Two-loop Corrections-to- the Cosmological Constant*

The two-loop contributions to the induced cosmological constant are computed in a matterless Einstein theory of gravity expanded about a Minkowski background with no cosmological term present in the classical action. The regularization-independent cancellation of the contribution to one-loop order is found not to occur to two-loop order. Submitted to Physics Letters B * Work supported by the Department of Energy, contract DE AC03 76SF00515. Introduction The cosmological constant problem is one of the more tenacious problems of modern quantum field theory. In order to account for the observed vanishingly small value one is required, in a perturbative quantum theory-of gravity, to fine tune the classical cosmological constant (A) against an infinite set of counterterms. Ideally, one would prefer a theory in which there was a symmetry that insured the vanishing of all orders of corrections to the cosmological constant. Another possibility would be a prescription to identify the ground state or background field about which a perturbative theory would give a zero cosmological constant to all orders. The first calculation of the one-loop counterterms in a theory with no classical cosmological term in the action was performed by ‘t Hooft and Veltman’l’ using dimensional regularization and the background field method. They found no contribution to this order because all of the contributing diagrams are quartically divergent and hence are set equal to zero within the context of dimensional regularization. A similar calculation was done later by M. Mueller, Ia1 who found that the diagrams that contribute to the cosmological constant vanish even when no regularization method is specified. This occurs because the coefficients of the divergent loop integrals sum to zero; in fact, this cancellation occurs for arbitrary space-time dimensionality. The present letter uses the arbitrary-dimension unregulated quantization procedure of ,M. Mueller. This procedure differs from the formulation of ‘t Hooft and Veltman in that it takes into account the dependence of the measure on the fluctuating metric.