Related papers: The functional $f(R)$ approximation
We study an $f(R)$ approximation to asymptotic safety, using a family of non-adaptive cutoffs, kept general to test for universality. Matching solutions on the four-dimensional sphere and hyperboloid, we prove properties of any such global…
We explain how to find the asymptotic form of fixed point solutions in functional truncations, in particular $f(R)$ approximations. We find that quantum fluctuations do not decouple at large $R$, typically leading to elaborate asymptotic…
In the asymptotic safety programme for quantum gravity, it is important to go beyond polynomial truncations. Three such approximations have been derived where the restriction is only to a general function f(R) of the curvature R>0. We…
Finite dimensional truncations and the single field approximation have thus far played dominant roles in investigations of asymptotic safety for quantum gravity. This thesis is devoted to exploring asymptotic safety in infinite dimensional,…
In this work we study a significantly enlarged truncation of conformally reduced quantum gravity in the context of Asymptotic Safety, including all operators that can be resolved in such a truncation including up to the sixth order in…
This thesis is devoted to exploring various fundamental issues within asymptotic safety. Firstly, we study the reconstruction problem and present two ways in which to solve it within the context of scalar field theory, by utilising a…
Ultraviolet fixed point functions of the functional renormalisation group equation for $f(R)$-gravity coupled to matter fields are discussed. The metric is split via the exponential parameterisation into a background and a fluctuating…
Being interested in the compatibility of Asymptotic Safety with Hilbert space positivity (unitarity), we consider a local truncation of the functional RG flow which describes quantum gravity in $d>2$ dimensions and construct its limit of…
The current research of fractional Sturm-Liouville boundary value problems focuses on the qualitative theory and numerical methods, and much progress has been recently achieved in both directions. The objective of this paper is to explore a…
The Asymptotic Safety hypothesis states that the high-energy completion of gravity is provided by an interacting renormalization group fixed point. This implies non-trivial quantum corrections to the scaling dimensions of operators and…
We summarize the status of constructing fixed functionals within the f(R)-truncation of Quantum Einstein Gravity in three spacetime dimensions. Focusing on curvatures much larger than the IR-cutoff scale, it is shown that the fixed point…
In this thesis we investigate various fundamental aspects of asymptotically safe quantum gravity, in particular the compatibility of Asymptotic Safety with the requirements for background independence and unitarity. The first part contains…
Asymptotic Safety implies that observables including scattering amplitudes remain finite at the highest energy scales. Traditionally, this feature is connected to an interacting fixed point of the Wilsonian renormalization group that…
Modern density functional approximations achieve moderate accuracy at low computational cost for many electronic structure calculations. Some background is given relating the gradient expansion of density functional theory to the WKB…
Estimating function inference is indispensable for many common point process models where the joint intensities are tractable while the likelihood function is not. In this paper we establish asymptotic normality of estimating function…
We compute scaling solutions of functional flow equations for quantum gravity in a general truncation with up to four derivatives of the metric. They connect the asymptotically free ultraviolet fixed point, which is accessible to…
In this paper, we obtain analytical approximate black hole solutions in the framework of $f(R)$ gravity and the absence of a cosmological constant. In this area, we apply the equations of motion of the theory to a spherically symmetric…
We study the conformally reduced $R+R^2$ theory of gravity and we show that the theory is asymptotically safe with an ultraviolet critical manifold of dimension three. In particular, we discuss the universality properties of the fixed point…
Over the last years the Asymptotic Safety program has matured into a serious candidate for a quantum theory of gravity compatible with observations. The rapid technical progress in computing renormalisation group flows for gravity and…
Realizing a quantum theory for gravity based on Asymptotic Safety hinges on the existence of a non-Gaussian fixed point of the theory's renormalization group flow. In this work, we use the functional renormalization group equation for the…