General relativity in three spacetime dimensions is used to explore three approaches to the “problem of time” in quantum gravity: the internal Schrödinger approach with mean extrinsic curvature as a time variable, the Wheeler-DeWitt equation, and covariant canonical quantization with “evolving constants of motion.” (To appear in Proc. of the Lanczos Centenary Conference, Raleigh, NC, December 1...

Research during the last decade demonstrates that effects originating on the Planck scale are currently being tested in multiple observational contexts. In this review we discuss quantum gravity phenomenological models and their possible links to loop quantum gravity. Particle frameworks, including kinematic models, broken and deformed Poincaré symmetry, non-commutative geometry, relative local...

The semiclassical approach to quantum gravity would yield the Schrödinger formalism for the wave function of metric perturbations or gravitons plus quantum gravity correcting terms in pure gravity; thus, in the inflationary scenario, we should expect correcting effects to the relic graviton (Zel'dovich) spectrum of the order of (λ/m 2 P l). These, on the other hand, could possibly be measured i...

We study perturbative noncommutative quantum gravity by expanding the gravitational field about a fixed classical background. A calculation of the one loop gravitational self-energy graph reveals that only the non-planar graviton loops are damped by oscillating internal momentum dependent factors. The noncommutative quantum gravity perturbation theory is not renormalizable beyond one loop for m...

The non-trivial ultraviolet fixed point in quantum gravity is calculated by means of the exact renormalization group equation in d-dimensions (2 ≃ d ≤ 4). It is shown that the ultraviolet non-Gaussian fixed point which is expected from the perturbativelly ǫ-expanded calculations in 2 + ǫ gravity theory remains in d = 4. Hence it is possible that quantum gravity is an asymptotically safe theory ...

In this paper we obtain the black hole metric from a semiclassical analysis of loop quantum black hole. Our solution and the Schwarzschild one tend to match well at large distances from Planck region. In r = 0 the semiclassical metric is regular and singularity free in contrast to the classical one. By using the new metric we calculate the Hawking temperature and the entropy. For the entropy we...

The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field is represented by gauge field. In leading order approximation, it gives out classical Newton’s theory of gravity. It can also give out Einstein’s field equation with cosmological constant. For classical tests, it gives o...

We study the short distance behaviour of euclidean quantum gravity in the light of Weinberg’s asymptotic safety scenario. Implications of a non-trivial ultraviolet fixed point are reviewed. Based on an optimised renormalisation group, we provide analytical flow equations in the Einstein-Hilbert truncation. A non-trivial ultraviolet fixed point is found for arbitrary dimension. We discuss a bifu...