Towards the map of quantum gravity

Abstract

In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between Loop Quantum Gravity, Causal Dynamical Triangulations, Hořava-Lifshitz gravity, Asymptotic Safety scenario, Quantum Graphity, deformations of relativistic symmetries and nonlinear phase space models are discussed. The main focus is on quantum deformations of the Hypersurface Deformations Algebra and Poincaré algebra, nonlinear structure of phase space, the running dimension of spacetime and nontrivial phase diagram of quantum gravity. We present an attempt to arrange the observed relations in the form of a graph, highlighting different aspects of quantum gravity. The analysis is performed in the spirit of a mind map, which represents the architectural approach to the studied theory, being a natural way to describe the properties of a complex system. We hope that the constructed graphs (maps) will turn out to be helpful in uncovering the global picture of quantum gravity as a particular complex system and serve as a useful guide for the researchers. arXiv:1708.07445v3 [hep-th] 25 May 2018 ‡ The importance of quantum effects in gravity was noted by Einstein already in 1916 [1].

Quantum gravity and gravitational-wave astronomy

“…In contrast, higher-order or non-local derivative operators acting on h ij would modify its dispersion relation and, consequently, the spectral dimension as probed by gravitons. 11 While in modified-gravity models the dimensional flow of d H is driven by the dynamics and is essentially an IR effect, in quantum gravity it originates in a deep modification of the spacetime texture in the UV.…”

“…Standard general relativity (GR) perfectly explains our current observations [5][6][7] but one cannot exclude the possibility that GW astronomy could be the window theories beyond GR have been waiting for. For instance, the landscape of quantum gravities (e.g., [8][9][10][11]) is populated by a number of top-down candidates, each with its own characteristic assumptions and predictions (or lack of them). It is generally accepted that some of them could indeed unify quantum mechanics and gravity in a consistent way, while offering a rich phenomenology prone to experimental verification.…”

The phase structure of causal dynamical triangulations with toroidal spatial topology

“…The idea of an imposed global time-foliation also appears in Hořava-Lifshitz gravity [20], which is an attempt to define the UV completion of general relativity by introducing anisotropic scaling of space-time coordinates in the high-energy regime. It has been actually shown that the continuum limit of two-dimensional CDT is compatible with the two-dimensional projectable Hořava-Lifshitz gravity [21,22], and that both approaches share many features in three [23,24,25,26] and four [27,28,29] space-time dimensions.…”

Untitled

“…It competes with string and M-theory that begins with quantum field and adds gravity. [18] According to Einstein, gravity is not a forceit is a geometrical property of space-time itself. Loop quantum gravity is an attempt to develop a quantum hypothesis of gravity based directly on Einstein's geometric formulation.…”