Precision of Hubble constant derived using black hole binary absolute distances and statistical redshift information

Abstract

Measured gravitational waveforms from black hole binary inspiral events directly determine absolute luminosity distances. To use these data for cosmology, it is necessary to independently obtain redshifts for the events, which may be difficult for those without electromagnetic counterparts. Here it is demonstrated that certainly in principle, and possibly in practice, clustering of galaxies allows extraction of the redshift information from a sample statistically for the purpose of estimating mean cosmological parameters, without identification of host galaxies for individual events. We extract mock galaxy samples from the 6th Data Release of the Sloan Digital Sky Survey resembling those that would be associated with inspiral events of stellar mass black holes falling into massive black holes at redshift z ≈ 0.1 to 0.5. A simple statistical procedure is described to estimate a likelihood function for the Hubble constant H0: each galaxy in a LISA error volume contributes linearly to the log likelihood for the source redshift, and the log likelihood for each source contributes linearly to that of H0. This procedure is shown to provide an accurate and unbiased estimator of H0. It is estimated that a precision better than one percent in H0 may be possible if the rate of such events is sufficiently high, on the order of 20 to z = 0.5.

Reducing the weak lensing noise for the gravitational wave Hubble diagram using the non-Gaussianity of the magnification distribution

“…This question has been considered by several authors, including [12,[28][29][30][31], with the importance of weak lensing as the dominant effect in limiting LISA's distance-measurement accuracy first being stressed by Hughes and Holz [32]. The main result of this paper-that previous analyses considerably underestimated the improvement in D L -accuracy that comes from combining several measurements-suggests a reexamination of the LISA case.…”

Observational probes of cosmic acceleration

“…However, both the event rates and the characteristics of the electromagnetic signatures are poorly understood at present. One can also make identifications statistically using large scale structure (MacLeod and Hogan, 2008). A third complication, important for the high S/N observations expected from LISA, is that weak lensing magnification becomes a dominant source of noise at z 1, inducing a scatter in distance of several percent per observed source (Markovic, 1993;Holz and Linder, 2005;Jonsson et al, 2007).…”

Fundamental physics with LISA

“…Advanced LIGO and VIRGO can also do this with inspiralling neutron-star signals, and these observations should yield an independent measurement of the Hubble constant locally, say out to 100 Mpc [12]. Beyond that, LISA can use measurements of EMRI events out to modest redshifts (say z = 0.5, depending on the event rate) to get a much more accurate value for H 0 (accurate to 1% with 20 events) [14]. And with black-hole coalescences at even larger distances, LISA can measure the acceleration of the universe and thereby the present value of the 'dark energy equation of state' [15].…”