Consistent dS₃ Quantum Gravity: Probing Through Lens Spaces and holographic aspects.

De Sitter quantum gravity is important in order to understand stability of universe in terms of the Hartle-Hawking wave function and has recently emerged as a tool to understand dS3/CFT2. Practically this involves studying the partition function and considering contributions from all possible topologies. Euclideanized (thermal) de Sitter space and its ramifications are incorporated through Lens space topologies. Castro, Maloney et al (arXiv:1103.4620) found the partition function to be divergent for pure spin-2 fields. We, without inclusion of additional matter or topological mass, by introducing a dimensionless coupling made the theory free of divergences. Moreover we extended this work to spin-3 fields also. Through an analytic continuation of the cosmological length scale (Lal, Sahoo, arXiv:1209:4804), its holographic consequences is also studied.