Asymptotically Safe $f(R)$-Gravity Coupled to Matter II: Global Solutions

Understand

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 metric, 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.