In this work we investigate the spontaneous symmetry breaking (SSB) induced by a classical background spacetime’s curvature, via the two particle irreducible (2PI) nonperturbative effective action formalism. We use the standard Schwinger-DeWitt local expansion of the Feynman propagator, appropriate to probe the effect of spacetime curvature on the local or short scale physics. Recently it was shown using perturbative computations that such SSB is possible with a scalar with a quartic self interaction, positive rest mass squared, and positive nonminimal coupling. Here we confirm in the two loop Hartree approximation that curvature can indeed induce SSB for such a theory. SSB for such a model is not possible in a flat spacetime. The 2PI technique does not only resum the self-energy resulting in mass generation, but also resums, as we have discussed, curvature terms through such mass generation. We have explicitly discussed our results in the context of the de Sitter spacetime, although our calculations are valid for any nonsingular curved spacetime. We show that, in contrast to the perturbative results, SSB is possible with a vanishing nonminimal coupling. These results are further extended to the case of an $O(N)$ symmetric scalar field theory. Restoration of the broken symmetry in the thermal case is also briefly discussed.

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• Feynman diagrams
• Finite temperature field theory
• Inflation
• Large-N expansion in field theory
• Quantum cosmology
• Quantum field theory
• Quantum fields in curved spacetime
• Renormalization
• Resummation methods
• Schwinger-Dyson equations