Weak-field regime of the generalized hybrid metric-Palatini gravity

Abstract

In this work we explore the dynamics of the generalized hybrid metric-Palatini theory of gravity in the weak-field, slow-motion regime. We start by introducing the equivalent scalar-tensor representation of the theory, which contains two scalar degrees of freedom, and perform a conformal transformation to the Einstein frame. Linear perturbations of the metric in a Minkowskian background are then studied for the metric and both scalar fields. The effective Newton constant and the PPN parameter γ of the theory are extracted after transforming back to the (original) Jordan frame. Two particular cases where the general method ceases to be applicable are approached separately. A comparison of these results with observational constraints is then used to impose bounds on the masses and coupling constants of the scalar fields.

Swampland conjectures in hybrid metric-Palatini gravity

“…Now, we rewrite R in terms of the scalar field dynamics. In doing so, one may use the following relation between R and potential V (Φ) [77][78][79][80][81][82][83][84][85]87, 100]…”

“…where Φ e is the value of inflaton field at the end time t e of inflation, and H and Φ are given in the aforementioned equations. In the cosmic inflation studies, it is necessary to introduce cosmological parameters such as slow-roll, scalar spectral index, and tensor-to-scalar ratio [84,85,87,99,100]. Slow-roll parameters are used to calculate and determine the most important cosmological quantities, such as the scalar spectrum index and the tensor-to-scalar ratio [84,85,87,88].…”

“…In the cosmic inflation studies, it is necessary to introduce cosmological parameters such as slow-roll, scalar spectral index, and tensor-to-scalar ratio [84,85,87,99,100]. Slow-roll parameters are used to calculate and determine the most important cosmological quantities, such as the scalar spectrum index and the tensor-to-scalar ratio [84,85,87,88]. Of course, there are two completely different approaches for slow-roll approximation.…”

“…The first model imposes constraints on the shape of the potential and requires that the evolution of the scalar field be asymptotic, which is used as a suitable approach to examine inflation at a particular potential [84,85,87,88]. The second form is an approximation of the conditions applied to the Hubble parameter's evolution in the inflation period.…”

Tensor-Multi-Scalar Gravity: Equations of Motion to 2.5 post-Newtonian Order

“…Those theories are mathematically well-defined and they are able to pass all known experimental and observational tests [2,7,8]. Moreover, it turns out that other alternative theories of gravity are mathematically equivalent to certain classes of TMST [9], thus expanding the range of applicability of certain results.…”