Related papers: Conformal variations and quantum fluctuations in d…
We discuss some aspects of the metric configuration space in quantum gravity in the background field formalism. We give a necessary and sufficient condition for the parameterization of Euclidean metric fluctuations such that i) the…
Conformal and disformal transformations are now being very intensively studied in the context of various modified gravity theories. In particular, some special classes of them can be used for constructing Mimetic Dark Matter models.…
We derive a set of equations describing the linear response of the convergence properties of a geodesic congruence to arbitrary geometry variations. It is a combination of equations describing the deviations from the standard…
Different versions of consistent canonical realizations of hypersurface deformations of spherically symmetric space-times have been derived in models of loop quantum gravity, modifying the classical dynamics and sometimes also the structure…
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic…
There is strong evidence coming from Lorentzian dynamical triangulations that the unboundedness of the gravitational action is no obstacle to the construction of a well-defined non-perturbative path integral. In a continuum approach, a…
Lorentzian quantum gravity is believed to cure the pathologies encountered in Euclidean quantum gravity, such as the conformal factor problem. We show that this is the case for the Lorentzian Regge path integral expanded around a flat…
A proper understanding of boundary-value problems is essential in the attempt of developing a quantum theory of gravity and of the birth of the universe. The present paper reviews these topics in light of recent developments in spectral…
We present a brief description of the ``consistent discretization'' approach to classical and quantum general relativity. We exhibit a classical simple example to illustrate the approach and summarize current classical and quantum…
We summarise a recently introduced general canonical formulation of discrete systems which is fully equivalent to the covariant formalism. This framework can handle varying phase space dimensions and is applied to simplicial gravity in…
We present the first steps needed for an analysis of the perturbations that occur in the cosmology associated with the conformal gravity theory. We discuss the implications of conformal invariance for perturbative coordinate gauge choices,…
Fruitful ideas on how to quantize gravity are few and far between. In this paper, we give a complete description of a recently introduced non-perturbative gravitational path integral whose continuum limit has already been investigated…
Using the Steiner-Weyl expansion formula for parallel manifolds and the so called gonihedric principle we find a large class of discrete integral invariants which are defined on simplicial manifolds of various dimensions. These integral…
We investigate the problem of metric fluctuations in the presence of the vacuum fluctuations of matter fields and critically assess the usual assertion that vacuum energy implies a Planckian cosmological constant. A new stochastic classical…
The conformal transformation in the Einstein - Hilbert action leads to a new frame where an extra scalar degree of freedom is compensated by the local conformal-like symmetry. We write down a most general action resulting from such…
The 1+3 covariant approach and the covariant gauge-invariant approach to perturbations are used to analyze in depth conformal transformations in cosmology. Such techniques allow us to obtain very interesting insights on the physical content…
Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and…
A positive semi-definite Euclidean action for arbitrary four-topologies can be constructed by adding appropriate Yang-Mills and topological terms to the Samuel-Jacobson-Smolin action of gravity with (anti)self-dual variables. Moreover,…
We study the problem of how to derive conformal symmetry in the framework of quantum gravity. We start with a generic gravitational theory which is invariant under both the general coordinate transformation (GCT) and Weyl transformation (or…
Quantum mechanical transition amplitudes directly tells the probability of each transition and which one is more favourable. Path-integrals offers a systematic methodology to compute this quantum mechanical process in a consistent manner.…