Related papers: Herglotz Action for Homogeneous Cosmology
In metric-affine gravity, both the gravitational and matter actions depend not just on the metric, but also on the independent affine connection. Thus matter can be modeled as a hyperfluid, characterized by both the energy-momentum and…
The stability criteria for spatially flat homogeneous and isotropic cosmological dynamical system is investigated with the interaction of a scalar field endowed with a perfect fluid.In this paper, we depict the dynamical system perspective…
We consider a connected symplectic manifold $M$ acted on properly and in a Hamiltonian fashion by a connected Lie group $G$. Inspired to the recent paper \cite{gb2}, see also \cite{ch} and \cite{pacini}, we study Lagrangian orbits of…
We give a short account of the quantisation of the Szekeres spacetime by considering the symmetries of a reduced action principle. This is an alternative approach than the one followed in the literature for the study of inhomogeneities,…
The field equations of general relativity can be derived from the Einstein action, which is quadratic in connection coefficients, rather than the standard action involving the Gibbons-Hawking-York term and counterterm. We show that it is…
The linearly polarized Gowdy $T^3$ model with a massless scalar field with the same symmetries as the metric is quantized by applying a hybrid approach. The homogeneous geometry degrees of freedom are loop quantized, fact which leads to the…
We consider $d>4$-dimensional space-times which are asymptotically flat at spatial infinity and show that, in the first order framework, the action principle is well-defined \emph{without the need of infinite counter terms.} It naturally…
For gravity coupled to N scalar fields with arbitrary potential V, it is shown that all flat (homogeneous and isotropic) cosmologies correspond to geodesics in an (N+1)-dimensional `augmented' target space of Lorentzian signature (1,N),…
We discuss a mechanism that induces a time-dependent vacuum energy on cosmological scales. It is based on the instability induced renormalization triggered by the low energy quantum fluctuations in a Universe with a positive cosmological…
We show that polar actions of cohomogeneity two on simple compact Lie groups of higher rank, endowed with a biinvariant Riemannian metric, are hyperpolar. Combining this with a recent result of the second-named author, we are able to prove…
The study of actions of countable groups by automorphisms of compact abelian groups has recently undergone intensive development, revealing deep connections with operator algebras and other areas. The discrete Heisenberg group is the…
An energy for the homogeneous cosmological models is presented. More specifically, using an appropriate natural prescription, we find the energy within any region with any gravitational source for a large class of gravity theories--namely…
We develop several formal analogies between the logistic equation and the spatially homogeneous and isotropic relativistic cosmology described by the Einstein-Friedmann equations. These analogies produce an effective Lagrangian and…
In multi-scalar field cosmologies new dynamical degrees of freedom are introduced which can explain the observational phenomena. Unlike the usual scalar field theory where a single scalar field is considered, the multi-scalar field…
The Einstein field equations for a class of irrotational non-orthogonally transitive $G_{2}$ cosmologies are written down as a system of partial differential equations. The equilibrium points are self-similar and can be written as a…
We study the motion of charged particle under a natural choice of electromagnetic field in a general class of compact homogeneous spaces. As a special case we describe the motion in homogeneous Riemannian spaces $(G/H,g)$, where $g$ is any…
In this paper we construct a path integral formulation of quantum mechanics on noncommutative phase-space. We first map the system to an equivalent system on the noncommutative plane. Then by applying the formalism of representing a quantum…
We classify compact homogeneous geometries of irreducible spherical type and rank at least 2 which admit a transitive action of a compact connected group, up to equivariant 2-coverings. We apply our classification to polar actions on…
The Universe is not completely homogeneous. Even if it is sufficiently so on large scales, it is very inhomogeneous at small scales, and this has an effect on light propagation, so that the distance as a function of redshift, which in many…
A natural and very important development of constrained system theory is a detail study of the relation between the constraint structure in the Hamiltonian formulation with specific features of the theory in the Lagrangian formulation,…