Related papers: Natural coordinates and horizontal approximations …
We construct Grassmann spaces associated with the incidence geometry of regular and tangential subspaces of a symplectic copolar space, show that the underlying metric projective space can be recovered in terms of the corresponding…
Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…
The aim of this set of lectures is a systematic presentation of a 1+3 covariant approach to studying the geometry, dynamics, and observational properties of relativistic cosmological models. In giving (i) the basic 1+3 covariant relations…
Based on a more careful canonical analysis, we motivate a reduced quantization - in the sense of superspace quantization - of slightly inhomogeneous cosmology in place of the Dirac quantization in the existing literature, and provide it in…
A time-dependent model of space-time is used to describe the gravitational field of the sun. This model is a spherically symmetric approximate solution of Einstein's equations in vacuum. Near the sun it approximates one of the models…
We analyse spacetimes with a conformal scalar field source, a cosmological constant and a quartic self-interaction term for the scalar field. We also consider additional matter contents in the form of Maxwell and Yang-Mills fields or…
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 derive an effective dynamics for scalar cosmological perturbations from quantum gravity, in the framework of group field theory (GFT) condensate cosmology. The emergent spacetime picture is obtained from the mean field hydrodynamic…
It is shown here how prior estimates on the local shape of the universe can be used to reduce, to a small region, the full parameter space for the search of circles in the sky. This is the first step towards the development of efficient…
We develop a framework to study the phase space of a system consisting of a scalar field rolling down an arbitrary potential with varying slope and a background fluid, in a cosmological setting. We give analytical approximate solutions of…
We solve isotropic, homogeneous cosmological models containing a self-interacting scalar field. Calculations are performed in four and two-dimensional spacetimes. We find several exact solutions that have an inflationary regime or has a…
A geodesic circle in Finsler geometry is a natural extension of that in a Euclidean space. In this paper, we apply Lie derivatives and the Cartan $Y$-connection to study geodesic circles and (infinitesimal) concircular transformations on a…
Discretizing variational principles, as opposed to discretizing differential equations, leads to discrete-time analogues of mechanics, and, systematically, to geometric numerical integrators. The phase space of such variational…
From higher dimensional theories, e.g. string theory, one expects the presence of non-minimally coupled scalar fields. We review the notion of conformal frames in cosmology and emphasize their physical equivalence, which holds at least at a…
We identify a class of condensate states in the group field theory (GFT) approach to quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from…
We study the dynamics of the field equations in a four-dimensional isotropic and homogeneous spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker geometry in the context of Einstein-Gauss-Bonnet theory with a matter source and a…
This review paper is concerned with the generalizations to field theory of the tangent and cotangent structures and bundles that play fundamental roles in the Lagrangian and Hamiltonian formulations of classical mechanics. The paper…
We describe scalar-bimetric theories where the dynamics of the Universe are governed by two separate metrics, each with an Einstein-Hilbert term. In this setting, the baryonic and dark matter components of the Universe couple to metrics…
We find initial data for numerical relativity simulations of inhomogeneous cosmologies. This involves treating an exceptional case of the general relativity constraint equations. We devise analytic and numerical methods to treat this…
We apply the statefinder diagnostic to the torsion cosmology, in which an accounting for the accelerated universe is considered in term of a Riemann-Cartan geometry: dynamic scalar torsion. We find that there are some typical characteristic…