Determining the Cosmological Constant Using Gravitational Wave Observations
- 1 Johnson Space Center, NASA, Houston, TX, USA
Abstract
It is shown in Einstein gravity that the cosmological constant Λ 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 Λ ≠ 0. The value of mg is precisely the Spin-2 gauge line appearing on the Λ - <span style="white-space:nowrap;">m<sup>2</sup><sub style="margin-left:-6px;">g</sub></span> phase diagram for Spin-2, the partially massless gauge lines introduced by Deser & Waldron in the <span style="white-space:nowrap;">m<sup>2</sup><sub style="margin-left:-6px;">g</sub></span> , Λ ) phase plane and described as the Higuchi bound <span style="white-space:nowrap;">m<sup>2</sup><sub style="margin-left:-6px;">g</sub></span> = 2 Λ /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 H o from LIGO-Virgo data, it is then shown that Λ 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 Λ , m g , and H o in astrophysics and cosmology, at a time when there is much disparity in measurements of H o .
- Regge, T. and Wheeler, J.A. (1957) Physical Review, 108, 1063. https://doi.org/10.1103/PhysRev.108.1063
- Peters, P.C. (1966) Physical Review, 146, 938. https://doi.org/10.1103/PhysRev.146.938
- Isaacson, R.A. (1968) Physical Review, 166, 1263. https://doi.org/10.1103/PhysRev.166.1272
- Zerilli, F.J. (1970) Physical Review D, 2, 2141. https://doi.org/10.1103/PhysRevD.2.2141
- Zerilli, F.J. (1970) Physical Review Letters, 24, 737. https://doi.org/10.1103/PhysRevLett.24.737
- Penrose, R. (1964) Conformal Treatment of Infinity. In: DeWitt, C.B., Ed., Relativity, Groups, & Topology, Gordon & Breach, London, 565-584.
- Gibbons, G.W. and Hawking, S. (1977) Physical Review D, 15, 2738. https://doi.org/10.1103/PhysRevD.15.2738
- Weinberg, S. (1989) Reviews of Modern Physics, 61, 1. https://doi.org/10.1103/RevModPhys.61.1
- Wilson, T.L. (1973) Gravitational Radiation Theory. Master’s Thesis, Rice University, Houston. Available Online as NASA TMX-58132.
- 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
- Deser, S. and Waldron, A. (2001) Physical Review Letters, 87, Article ID: 031601. https://doi.org/10.1103/PhysRevLett.87.031601
- Deser, S. and Waldron, A. (2001) Physics Letters B, 508, 347-353. https://doi.org/10.1016/S0370-2693(01)00523-8
- Deser, S. and Waldron, A. (2001) Physics Letters B, 513, 137-141. https://doi.org/10.1016/S0370-2693(01)00756-0
- Deser, S. and Waldron, A. (2001) Nuclear Physics B, 607, 577-604. https://doi.org/10.1016/S0550-3213(01)00212-7
- Deser, S. and Waldron, A. (2002) Nuclear Physics B, 631, 369-387. https://doi.org/10.1016/S0550-3213(02)00199-2
- Deser, S. and Waldron, A. (2003) Nuclear Physics B, 662, 379-392. https://doi.org/10.1016/S0550-3213(03)00348-1
- Deser, S. and Waldron, A. (2004) Physics Letters B, 603, 30-34. https://doi.org/10.1016/j.physletb.2004.10.007
- Higuchi, A. (1987) Nuclear Physics B, 282, 397-436. https://doi.org/10.1016/0550-3213(87)90691-2