Abstract
We discuss general one and two-loops banana diagrams with arbitrary masses on the de Sitter spacetime by using direct methods of dS quantum field theory in the dimensional regularization approach. In the one-loop case we also compute the effective potential for an O(N) model in d = 4 dimension as an explicit function of the cosmological constant Λ, both exactly and perturbatively up to order Λ. For the two-loop case we show that the calculation is made easy thanks to a remarkable Källén-Lehmann formula that has been in the literature for a while. We discuss the divergent cases at d = 3 using a contiguity formula for generalized hypergeometric functions and we extract the dominant term at d = 4 proving a general formula to deal with a divergent hypergeometric series.
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Cacciatori, S.L., Epstein, H. & Moschella, U. Loops in de Sitter space. J. High Energ. Phys. 2024, 182 (2024). https://doi.org/10.1007/JHEP07(2024)182
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DOI: https://doi.org/10.1007/JHEP07(2024)182