Related papers: The Dynamics of Shape
The Immirzi parameter of loop quantum gravity is a one parameter ambiguity of the theory whose precise interpretation is not universally agreed upon. It is an inherent characteristic of the quantum theory as it appears in the spectra of…
We perform a phase space analysis of a generalized modified gravity theory with nonminimally coupling between geometry and matter. We apply the dynamical system approach to this generalized model and find that in the cosmological context,…
A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the positions and orientations of the…
Minimally modified gravity theories are modifications of general relativity with two local gravitational degrees of freedom in four dimensions. Their construction relies on the breaking of 4D diffeomorphism invariance keeping however the…
Since the main open problem of contemporary physics is to find a unified description of the four interactions, we present a possible scenario which, till now only at the classical level, is able to englobe experiments ranging from…
Metric-affine theories of gravity provide an interesting alternative to General Relativity: in such an approach, the metric and the affine (not necessarily symmetric) connection are independent quantities. Furthermore, the action should…
We develop a generalized projective gauge theory of gravity and spinorial matter, incorporating both non-metricity and torsion. The work is divided into three parts. Part I provides a thorough review of General Relativity, Metric-Affine…
Based on a family of indefinite unitary representations of the diffeomorphism group of an oriented smooth $4$-manifold, a manifestly covariant $4$ dimensional and non-perturbative algebraic quantum field theory formulation of gravity is…
We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The…
We investigate several problems in relativity and particle physics where symmetries play a central role; in all cases geometric properties of Lie groups and their quotients are related to physical effects. The first part is concerned with…
In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…
We present a Pure Shape Dynamics (PSD) formulation of General Relativity (GR), which implements full relationalism by eliminating absolute scale and external time references from the fundamental description of gravity. Starting from the…
In this paper three notions of emergent geometry arising from the study of gauge/gravity duals are discussed. The unifying theme behind these notions of emergent geometry is that one can derive properties of the effective action of a probe…
This thesis covers several developments performed in metric-affine gravity. This alternative framework extends General Relativity by considering a more general connection than the one induced by the metric (i.e., arbitrary torsion and…
Observations of weak gravitational lensing combined with statistical tomographic techniques have revealed that galaxies have formed along filaments, essentially one-dimensional lines or strings, which form sheets and voids. These have, in…
We study various dynamical aspects of systems possessing a first order phase transition in their phase diagram. We isolate three qualitatively distinct types of theories depending on the structure of instabilities and the nature of the low…
A new path equation in absolute parallelism (AP) geometry is derived. The equation is a generalization of three path equations derived in a previous work. It can be considered as a geodesic equation modified by a torsion term, whose…
The notion of "reference frame" is a central theoretical construct for interpreting the physical implications of spacetime diffeomorphism invariance in General Relativity. However, the alternative formulation of classical General Relativity…
Motivated by situations with temporal evolution and spatial symmetries both singled out, we develop a new 2+1+1 decomposition of spacetime, based on a nonorthogonal double foliation. Time evolution proceeds along the leaves of the spatial…
Kendall's Shape Theory covers shapes formed by $N$ points in $\mathbb{R}^d$ upon quotienting out the similarity transformations. This theory is based on the geometry and topology of the corresponding configuration space: shape space.…