Mathematical analysis

Operations management

Scalar (mathematics)

Asymptotic safety in quantum gravity

Economics

Curvature

Geometry

Quantum

Quantum gravity

Physics

Metric (unit)

Pure mathematics

Mathematics

Mathematical physics

Quadratic equation

Quantum mechanics

Endomorphism

Scalar curvature

Fixed point

Physics Letters B

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 metric and a fluctuating part, the former is chosen to be the one of a four-sphere. Also when scalar, fermion and vector fields are included global quadratic solutions exist as in the pure gravity case for discrete sets of values for some endomorphism parameters defining the coarse-graining scheme. The asymptotic, large-curvature behaviour of the fixed point functions is analysed for generic values of these parameters. Examples for global numerical solutions are provided. A special focus is given to the question whether matter fields might destabilise the ultraviolet fixed point function. Similar to a previous analysis of a polynomial, small-curvature approximation to the fixed point functions different classes for such functions are found.

Asymptotically safe f(R)-gravity coupled to matter II: Global solutions