Determining the Cosmological Constant Using Gravitational Wave Observations: Recent Advancements

Abstract

It is shown in Einstein gravity that the cosmological constant ? introduces a graviton mass m_g 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 ?? 0. The value of m_g is precisely the Spin-2 gauge line appearing on the ?-m_g² phase diagram for Spin-2, the partially massless gauge lines introduced by Deser & Waldron in the (m_g², ?) phase plane and described as the Higuchi boundm_g²= 2?/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, ?? 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 H_o from LIGO-Virgo data, it is then shown that ? can be determined from the LIGO results for the graviton mass m_g and H_o. This is yet another multi-messenger source for determining the three parameters ?, m_g, and H_o in astrophysics and cosmology, at a time when there is much disparity in measurements of H_o.