The spatial Functional Renormalization Group and Hadamard states on cosmological spacetimes

Banerjee, Rudrajit; Niedermaier, M.

doi:10.1016/j.nuclphysb.2022.115814

Cited by 12 publications

(6 citation statements)

References 37 publications

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“…In particular, we have constructed an explicit example which shows that parameterizations that work for Euclidean spacetimes fail in the Lorentzian case. This could constitute a major challenge for the Asymptotic Safety program using FRG techniques, which is currently explored almost exclusively in a Euclidean setting (see [65,[72][73][74] for exceptions).…”

Section: Discussionmentioning

confidence: 99%

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Configuration space for quantum gravity in a locally regularized path integral

Knorr¹,

Platania²,

Schiffer³

2022

Preprint

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We discuss some aspects of the metric configuration space in quantum gravity in the background field formalism. We give a necessary and sufficient condition for the parameterization of Euclidean metric fluctuations such that i) the signature of the metric is preserved in all configurations that enter the gravitational path integral, and ii) the parameterization provides a bijective map between full Euclidean metrics and metric fluctuations about a fixed background. For the case of foliatable manifolds, we show how to parameterize fluctuations in order to preserve foliatability of all configurations. Moreover, we show explicitly that preserving the signature on the configuration space for the Lorentzian quantum gravitational path integral is most conveniently achieved by inequality constraints. We discuss the implementation of these inequality constraints in a non-perturbative renormalization group setup.

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Section: Discussionmentioning

confidence: 99%

“…The more challenging investigation of Lorentzian Asymptotic Safety with the FRG is one of the open questions outlined in [64]. First steps towards a Lorentzian formulation have been taken in [31,[65][66][67][68][69][70][71][72][73][74].…”

Section: The Path Integral Over Metricsmentioning

confidence: 99%

Configuration space for quantum gravity in a locally regularized path integral

Knorr¹,

Platania²,

Schiffer³

2022

Preprint

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“…ADM-formalism [18][19][20][21][22][23] and covariant computations utilizing a foliation gauge fixing [24][25][26]. It is also closely related to the Lorentzian signature computations based on the Wetterich equation [27][28][29]. At the technical level, these computations are significantly more complex than their counterparts in the covariant setting reviewed in [16].…”

Section: Jhep09(2023)064mentioning

confidence: 99%

Foliated asymptotically safe gravity in the fluctuation approach

Saueressig,

Wang

2023

J. High Energ. Phys.

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The gravitational asymptotic safety program envisions a high-energy completion of gravity based on a non-Gaussian renormalization group fixed point. A key step in this program is the transition from Euclidean to Lorentzian signature spacetimes. One way to address this challenge is to formulate the quantum theory based on the Arnowitt-Deser-Misner decomposition of the metric field. This equips the Euclidean spacetime with a preferred direction which may serve as the time-direction in the Lorentzian setting. In this work we use the Wetterich equation in order to compute the renormalization group flow of the graviton two-point function. The resulting beta functions possess a non-Gaussian renormalization group fixed point suitable for rendering the theory asymptotically safe. The phase diagram underlying the flow of the two-point function is governed by the interplay between this non-Gaussian fixed point, the Gaussian fixed point, and an infrared fixed point. The latter ensures that the renormalized squared graviton mass cannot take negative values. These results are in qualitative agreement with fluctuation computations carried out in the covariant setting. We take this as non-trivial evidence that the asymptotic safety mechanism remains intact when considering quantum gravity on spacetimes carrying a foliation structure. Technically, our work constitutes the first fluctuation computation carried out within the ADM-framework. Therefore, we also provide a detailed discussion of the conceptual framework, highlighting the elements which differ from fluctuation computations in the covariant setting.

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“…Yet another avenue is a purely spatial coarse graining that would leave time dependencies untouched, see ref. [31] for recent progress in a gravitational context. For a different, but likewise state-sensitive approach, see ref.…”

Section: Jhep08(2022)040mentioning

confidence: 99%

The spectral geometry of de Sitter space in asymptotic safety

Ferrero

Reuter

2022

J. High Energ. Phys.

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Within the functional renormalization group approach to Background Independent quantum gravity, we explore the scale dependent effective geometry of the de Sitter solution dS4. The investigation employs a novel approach whose essential ingredient is a modified spectral flow of the metric dependent d’Alembertian, or of similar hyperbolic kinetic operators. The corresponding one-parameter family of spectra and eigenfunctions encodes information about the nonperturbative backreaction of the dynamically gravitating vacuum fluctuations on the mean field geometry of the quantum spacetime. Used as a diagnostic tool, the power of the spectral flow method resides in its ability to identify the scale dependent subsets of field modes that supply the degrees of freedom which participate in the effective field theory description of the respective scale. A central result is that the ultraviolet of Quantum Einstein Gravity comprises far less effective degrees of freedom than predicted (incorrectly) by background dependent reasoning. The Lorentzian signature of dS4 is taken into account by selecting a class of renormalization group trajectories which are known to apply to both the Euclidean and a Lorentzian version of the approach. Exploring the quantum spacetime’s spatial geometry carried by physical fields, we find that 3-dimensional space disintegrates into a collection of coherent patches which individually can, but in their entirety cannot be described by one of the effective average actions occurring along the renormalization group trajectory. A natural concept of an entropy is introduced in order to quantify this fragmentation effect. Tentatively applied to the real Universe, surprising analogies to properties of the observed cosmic microwave background are uncovered. Furthermore, a set of distinguished field modes is found which, in principle, has the ability to transport information about the asymptotic fixed point regime from the ultraviolet, across almost the entire “scale history”, to cosmological distances in the observed Universe.

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The spatial Functional Renormalization Group and Hadamard states on cosmological spacetimes

Cited by 12 publications

References 37 publications

Configuration space for quantum gravity in a locally regularized path integral

Configuration space for quantum gravity in a locally regularized path integral

Foliated asymptotically safe gravity in the fluctuation approach

The spectral geometry of de Sitter space in asymptotic safety

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