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**Tim** **R**. **Morris**
Open Access
Regular Article - Theoretical Physics
First Online: 07 August 2018
Received: 14 February 2018
Revised: 13 March 2018
Accepted: 27 July 2018
21

In single-metric approximations to the exact renormalization group (RG) for quantum gravity, it has been not been clear how to treat the large curvature domain beyond the point where the effective cutoff scale k is less than the lowest eigenvalue of the appropriate modified Laplacian. We explain why this puzzle arises from background dependence, resulting in Wilsonian RG concepts...

We construct a manifestly diffeomorphism invariant Wilsonian (Exact) Renor-malization Group for classical gravity, and begin the construction for quantum gravity. We demonstrate that the effective action can be computed without gauge fixing the diffeo-morphism invariance, and also without introducing a background space-time. We compute classical contributions both within a...

Starting from a full renormalised trajectory for the effective average action (a.k.a. infrared cutoff Legendre effective action) Γ k , we explicitly reconstruct corresponding bare actions, formulated in one of two ways. The first step is to construct the corresponding Wilsonian effective action S k through a tree-level expansion in terms of the vertices provided by Γ k . It forms...

Within the conformally reduced gravity model, where the metric is parametrised by a function f (ϕ) of the conformal factor ϕ, we keep dependence on both the background and fluctuation fields, to local potential approximation and \( \mathcal{O}\left({\partial}^2\right) \) respectively, making no other approximation. Explicit appearances of the background metric are then dictated...

I. Hamzaan Bridle
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Juergen A. Dietz
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**Tim** **R**. **Morris**
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School of Physics and Astronomy, University of Southampton
, Highfield, Southampton, SO17 1BJ,
U.K
Working within the familiar local