hand, the matter sector which has such geometry as a playground. We use this interpretation to build a model where the fact that a curvaton couples to a particular frame metric could leave an imprint in the cosmic microwave background (CMB).

THEORY OF GRAVITATION THEORIES: A NO-PROGRESS REPORT

Already in the 1970s there where attempts to present a set of ground rules, sometimes referred to as a theory of gravitation theories, which theories of gravity should satisfy in order to be considered viable in principle and, therefore, interesting enough to deserve further investigation. From this perspective, an alternative title of this paper could be "Why Are We Still Unable to Write a Guide on How to Propose Viable Alternatives to General Relativity?". Attempting to answer this question, it is argued here that earlier efforts to turn qualitative statements, such as the Einstein equivalence principle, into quantitative ones, such as the metric postulates, stand on rather shaky ground — probably contrary to popular belief — as they appear to depend strongly on particular representations of the theory. This includes ambiguities in the identification of matter and gravitational fields, dependence of frequently used definitions (such as those of the stress–energy tensor or classical vacuum) on the choice of variables, etc. Various examples are discussed and possible approaches to this problem are pointed out. In the course of this study, several common misconceptions related to the various forms of the equivalence principle, the use of conformal frames and equivalence between theories are clarified.