Some aspects of modified theory of gravity in Palatini formalism unveiled

Abstract

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.

Inflation with F(T) teleparallel gravity

“…Hamiltonian has been constructed following Dirac constrained analysis, but it contains momenta in the denominator and hence impossible to handle [65]. In the context of RW metric, it is therefore suggestive either to incorporate lapse function (N ) in the symmetry equation, without fixing it a priori [66,67], or to incorporate the constraint in the Noether equation, through a Lagrange multiplier [68,69]. However, in both the situations, the lapse function and the Lagrange multiplier remain arbitrary, and one does not know, which form would give a symmetry.…”

Reconstructing Modified and Alternative Theories of Gravity

“…But, prior to that, it is somehow required to relate R with R, so that one can study cosmological evolution. This is possible under the conformal transformation, g µν = F ′ (R) gµν , whence the action takes the following form [53]:…”