Determining Cosmological Constant Using Gravitational Wave Information

It is shown in Einstein gravity that the cosmological constant Lambda introduces a graviton mass m 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 Lambda. The value of m is precisely the Spin-2 gauge line appearing on the Lambda versus m2 phase diagram for Spin-2, the partially massless gauge lines introduced by Deser & Waldron and described as the Higuchi bound. Note that this graviton is unitary with only four polarization degrees of freedom (helicities plus & minus 2 and 1, but not 0 because a scalar gauge symmetry removes it). The conclusion is drawn that Einstein gravity (with Lambda) 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 Lambda can be determined from the LIGO results for the graviton mass m and Ho. This is yet another multi-messenger source for determining the three parameters Lambda, m, and Ho in astrophysics and cosmology, at a time when there is much disparity in measurements of Ho.