Renormalization in theories with modified dispersion relations: weak gravitational fields

D. LÓPEZ NACIR; F. D. MAZZITELLI

Instituto de Astronomía y Física del Espacio (IAFE), Capital Federal, Argentina

Otro; String@ae:XXXV Encuentro; 2009

Instituto de Astronomía y Física del Espacio (IAFE)

We consider a free quantum scalar field satisfying modified dispersion relations in curved spacetimes,  within the framework of Einstein-Aether theory. Using a power counting analysis, we study the divergences in the adiabatic expansion o \langle\phi^2\rangle and \langle T_{\mu\nu}\rangle, working in the weak field approximation. We show that for dispersion relations containing up to 2s powers of the spatial momentum, the subtraction necessary to renormalize these two quantities on general backgrounds depends on s in a qualitatively different way: while \langle\phi^2\rangle becomes convergent for a sufficiently large value of s, the number of divergent terms in the adiabatic expansion of \langle T_{\mu\nu}\rangle increases with s. This property was not apparent in previous results for spatially homogeneous backgrounds.