FURTHER EXTENDED THEORIES OF GRAVITATION: PART II (original) (raw)

Further Extended Theories of Gravitation: Part I

International Journal of Geometric Methods in Modern Physics, 2010

We shall here propose a class of relativistic theories of gravitation, based on a foundational paper of Ehlers Pirani and Schild (EPS). All "extended theories of gravitation" (also known as f(R) theories) in Palatini formalism are shown to belong to this class. In a forthcoming paper, we shall show that this class of theories contains other more general examples. EPS framework helps in the interpretation and solution of these models that however have exotic behaviors even compared to f(R) theories.

Extended Theories of Gravitation

EPJ Web of Conferences, 2013

Extended theories of gravitation are naturally singled out by an analysis inspired by the Ehelers-Pirani-Schild framework. In this framework the structure of spacetime is described by a Weyl geometry which is enforced by dynamics. Standard General Relativity is just one possible theory within the class of extended theories of gravitation. Also all Palatini f (R) theories are shown to be extended theories of gravitation. This more general setting allows a more general interpretation scheme and more general possible couplings between gravity and matter. The definitions and constructions of extended theories will be reviewed. A general interpretation scheme will be considered for extended theories and some examples will be considered.

Some aspects of modified theory of gravity in Palatini formalism unveiled

Modern Physics Letters A, 2020

Under conformal transformation, [Formula: see text] theory of gravity in Palatini formalism leads to a Brans–Dicke type of scalar-tensor equivalent theory with a wrong sign in the effective kinetic energy term. This means that the effective scalar acts as the dark energy and so late-time cosmic acceleration in the matter-dominated era is accountable. However, we unveil some aspects of Palatini formalism, which reveals the fact that the formalism is not suitable to explain the cosmological evolution of the early universe with [Formula: see text] gravity alone. Additionally, it is noticed that some authors, in an attempt to explore Noether symmetry of the theory changed the sign of the kinetic term and hence obtained the wrong answer. Here, we make the correction and unmask a very interesting aspect of symmetry analysis. Mathematical inequivalence between Jordan’s and Einstein’s frame in Palatini [Formula: see text] theory has also been revealed.

PALATINI FORMULATION OF MODIFIED GRAVITY WITH A NON-MINIMAL CURVATURE-MATTER COUPLING

Modern Physics Letters A, 2011

We derive the field equations and the equations of motion for massive test particles in modified theories of gravity with an arbitrary coupling between geometry and matter by using the Palatini formalism. We show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, matter Lagrangian dependent metric, which is related with the physical metric by means of a conformal transformation. Similarly to the metric case, the field equations impose the non-conservation of the energy-momentum tensor. We derive the explicit form of the equations of motion for massive test particles in the case of a perfect fluid, and the expression of the extra-force is obtained in terms of the matter-geometry coupling functions and of their derivatives. Generally, the motion is non-geodesic, and the extra force is orthogonal to the four-velocity.

Beyond Einstein’s General Relativity: Hybrid metric-Palatini gravity and curvature-matter couplings

International Journal of Modern Physics D, 2020

Einstein’s General Relativity (GR) is possibly one of the greatest intellectual achievements ever conceived by the human mind. In fact, over the last century, GR has proven to be an extremely successful theory, with a well established experimental footing, at least for weak gravitational fields. Its predictions range from the existence of black holes and gravitational radiation (now confirmed) to the cosmological models. Indeed, a central theme in modern Cosmology is the perplexing fact that the Universe is undergoing an accelerating expansion, which represents a new imbalance in the governing gravitational equations. The cause of the late-time cosmic acceleration remains an open and tantalizing question, and has forced theorists and experimentalists to question whether GR is the correct relativistic theory of gravitation. This has spurred much research in modified theories of gravity, where extensions of the Hilbert–Einstein action describe the gravitational field, in particular, [...

Extended gravity

International Journal of Geometric Methods in Modern Physics, 2014

We shall show equivalence between Palatini-f (R) theories and Brans-Dicke (BD) theories at the level of action principles in generic dimension with generic matter coupling. We do that by introducing the Helmholtz Lagrangian associated to Palatini-f (R) theory and then performing frame transformations in order to recover Einstein frame and Brans-Dicke frame. This clarifies the relation among different formulations and the transformations among different frames. Additionally, it defines a formulation a lá Palatini for the Brans-Dicke theory which is dynamically equivalent to metric BD (unlike the standard Palatini-formulation of metric BD theory which are not dynamically equivalent).

Palatini formulation of f(R, T) gravity theory, and its cosmological implications

The European Physical Journal C

We consider the Palatini formulation of f (R, T) gravity theory, in which a non-minimal coupling between the Ricci scalar and the trace of the energy-momentum tensor is introduced, by considering the metric and the affine connection as independent field variables. The field equations and the equations of motion for massive test particles are derived, and we show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, energy-momentum trace dependent metric, related to the physical metric by a conformal transformation. Similar to the metric case, the field equations impose the nonconservation of the energy-momentum tensor. We obtain the explicit form of the equations of motion for massive test particles in the case of a perfect fluid, and the expression of the extra force, which is identical to the one obtained in the metric case. The thermodynamic interpretation of the theory is also briefly discussed. We investigate in detail the cosmological implications of the theory, and we obtain the generalized Friedmann equations of the f (R, T) gravity in the Palatini formulation. Cosmological models with Lagrangians of the type f = R − α 2 /R + g(T) and f = R + α 2 R 2 + g(T) are investigated. These models lead to evolution equations whose solutions describe accelerating Universes at late times.

Palatini approach to modified f(R) gravity and its bi-metric structure

2012

f(R) gravity theories in the Palatini formalism has been recently used as an alternative way to explain the observed late-time cosmic acceleration with no need of invoking either dark energy or extra spatial dimension. However, its applications have shown that some subtleties of these theories need a more profound examination. Here we are interested in the conformal aspects of the Palatini approach in extended theories of gravity. As is well known, extremization of the gravitational action a la Palatini, naturally "selects" a new metric h related to the metric g of the subjacent manifold by a conformal transformation. The related conformal function is given by the derivative of f(R). In this work we examine the conformal symmetries of the flat (k=0) FLRW spacetime and find that its Conformal Killing Vectors are directly linked to the new metric h and also that each vector yields a different conformal function.