LAUSR

In this paper we will consider the most general quadratic curvature action of massless gravity in 3 space time dimensions which is parity invariant and torsion free and contains the same off-shell degrees of freedom as the Einstein-Hilbert action in general relativity. In the ultraviolet, with an appropriate choice of the propagator given by the exponential of an entire function, the point-like curvature singularity can be smoothened by a Gaussian distribution, while in the infrared the theory reduces to that of the predictions of general relativity. We will also show how to embed new massive gravity in ghost free infinite derivative gravity in Minkowski background as one of the infrared limits. Finally, we will provide the perturbative unitarity conditions for infinite derivative gravity in presence of a cosmological constant in deSitter and Anti-deSitter space times in 3 spacetime dimensions.