Foliated asymptotically safe gravity in the fluctuation approach

Abstract

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.

Weak-gravity bound in asymptotically safe gravity-gauge systems

“…Fourth, the constraints on the gravitational parameter space can be compared with other phenomenological constraints, such as, e.g., viability of the Standard Model of particle physics [128][129][130][131]. Fifth, instead of working in a Euclidean regime, beta functions could be calculated either in the presence of a (Euclidean) foliation which ensures that a continuation to Lorentzian signature is more readily available, as in [29,30,[132][133][134][135][136][137][138], or even directly in Lorentzian signature [64], see also [139][140][141][142]. By carrying out this program, we can collect evidence as to whether asymptotically safe gravity constitutes a physically viable quantum theory of gravity.…”

“…Following a proposal by Weinberg [4] and early evidence in 2+ϵ dimensions [6][7][8], see also [9][10][11] for recent studies, a breakthrough came with Reuter's adaptation of functional Renormalization Group techniques [12][13][14] to quantum gravity [5]. With these techniques, compelling evidence for the requisite interacting RG fixed point has been collected, both in pure gravity and in gravity-matter theories, see [15][16][17][18][19][20][21][22][23] for early evidence and [24][25][26][27][28][29][30][31][32] and references therein for the most recent evidence, as well as [33][34][35][36][37][38][39][40][41] for recent reviews. There is a critical open question, namely whether the theory is physically viable in that it respects causality and unitarity.…”