Scaling solutions for gauge invariant flow equations in dilaton quantum gravity (2512.14009v1)

Abstract: We investigate the effects of quantum gravity for models of a scalar singlet coupled to the metric. Such models describe inflation for early cosmology and dynamical dark energy for late cosmology. We work within the ''variable gravity approximation" keeping in the effective action an arbitrary field dependence for terms with up to two derivatives. We focus on the scaling solutions of the gauge invariant functional flow equation which describes the dependence of the effective action on a momentum or length scale. The existence of such solutions is required for the ultraviolet fixed point defining an ultraviolet complete renormalizable quantum field theory for gravity. Our findings strengthen the case for the presence of a ''dilaton quantum gravity fixed point" for which the Planck mass increases proportional to the scalar field for large field values. This fixed point is different from the extended Reuter fixed point with a flat scalar potential and field-independent Planck mass, which is also seen in our setting.