Several Action and Action Deformation Proposals in f(R) Variable G Modified Gravities and a Brief Expose on Variable G Ontology

TL;DR

This paper explores various f(R) gravity models with variable G, proposes deformation methods for actions, and discusses the implications of variable G and VSL on fundamental physics and cosmology.

Contribution

It introduces new f(R) Lagrangians, deformation techniques for gravity-matter actions, and novel perspectives on G(x) ontology and variable speed of light in the context of fundamental theories.

Findings

Proposed aesthetically motivated f(R) Lagrangians with variable G.

Developed deformation methods for gravity-matter actions to derive constraint equations.

Explored the impact of variable G and VSL on quantum gravity, SUSY, superstring models, and cosmology.

Abstract

This note includes five sections. In section 2 a number of aesthetically motivated f(R) Lagrangians is proposed and frivolously explored in the metric formalism with variable Newton constant G(x). In section 3 the idea of deforming the terms in a given f(R) gravity-matter action S, and prior to extremizing it, is promoted with the aim of reducing S via an algebraic mixing between few selected gravity and matter terms without invoking new fields. The result of this is a number of constraint equations among the fields and often eccentric looking field equations derived from the reduced action. Section 4 has a similar upshot as section 3 but the difference is the action term mixing is carried out only after extremizing S and prior to any integration by part. Section 5 pertains to G(x) ontology where various personal views on G(x) gravity are expressed in the context of the Standard Model fermions (SMF). The prospect of mitigating gravity field effects for the SMF is investigated at the end via the variable speed of light (VSL) and new global Lorentz transformations fusing two upper speeds: the light speed c and a proper maximal speed given in the text assigned to all point mass mo and involving the Planck mass. The new LT in combination with VSL also houses a family of special noninertial frames in linear motions. The (spin sensitive) spacetime and momentum dependent VSL is modeled via the Hamiltonian formalism with the aim of canceling the effect of Newtonian gravity felt by a SMF test particle. I also model variable G for yielding finite gravity at all distances, including zero. Excising gravity from the SMF rank (via VSL plus G(x), or by gauging to zero the SMF gravitational masses) has epic brunt on quantum gravity, local SUSY, superstring models, leptoquarks (if any) and cosmology.