We study quantum modifications to cosmology in a Friedmann-Robertson-Walker
universe with and without scalar fields by taking the renormalisation group
running of gravitational and matter couplings into account. We exploit the
Bianchi identity to relate the renormalisation group scale with scale factor
and derive the improved cosmological evolution equations. We find two types of
cosmological fixed points where the renormalisation group scale either freezes
in, or continues to evolve with scale factor. We discuss the implications of
each of these, and classify the different cosmological fixed points with and
without gravity displaying an asymptotically safe renormalisation group fixed
point. We state conditions of existence for an inflating ultraviolet
cosmological fixed point for Einstein gravity coupled to a scalar field. We
also discuss other fixed point solutions such as "scaling" solutions, or fixed
points with equipartition between kinetic and potential energies.Comment: 8 pages; v2: explanations and references added, accepted for
publication in JCA
