Scrutinizing the Cosmological Constant Problem and a possible resolution
(Submitted on 20 Nov 2012 (v1), last revised 13 Dec 2012 (this version, v2))
We suggest a new perspective on the Cosmological Constant Problem by scrutinizing its standard formulation. In classical and quantum mechanics without gravity, there is no definition of the zero point of energy. Furthermore, the Casimir effect only measures how the vacuum energy changes as one varies a geometric modulus. This leads us to propose that the physical vacuum energy in a Friedman-Lemaitre-Robertson-Walker expanding universe only depends on the time variation of the scale factor a(t). Equivalently, requiring that empty Minkowski space is stable is a principle that fixes the ambiguity in the zero point energy. We describe two different choices of vacuum, one of which is consistent with the current universe consisting only of matter and vacuum energy. The resulting vacuum energy density is proportional to (k_c H_0)^2, where k_c is a momentum cut-off and H_0 is the Hubble constant; for a cut-off close to the Planck scale, values of the vacuum energy density in agreement with astrophysical measurements are obtained. Another choice of vacuum is more relevant to the early universe consisting of only radiation and vacuum energy, and we suggest it as a possible model of inflation.