During inflation, spacetime is approximately described by de Sitter space
which is conformally invariant with the symmetry group SO(1,4). This symmetry
can significantly constrain the quantum perturbations which arise in the
inflationary epoch. We consider a general situation of single field inflation
and show that the three point function involving two scalar modes and one
tensor mode is uniquely determined, up to small corrections, by the conformal
symmetries. Special conformal transformations play an important role in our
analysis. Our result applies only to models where the inflaton sector also
approximately preserves the full conformal group and shows that this three
point function is a good way to test if special conformal invariance was
preserved during inflation.Comment: 46 page
In Proc Math Sci 129, 70(219), Rakesh Pawar considers and solves a certain diagram extension problem. In this note, we observe that the existence and uniqueness of differential characters (defined as objects which fit into a certain hexagon diagram) follow directly from Rakesh Pawar's results. This provides an alternate proof of a weaker version of J. Simons and D. Sullivan's results (Journal of Topology, 2008, 1:45-56 ). Further, this approach directly shows that the hexagon diagram uniquely determines the differential K-theory groups upto an isomorphism.
Let E → B be a smooth vector bundle of rank n, and let P ∈ I p (GL(n, R)) be a GL(n, R)-invariant polynomial of degree p compatible with a universal integral characteristic class u ∈ H 2p (BGL(n, R), Z). Cheeger-Simons theory associates a rigid invariant in H 2p−1 (B, R/Z) to any flat connection on this bundle. Generalizing this result, Jaya Iyer (Letters in Mathematical Physics, 2016, 106 (1) is the simplicial set of relatively flat connections, thereby associating invariants to families of flat connections. In this article we construct such maps for the cases p < r and p > r + 1 using fiber integration of differential characters. We find that for p > r + 1 case, the invariants constructed here coincide with those obtained by Jaya Iyer, and that in the p < r case the invariants are trivial. We further compare our construction with other results in the literature.
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