  Recently we have proposed models of topological field theory including
gravity in Mod. Phys. Lett. A 31 (2016) no.37, 1650213 and Phys. Rev. D 96
(2017) no.2, 024009, in order to solve the problem of the cosmological
constant. The Lagrangian densities of the models are BRS (Becchi-Rouet-Stora)
exact and therefore the models can be regarded as topological theories. In the
models, the coupling constants, including the cosmological constant, look as if
they run with the scale of the universe and its behavior is very similar to the
renormalization group. Motivated by these models, we propose new models with an
the infrared fixed point, which may correspond to the late time universe, and
an ultraviolet fixed point, which may correspond to the early universe.
Especially we construct a model with the solutions corresponding to the de
Sitter space-time both in the ultraviolet and the infrared fixed points.
