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Unimodular Gravity is one of the oldest geometric gravity theory alternative to General Relativity. Essentially, it is based on the Einstein-Hilbert Lagrangian with an additional constraint on the determinant of the metric. It can be…
A thorough study and analysis on the conceptual foundations of unimodular gravity shows that this theory is essentially general relativity disguised as unimodular relativity in the literature. The main reason for this dilemma is accepting…
We revisit the question of frame equivalence in Quantum Field Theory in the presence of gravity, a situation of relevance for theories aiming to describe the early Universe dynamics and Inflation in particular. We show that in those cases,…
A general diffeomorphism invariant SU(2) gauge theory is a gravity theory with two propagating polarizations of the graviton. We develop this description of gravity, in particular for future applications to the perturbative quantization.…
As a toy model for the implementation of the diffeomorphism constraint, the interpretation of the resulting states, and the treatment of ordering ambiguities in loop quantum gravity, we consider the Hilbert space of spatially diffeomorphism…
In order to test the canonical quantization programme for general relativity we introduce a reduced model for a real sector of complexified Ashtekar gravity which captures important properties of the full theory. While it does not…
Unimodular gravity (UG) is an important theory which may explain the smallness of the cosmological constant. To get insight into the covariant quantization of UG, we discuss the BRST quantization of General Relativity (GR) with a…
Recently a scale invariant theory of gravity was constructed by imposing a conformal symmetry on general relativity. The imposition of this symmetry changed the configuration space from superspace - the space of all Riemannian 3-metrics…
General Relativity is usually formulated as a theory with gauge invariance under the diffeomorphism group, but there is a 'dilaton' formulation where it is in addition invariant under Weyl transformations, and a 'unimodular' formulation…
Unimodular gravity can be formulated so that transverse diffeomorphisms and Weyl transformations are symmetries of the theory. For this formulation of unimodular gravity, we work out the two-point and three-point $h_{\mu\nu}$ contributions…
BRST-invariant action of general relativity in the unimodular gauge proposed by Baulieu is studied without using perturbative expansions. The expression for the path integral in the unimodular gauge is reduced to a form in which a…
Unimodular gravity is classically equivalent to General Relativity. This equivalence extends to actions which are functions of the curvature scalar. At the quantum level, the dynamics could differ. Most importantly, the cosmological…
We study the Hamiltonian structure of unimodular-like theories, where the cosmological constant (or other supposed constants of nature) are demoted from fixed parameters to classical constants of motion. No new local degrees of freedom are…
We consider functional-integral quantisation of the moduli of all quantum metrics defined as square-lengths $a$ on the edges of a Lorentzian square graph. We determine correlation functions and find a fixed relative uncertainty $\Delta…
We develop the quantization of unimodular gravity in the Plebanski and Ashtekar formulations and show that the quantum effective action defined by a formal path integral is unimodular. This means that the effective quantum geometry does not…
Treating the gravitational force on the same footing as the electroweak and strong forces, we present a quantum field theory of gravity based on spin and scaling gauge symmetries. A biframe spacetime is initiated to describe such a quantum…
In the present paper, we revisit gravitational theories which are invariant under TDiffs -- transverse (volume preserving) diffeomorphisms and global scale transformations. It is known that these theories can be rewritten in an equivalent…
A quantum hamiltonian which evolves the gravitational field according to time as measured by constant surfaces of a scalar field is defined through a regularization procedure based on the loop representation, and is shown to be finite and…
We apply the ``consistent discretization'' approach to general relativity leaving the spatial slices continuous. The resulting theory is free of the diffeomorphism and Hamiltonian constraints, but one can impose the diffeomorphism…
Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac: First one defines an algebra of basic…