Determining the Cosmological Constant Using Gravitational Wave Observations: Recent Advancements

It is shown in Einstein gravity that the cosmological constant Λ introduces a graviton mass mg into the theory, a result that will be derived from the Regge-Wheeler-Zerilli problem for a particle falling onto a Kottler-Schwarzschild mass with Λ≠ 0. The value of mg is precisely the Spin-2 gauge line appearing on the Λ-mg 2 phase diagram for Spin-2, the partially massless gauge lines introduced by Deser & Waldron in the (mg 2, Λ) phase plane and described as the Higuchi boundmg 2= 2Λ/3. Note that this graviton is unitary with only four polarization degrees of freedom (helicities ±2, ±1, but not 0 because a scalar gauge symmetry removes it). The conclusion is drawn that Einstein gravity (EG, Λ≠ 0) is a partially massless gravitation theory which has lost its helicity 0 due to a scalar gauge symmetry. That poses a challenge for gravitational wave antennas as to whether they can measure the loss of this gauge symmetry. Also, given the recent results measuring the Hubble constant Ho from LIGO-Virgo data, it is then shown that Λ can be determined from the LIGO results for the graviton mass mg and Ho. This is yet another multi-messenger source for determining the three parameters Λ, mg, and Ho in astrophysics and cosmology, at a time when there is much disparity in measurements of Ho.