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On the renormalization procedure for quantum fields with modified dispersion relation in curved spacetimes

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 $<ϕ^2>$ and $<T_{μν}>$ depends on $s$. We first describe our previous analysis for spatially flat Friedman-Robertson-Walker and Bianchi type I metrics. Then we present a new power counting analysis for general background metrics in the weak field approximation.