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We investigate the high-energy properties of matter theories coupled to quantum gravity. Specifically, we show that quantum gravity fluctuations generically induce matter self-interactions in a scalar theory. Our calculations apply within asymptotically safe quantum gravity, where our results indicate that the UV is dominated by an interacting fixed point, with nonvanishing gravitational as well as matter couplings. In particular, momentum-dependent scalar self-interactions are nonzero and induce a nonvanishing momentum-independent scalar potential. Furthermore, we point out that terms of this type can have observable consequences in the context of scalar-field driven inflation, where they can induce potentially observable non-Gaussianities in the cosmic microwave background.
Astrid Eichhorn (Thu,) studied this question.