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Abstract
We review our recent results on the renormalization procedure for a free quantum scalar field with modified dispersion relations in curved spacetimes. For dispersion relations containing up to 2s powers of the spatial momentum, the subtraction necessary to renormalize 〈ϕ2〉 and 〈Tµν〉 depends on s. We first describe our previous analysis for spatially flat Friedmann-Robertson-Walker and Bianchi type I metrics. Then we present a new power counting analysis for general background metrics in the weak field approximation.
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