Related papers: Scalar Curvature in Discrete Gravity
We study new classes of metric transformations in the context of scalar-tensor theories, which involve both higher derivatives of the scalar field and derivatives of the metric itself. In general, such transformations are not invertible as…
We study a system of equations on a compact complex manifold, that couples the scalar curvature of a Kaehler metric with a spectral function of a first-order deformation of the complex structure. The system comes from an…
Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…
The metric-affine gravity provides a useful framework for analyzing gravitational dynamics since it treats metric tensor and affine connection as fundamentally independent variables. In this work, we show that, a metric-affine gravity…
I discuss a model for quantized gravitation based on the simplicial lattice discretization. It has been studied in some detail using a comprehensive finite size scaling analysis combined with renormalization group methods. The results are…
Deformations of the canonical spectral triples over the n-dimensional torus are considered. These deformations have a discrete dimension spectrum consisting of non-integer values less than n. The differential algebra corresponding to these…
In this thesis, I investigate how to construct a self-consistent model of deformed general relativity using canonical methods and metric variables. The specific deformation of general covariance is predicted by some studies into loop…
Models of folding of a triangular lattice embedded in a discrete space are studied as simple models of the crumpling transition of fixed-connectivity membranes. Both the case of planar folding and three-dimensional folding on a…
We discuss some classical and quantum properties of 2d gravity models involving metric and a scalar field. Different models are parametrized in terms of a scalar potential. We show that a general Liouville-type model with exponential…
We examine three-dimensional metric deformations based on a tetrad transformation through the action the matrices of scalar fields. We describe by this approach to deformation the results obtained by Coll et al. in [1], where it is stated…
We investigate static cylindrical solutions within an extended theory of modified gravity. By incorporating various coupling functions through a straightforward boost symmetry approach, we establish the equations of motion in a…
Within the scheme of modified gravity, an exponential Lagrangian density will be considered, and the corresponding scalar-tensor description will be addressed for both positive and negative values of the cosmological constant. For negative…
Scalar-tensor gravity is the simplest and best understood modification of general relativity, consisting of a real scalar field coupled directly to the Ricci scalar curvature. Models of this type have self-accelerating solutions. In an…
Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations…
Investigations of the dynamic modes of the Poincare gauge theory of gravity found only two good propagating torsion modes; they are effectively a scalar and a pseudoscalar. Cosmology affords a natural situation where one might see…
There is a deformation of the ordinary differential calculus which leads from the continuum to a lattice (and induces a corresponding deformation of physical theories). We recall some of its features and relate it to a general framework of…
This paper is devoted to the problem of prescribing the scalar curvature under zero boundary conditions. Using dynamical and topological methods involving the study of critical points at infinity of the associated variational problem, we…
We look at smooth manifolds equipped with a possibly singular Riemannian metric. We give sufficient conditions for the existence of scalar curvature measures and Dirac operators.
We study second-order cosmological perturbations in scalar-tensor models of dark energy that satisfy local gravity constraints, including f(R) gravity. We derive equations for matter fluctuations under a sub-horizon approximation and…
The whole class of minimally coupled and massive scalar fields which may be responsible for flattening of galactic rotation curves is found. An interesting relation with a class of scalar-tensor theories able to isotropise anisotropic…