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 - m2g?phase diagram for Spin-2, the partially massless gauge lines introduced by Deser & Waldron in the m2g,?Λ)?phase plane and described as the Higuchi bound m2g= 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
References
[1]
Regge, T. and Wheeler, J.A. (1957) Physical Review, 108, 1063. https://doi.org/10.1103/PhysRev.108.1063
Penrose, R. (1964) Conformal Treatment of Infinity. In: DeWitt, C.B., Ed., Relativity, Groups, & Topology, Gordon & Breach, London, 565-584.
[7]
Gibbons, G.W. and Hawking, S. (1977) Physical Review D, 15, 2738. https://doi.org/10.1103/PhysRevD.15.2738
[8]
Weinberg, S. (1989) Reviews of Modern Physics, 61, 1. https://doi.org/10.1103/RevModPhys.61.1
[9]
Wilson, T.L. (1973) Gravitational Radiation Theory. Master’s Thesis, Rice University, Houston. Available Online as NASA TMX-58132.
[10]
Deser, S. and Nepomechie, R.I. (1983) Physics Letters B, 132, 321-324. https://doi.org/10.1016/0370-2693(83)90317-9 Deser, S. and Nepomechie, R.I. (1984) Annals of Physics, 154, 396-420. https://doi.org/10.1016/0003-4916(84)90156-8
[11]
Deser, S. and Waldron, A. (2001) Physical Review Letters, 87, Article ID: 031601. https://doi.org/10.1103/PhysRevLett.87.031601
[12]
Deser, S. and Waldron, A. (2001) Physics Letters B, 508, 347-353. https://doi.org/10.1016/S0370-2693(01)00523-8
[13]
Deser, S. and Waldron, A. (2001) Physics Letters B, 513, 137-141. https://doi.org/10.1016/S0370-2693(01)00756-0
[14]
Deser, S. and Waldron, A. (2001) Nuclear Physics B, 607, 577-604. https://doi.org/10.1016/S0550-3213(01)00212-7
[15]
Deser, S. and Waldron, A. (2002) Nuclear Physics B, 631, 369-387. https://doi.org/10.1016/S0550-3213(02)00199-2
[16]
Deser, S. and Waldron, A. (2003) Nuclear Physics B, 662, 379-392. https://doi.org/10.1016/S0550-3213(03)00348-1
[17]
Deser, S. and Waldron, A. (2004) Physics Letters B, 603, 30-34. https://doi.org/10.1016/j.physletb.2004.10.007
[18]
Higuchi, A. (1987) Nuclear Physics B, 282, 397-436. https://doi.org/10.1016/0550-3213(87)90691-2
[19]
Higuchi, A. (1989) Nuclear Physics B, 325, 745-765. https://doi.org/10.1016/0550-3213(89)90507-5
[20]
Higuchi, A. (1987) Journal of Mathematical Physics, 28, 1553. https://doi.org/10.1063/1.527513