Abstract
Background Independence is a sine qua non for every satisfactory theory of Quantum Gravity. In particular if one tries to establish a corresponding notion of Wilsonian renormalization, or coarse graining, it presents a major conceptual and technical difficulty usually. In this paper we adopt the approach of the gravitational Effective Average Action and demonstrate that generically coarse graining in Quantum Gravity and in standard field theories on a non-dynamical spacetime are profoundly different. By means of a concrete example, which in connection with the cosmological constant problem is also interesting in its own right, we show that the surprising and sometimes counterintuitive implications of Background Independent coarse graining are neither restricted to high energies, nor to strongly nonperturbative regimes. In fact, while our approach has been employed in most studies of Asymptotic Safety, this particular ultraviolet behaviour plays no essential role in the present context.
Highlights
The perhaps most remarkable feature of classical General Relativity is its ability to select and to describe the stage upon which all physics, both gravitational and non-gravitational, takes place
Because no large numbers are involved in the renormalization 0 → 2 0, we can say that it is incorrect to claim on the basis of the traditional argument that a small value of the cosmological constant is necessarily afflicted by a naturalness problem [26]
We emphasized that what defines modern Quantum Gravity and makes it radically different from all present theories of particle physics is the key desideratum of Background Independence
Summary
Independent RG and CC non-renormalizability of perturbatively quantized General Relativity and the problems in finding a satisfactory microscopic theory of Quantum Gravity of any other sort. (2) In this paper, we advocate the point of view that Quantum Gravity, regarded as a non-perturbative and Background Independent theory, can have substantial implications well beyond the areas envisaged in the past, questions of ultraviolet renormalizability, or tiny loop corrections due to gravitons To support this view, we analyzed the gravitational impact of vacuum fluctuations as an exemplary problem. (4) In this paper, we give a detailed account of the corresponding notion of Background Independent coarse graining, and we illustrate the discussion by studying explicitly the case where the self-consistent background metric is determined essentially by the cosmological constant and its RG flow D4x gφ (x) Rkφ (x), without resorting to an explicit mode decomposition, with the pseudo-differential operator
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