The appearance of non trivial torsion for some Ricci dependent theories in the Palatini formalism

As is known from studies of gravity models in the Palatini formalism, there exist two inequivalent definitions of the generalized Ricci tensor in terms of the generalized curvature namely, Reµν = Rρµρν and Rνµ = gαβRµανβ. A deep formal investigation of theories with lagrangians of the form L = L(Re(µν)) was initiated in [4]. In that work, the authors leave the connection free, and find out that the torsion only appears as a projective mode. This agrees with the widely employed condition of vanishing torsion in these theories as a simple gauge choice. In the present work the complementary scenario is studied namely, the one described by a lagrangian that depends on the other possible Ricci tensor L = L(R(µν)). The torsion is completely characterized in terms of the metric and the connection, and a rather detailed description of the equations of motion is presented. It is shown that these theories are non trivial even for 1+1 space time dimensions, and admit non zero torsion even in this apparently simple case. It is suggested that to impose zero torsion by force may result into an incompatible system. In other words, the presence of torsion may be beneficial for insuring that the equations of motion are well posed.

General Slow-Roll Inflation in f(R) Gravity under the Palatini Approach

Slow-roll inflation is analyzed in the context of modified gravity within the Palatini formalism. As shown in the literature, inflation in this framework requires the presence of non-traceless matter; otherwise, it does not occur just as a consequence of the nonlinear gravitational terms of the action. Nevertheless, by including a single scalar field that plays the role of the inflaton, slow-roll inflation can be performed in these theories, where the equations lead to an effective potential that modifies the dynamics. We obtain the general slow-roll parameters and analyze a simple model to illustrate the differences introduced by the gravitational terms under the Palatini approach, and the modifications on the spectral index and the tensor to scalar ratio predicted by the model.

Some aspects of modified theory of gravity in Palatini formalism unveiled

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.

Asymptotically Weyl-invariant gravity

We propose a novel theory of gravity that by construction is renormalizable, evades Ostrogradsky’s no-go theorem, is locally scale-invariant in the high-energy limit, and equivalent to general relativity in the low-energy limit. The theory is defined by a pure [Formula: see text] action in the Palatini formalism, where the dimensionless exponent [Formula: see text] runs from a value of two in the high-energy limit to one in the low-energy limit. We show that the proposed model contains no obvious cosmological curvature singularities. The viability of the proposed model is qualitatively assessed using several key criteria.