Non-local partner to the cosmological constant

Abstract

I show that quantum corrections due to a massive particle generates a non-local term in the gravitational effective action which is of zeroth order in the derivative expansion, much like the cosmological constant. It carries a fixed coefficient which is very much larger than the cosmological constant, and which cannot be fine-tuned. The interaction is active at scales above the particle's mass. This is of the form $m^4(\frac{1}{\square }R{)}_x"<x|\log (\square +m^2)|y>"(\frac{1}{\square }R{)}_y$, and I discuss the meaning of $"<x|\log (\square +m^2)|y>"$ and other aspects of its interpretation.

Comments: 10 pages, 1 figure, comments and relevant references have been added