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One-loop $λϕ^4$ theory in Robertson-Walker spacetimes: adiabatic regularization and analytic approximation

Carmen Molina-Paris·Paul R. Anderson·Stephen A. Ramsey
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Abstract

The renormalization of a scalar field theory with a quartic self-coupling (a $λϕ^4$ theory) via adiabatic regularization in a general Robertson-Walker spacetime is discussed. The adiabatic counterterms are presented in a way that is most conducive to numerical computations. A variation of the adiabatic regularization method is presented which leads to analytic approximations for the energy-momentum tensor of the field and the quantum contribution to the effective mass of the mean field. Conservation of the energy-momentum tensor for the field is discussed and it is shown that the part of the energy-momentum tensor which depends only on the mean field is not conserved but the full renormalized energy-momentum tensor is conserved as expected and required by the semiclassical Einstein's equation. It is also shown that if the analytic approximations are used then the resulting approximate energy-momentum tensor is conserved. This allows a self-consistent backreaction calculation to be performed using the analytic approximations. The usefulness of the approximations is discussed.

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Carmen Molina-Paris, Paul R. Anderson, Stephen A. Ramsey. 1999-08-11. One-loop $λϕ^4$ theory in Robertson-Walker spacetimes: adiabatic regularization and analytic approximation. https://doi.org/10.1103/physrevd.61.127501

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