Related papers: Pure Shape Dynamics: Relational General Relativity
We present a canonical Hamiltonian formulation of GR in which $\tau$, the parameter of system evolution, is external to spacetime, playing a role similar to what we call time in nonrelativistic mechanics. This approach, known as…
The inflation-free solution of problems of the modern cosmology (horizon, cosmic initial data, Planck era, arrow of time, singularity,homogeneity, and so on) is considered in the conformal-invariant unified theory given in the space with…
The dynamics of gravity can be described by two different systems. The first is the familiar spacetime picture of General Relativity, the other is the conformal picture of Shape Dynamics. We argue that the bulk equivalence of General…
The analysis of phase transitions in cosmological spacetimes shows that their existence requires a time-dependent apparent horizon radius, which in turn implies an equation of state different from that of a dark energy fluid. This condition…
In this study we explore the cosmological behavior of a non-minimally coupled scalar field that is linked to torsion gravity. We demonstrate the Sorkin-Schutz formalism with general power law teleparallel torsion coupling. The autonomous…
In this paper we present a framework in which the relational description of General Relativity can be used to smoothly continue cosmological dynamical systems through the Big Bang without invoking quantum gravity effects. Cosmological…
In this work, we apply the formalism of dynamical systems to analyze the viability of the $\Lambda$CDM model in a generalized form of the hybrid metric-Palatini gravity theory written in terms of its dynamically equivalent scalar-tensor…
Based on the Generalized Principle of Inertia, which states that: \emph{An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it,} we geometrize…
We propose a new approach to the quasitopological theory of gravity based on a modified classical double--copy construction. Focusing on static, spherically symmetric configurations, we show that all vacuum solutions of $D$--dimensional…
Of the various formalisms developed to treat relativistic phenomena, those based on Clifford's geometric algebra are especially well adapted for clear geometric interpretations and computational efficiency. Here we study relationships…
We propose a cosmological model in the framework of the Poincar\'e gauge theory of gravity (PG). The gravitational Lagrangian is quadratic in curvature and torsion. In our specific model, the Lagrangian contains (i) the curvature scalar $R$…
We discuss the nature of quantum field theories involving gravity that are classically scale-invariant. We show that gravitational radiative corrections are crucial in the determination of the nature of the vacuum state in such theories,…
The gravitational interaction, as described by the Einstein-Cartan theory, is shown to emerge as the by-product of the spontaneous symmetry breaking of a gauge symmetry in a pre-geometric four-dimensional spacetime. Starting from a…
A detailed analysis of dynamics of cosmological models based on $R^{n}$ gravity is presented. We show that the cosmological equations can be written as a first order autonomous system and analyzed using the standard techniques of dynamical…
The "Codazzi formulation", based on a Codazzi tensor, provides a more robust and straightforward theoretical framework for "Cotton Gravity" (CG) than its original formulation in terms of the Cotton tensor. Using this formulation we provide…
We work out the most general theory for the interaction of spacetime geometry and matter fields -- commonly referred to as geometrodynamics -- for spin-$0$ and spin-$1$ particles. The minimum set of postulates to be introduced is that (i)…
We propose a simple, nonlocal modification to general relativity (GR) on large scales, which provides a model of late-time cosmic acceleration in the absence of the cosmological constant and with the same number of free parameters as in…
A new geometric interpretation for General Relativity (GR) is proposed. We show that in the presence of an arbitrary affine connection, the gravitational field is described as nonmetricity of the affine connection. An affine connection can…
We consider a modified gravity model which we call "dynamical Henneaux-Teitelboim gravity" because of its close relationship with the Henneaux-Teitelboim formulation of unimodular gravity. The latter is a fully diffeomorphism-invariant…
This paper introduces a possible alternative model of gravity based on the theory of fractional-dimension spaces and its applications to Newtonian gravity. In particular, Gauss's law for gravity as well as other fundamental classical laws…