A Class of Renormalization Group Invariant Scalar Field Cosmologies

We present a class of scalar field cosmologies with a dynamically evolving Newton parameter $G$ and cosmological term $\Lambda$. In particular, we discuss a class of solutions which are consistent with a renormalization group scaling for $G$ and $\Lambda$ near a fixed point. Moreover, we propose a modified action for gravity which includes the effective running of $G$ and $\Lambda$ near the fixed point. A proper understanding of the associated variational problem is obtained upon considering the four-dimensional gradient of the Newton parameter.