Cosmological constant curiosities

I describe two features associated with the renormalization of the cosmological constant. The first is the cancellation of the leading cutoff dependence in zero-point-energy contributions to the cosmological constant – that depending on the fourth power of the cutoff. This is canceled by a term in the path integral measure, which vanishes in dimensional regularization but not when cutoffs are used. The second is a non-local partner to the cosmological constant. Loops of massive particles renormalize the cosmological constant, and also come with an associated non-local effect, schematically given as m^4R(“log”/Box^2)R which is of zeroth order in the derivative expansion. This new operator is active above the scales of the mass of the particle.