New class of hybrid metric-Palatini scalar-tensor theories of gravity

Abstract

A class of scalar-tensor theories (STT) including a non-metricity that unifies metric, Palatini and hybrid metric-Palatini gravitational actions with non-minimal interaction is proposed and investigated from the point of view of their consistency with generalized conformal transformations. It is shown that every such theory can be represented on-shell by a purely metric STT possessing the same solutions for a metric and a scalar field. A set of generalized invariants is also proposed. This extends the formalism previously introduced in [1]. We then apply the formalism to Starobinsky model, write down the Friedmann equations for three possible cases: metric, Palatini and hybrid metric-Palatini, and compare some inflationary observables.

Invariant quantities of scalar–tensor theories for stellar structure

“…In the presented paper we have obtained the stellar structure equations for a general family of the modified gravity theories, written with respect to the scalar field invariants, introduced some time ago in [61]. We found out the invariant representation very useful since it allows to study diverse theories of gravity, such as for example f (R) and scalartensor gravity in different approaches -metric, Palatini, or hybrid, at one go [100]. The relativistic hydrostatic equilibrium equation ( 34) and the mass function (33) are thus the master equations of our work, and their specific shape can help us to understand effects arising by the presence of such invariants, whose specific forms and characteristics, as shown by a few examples in the Sect.…”

Invariant quantities of Scalar-Tensor Theories for stellar structure

“…In the presented paper we have obtained the stellar structure equations for a general family of the modified gravity theories, written with respect to the scalar field invariants, introduced some time ago in [61]. We found out the invariant representation very useful since it allows to study diverse theories of gravity, such as for example f (R) and scalar-tensor gravity in different approachesmetric, Palatini, or hybrid, at one go [95]. The relativistic hydrostatic equilibrium equation (33) and the mass function (32) are thus the master equations of our work, and their specific shape can help us to understand effects arising by the presence of such invariants, whose specific forms and characteristics, as shown by a few examples in the section IV, are ruled by gravitational theories, which possess the invariant representation.…”

Estimating the parameters of Hybrid Palatini gravity model with the Schwarzschild precession of S2, S38 and S55 stars: case of bulk mass distribution

“…Also, it is known that on-shell formulation of Palatini gravity coincides with that of same metric gravity [94]. In paper [95] a class of scalartensor theories is proposed including a non-metricity that unifies metric, Palatini and hybrid metric-Palatini gravitational actions with non-minimal interaction. Authors present a new approach to scalar-tensor theories of gravity that unifies: metric, Palatini, and hybrid.…”