The Cosmological Constant and Lorentz Invariance of the Vacuum State

One hope to solve the cosmological constant problem is to identify a symmetry principle, based on which the cosmological constant can be reduced either to zero, or to a tiny value. Here, we note that requiring that the vacuum state is Lorentz invariant significantly reduces the theoretical value of the vacuum energy density. Hence, this also reduces the discrepancy between the observed value of the cosmological constant and its theoretical expectation, down from 123 orders of magnitude to 56 orders of magnitude. We find that, at one loop level, massless particles do not yield any contribution to the cosmological constant. Another important consequence of Lorentz symmetry is stabilization of the gravitational hierarchy: the cosmological constant (divided by Newton's constant) does not run as the quartic power of the renormalization group scale, but instead only logarithmically.