Ultrahigh precision cosmology from gravitational waves

We show that the Big Bang Observer (BBO), a proposed space-based gravitational-wave (GW) detector, would provide ultraprecise measurements of cosmological parameters. By detecting $\sim 3\times {10}^5$ compact-star binaries, and utilizing them as standard sirens, BBO would determine the Hubble constant to $\sim 0.1\%$, and the dark-energy parameters $w_0$ and $w_a$ to $\sim 0.01$ and $\sim 0.1$, respectively. BBO’s dark-energy figure-of-merit would be approximately an order of magnitude better than all other proposed, dedicated dark-energy missions. To date, BBO has been designed with the primary goal of searching for gravitational waves from inflation, down to the level ${\Omega }_{\mathrm{GW}}\sim {10}^{-17}$; this requirement determines BBO’s frequency band (deci-Hz) and its sensitivity requirement (strain measured to $\sim {10}^{-24}$). To observe an inflationary GW background, BBO would first have to detect and subtract out $\sim 3\times {10}^5$ merging compact-star binaries, out to a redshift $z\sim 5$. It is precisely this carefully measured foreground which would enable high-precision cosmology. BBO would determine the luminosity distance to each binary to $\sim$ percent accuracy. In addition, BBO’s angular resolution would be sufficient to uniquely identify the host galaxy for the majority of binaries; a coordinated optical/infrared observing campaign could obtain the redshifts. Combining the GW-derived distances and the electromagnetically-derived redshifts for such a large sample of objects, out to such high redshift, naturally leads to extraordinarily tight constraints on cosmological parameters. We emphasize that such “standard siren” measurements of cosmology avoid many of the systematic errors associated with other techniques: GWs offer a physics-based, absolute measurement of distance. In addition, we show that BBO would also serve as an exceptionally powerful gravitational-lensing mission, and we briefly discuss other astronomical uses of BBO, including providing an early warning system for all short/hard gamma-ray bursts.

Figure 1

Big-Bang Observer (BBO) consists of four LISA-like triangular constellations orbiting the Sun at 1 AU. The GW background is measured by cross-correlating the outputs of the two overlapping constellations, while time-of-flight across the Solar System gives BBO its angular resolution. A schematic of Decigo (a Japanese proposal similar to BBO) would be almost identical, except that the constellations are 50 times smaller than BBO’s, and their arms form Fabry-Perot cavities.

Figure 2

Amplitude of BBO’s instrumental noise, $\sqrt{f{S}_{\mathrm{h}}(f)}$, compared to the amplitude of the (presubtraction) NS binary foreground (plotted for ${\dot{n}}_0={10}^{-7}{\mathrm{Mpc}}^{-3}{\mathrm{yr}}^{-1}$) and the sought-for cosmic GW background (plotted for ${\Omega }_{\mathrm{GW}}(f)={10}^{-16}$). To reveal this cosmic background, the NS foreground must be subtracted off, with fractional residual of $\lesssim {10}^{-2.5}$.

Figure 3

The total number of NS-NS mergers closer than redshift $z$. The results are normalized to a 3-yr observation period and ${\dot{n}}_0={10}^{-7}{\mathrm{Mpc}}^{-3}{\mathrm{yr}}^{-1}$.

Figure 4

BBO’s angular resolution as a function of redshift, $z$. The three curves show BBO’s median $1\sigma$ angular resolution for three fiducial types of merging compact binaries: BH-BH, BH-NS, and NS-NS.

Figure 5

BBO’s median $1\sigma$ distance accuracy as a function of redshift, $z$, for merging BH-BH, BH-NS, and NS-NS binaries.

Figure 6

Number of galaxies in the BBO error cube, as a function of redshift. Even in the worst case, there is less than one galaxy within $1\sigma$ of a given binary on the sky, and therefore it should be possible to robustly identify the unique host galaxy.

Figure 7

Distance versus redshift for a sample BBO binary population. Distance is shown as distance modulus, and includes both BBO errors and gravitational lensing. The red curve is the true luminosity distance-redshift relation. Notice that lensing causes a small number of binaries to become tremendously magnified (to lower distance modulus), but there is a lower limit to the amount of demagnification.

Figure 8

Top: Measurement accuracy of the Hubble constant, $h$, and the dark-matter density, ${\Omega }_m$. The solid and dashed curves map the $1\sigma$ and $2\sigma$ contours, respectively. The red star denotes the true underlying model. Bottom: Measurement accuracy of the dark-energy equation-of-state parameters $w_0$ and $w_a$.

Figure 9

BBO’s measurement of the gravitational-lensing convergence power spectrum, based just on NS-NS mergers. The red curves show the error bars, for each individual $l$ mode. Each binary is a measure of the gravitational-lensing magnification (convolved with the intrinsic error) along that given line of sight. By observing many binaries, BBO produces a “magnification map” of the sky. This plot shows the power spectrum of this magnification map, which is sensitive to the growth of inhomogeneities in the Universe, as well as potential modifications to gravity.