| Summary: | Abstract We study the behaviour of a light quartically self-interacting scalar field ϕ on curved backgrounds that may be described with the cosmological equation state parameter w. At leading order in the non-perturbative 2PI expansion we find a general formula for the variance ϕ^2 $$ \left\langle {\widehat{\phi}}^2\right\rangle $$ and show for several previously unexplored cases, including matter domination and kination, that the curvature of space can induce a significant excitation of the field. We discuss how the generation of a non-zero variance for w ≠ −1 can be understood as a process of self-regulation of the infrared divergences very similarly to what is known to occur in de Sitter space. To conclude, the appearance of an effective mass due to self-interaction is generic for a light scalar in curved space and can have important implications for reheating, vacuum stability and dark matter generation.
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