Determination of Dark Energy by the Einstein Telescope: Comparing with CMB, BAO and SNIa Observations

A design study is currently in progress for a third generation gravitational-wave (GW) detector called Einstein Telescope (ET). An important kind of source for ET will be the inspiral and merger of binary neutron stars (BNS) up to $z \sim 2$. If BNS mergers are the progenitors of short-hard $\gamma$-ray bursts, then some fraction of them will be seen both electromagnetically and through GW, so that the luminosity distance and the redshift of the source can be determined separately. An important property of these `standard sirens' is that they are \emph{self-calibrating}: the luminosity distance can be inferred directly from the GW signal, with no need for a cosmic distance ladder. Thus, standard sirens will provide a powerful independent check of the $\Lambda$CDM model. In previous work, estimates were made of how well ET would be able to measure a subset of the cosmological parameters (such as the dark energy parameter $w_0$) it will have access to, assuming that the others had been determined to great accuracy by alternative means. Here we perform a more careful analysis by explicitly using the potential Planck CMB data as prior information for these other parameters. We find that ET will be able to constrain $w_0$ and $w_a$ with accuracies $\Delta w_0 = 0.099$ and $\Delta w_a = 0.302$, respectively. These results are compared with projected accuracies for the JDEM Baryon Acoustic Oscillations project and the SNAP Type Ia supernovae observations.Comment: 28 pages, 5 figures, 5 tables; Published Versio

Gravitational wave astronomy and cosmology

The first direct observation of gravitational waves' action upon matter has recently been reported by the BICEP2 experiment. Advanced ground-based gravitational-wave detectors are being installed. They will soon be commissioned, and then begin searches for high-frequency gravitational waves at a sensitivity level that is widely expected to reach events involving compact objects like stellar mass black holes and neutron stars. Pulsar timing arrays continue to improve the bounds on gravitational waves at nanohertz frequencies, and may detect a signal on roughly the same timescale as ground-based detectors. The science case for space-based interferometers targeting millihertz sources is very strong. The decade of gravitational-wave discovery is poised to begin. In this writeup of a talk given at the 2013 TAUP conference, we will briefly review the physics of gravitational waves and gravitational-wave detectors, and then discuss the promise of these measurements for making cosmological measurements in the near future.Comment: 11 pages. Proceedings writeup of a talk given at the 2013 Topics in Astroparticle and Underground Physics (TAUP) conferenc

Gravitational waveforms from the inspiral of compact binaries in the Brans-Dicke theory in an expanding Universe

In modified gravity theories, such as the Brans-Dicke theory, the background evolution of the Universe and the perturbation around it are different from that in general relativity. Therefore, the gravitational waveforms used to study standard sirens in these theories should be modified. The modifications of the waveforms can be classified into two categories: wave generation effects and wave propagation effects. Hitherto, the waveforms used to study standard sirens in the modified gravity theories incorporate only the wave propagation effects and ignore the wave generation effects; while the waveforms focusing on the wave generation effects, such as the post-Newtonian waveforms, do not incorporate the wave propagation effects and cannot be directly applied to the sources with non-negligible redshifts in the study of standard sirens. In this work, we construct the consistent waveforms for standard sirens in the Brans-Dicke theory. The wave generation effects include the emission of the scalar breathing polarization $h_b$ and the corrections to the tensor polarizations $h_+$ and $h_\times$; the wave propagation effect is the modification of the luminosity distance for the gravitational waveforms. Using the consistent waveforms, we analyze the parameter estimation biases due to the ignorance of the wave generation effects. Considering the observations by the Einstein Telescope, we find that the ratio of the theoretical bias to the statistical error of the redshifted chirp mass is two orders of magnitude larger than that of the source distance. For black hole-neutron star binary systems like GW191219, the theoretical bias of the redshifted chirp mass can be several times larger than the statistical error.Comment: 20 pages. Accepted for publication in PR

Measuring the Hubble Constant Near and Far in the Era of ELT's

Many of the fundamental physical constants in Physics, as a discipline, are measured to exquisite levels of precision. The fundamental constants that define Cosmology, however, are largely determined via a handful of independent techniques that are applied to even fewer datasets. The history of the measurement of the Hubble Constant (H0), which serves to anchor the expansion history of the Universe to its current value, is an exemplar of the difficulties of cosmological measurement; indeed, as we approach the centennial of its first measurement, the quest for H0 still consumes a great number of resources. In this white paper, we demonstrate how the approaching era of Extremely Large Telescopes (ELTs) will transform the astrophysical measure of H0 from the limited and few into a fundamentally new regime where (i) multiple, independent techniques are employed with modest use of large aperture facilities and (ii) 1% or better precision is readily attainable. This quantum leap in how we approach H0 is due to the unparalleled sensitivity and spatial resolution of ELT's and the ability to use integral field observations for simultaneous spectroscopy and photometry, which together permit both familiar and new techniques to effectively by-pass the conventional 'ladder' framework to minimize total uncertainty. Three independent techniques are discussed -- (i) standard candles via a two-step distance ladder applied to metal, poor stellar populations, (ii) standard clocks via gravitational lens cosmography, and (iii) standard sirens via gravitational wave sources -- each of which can reach 1% with relatively modest investment from 30-m class facilities.Comment: Submitted as an Astro2020 White Paper. Please send comments to both Rachael Beaton & Simon Birrer. Development of this paper occurred as part of the The US Extremely Large Telescope Program Workshop in Oct 2018. We wish to acknowledge NOAO for bringing the co-authors together, in particular the enthusiasm and tireless leadership of Mark Dickinso

Higher signal harmonics, LISA's angular resolution, and dark energy

It is generally believed that the angular resolution of the Laser Interferometer Space Antenna (LISA) for binary supermassive black holes (SMBH) will not be good enough to identify the host galaxy or galaxy cluster. This conclusion, based on using only the dominant harmonic of the binary SMBH signal, changes substantially when higher signal harmonics are included in assessing the parameter estimation problem. We show that in a subset of the source parameter space the angular resolution increases by more than a factor of 10, thereby making it possible for LISA to identify the host galaxy/galaxy cluster. Thus, LISA's observation of certain binary SMBH coalescence events could constrain the dark energy equation of state to within a few percent, comparable to the level expected from other dark energy missions.Comment: 15 pages, no figures. Final version to appear in Phys. Rev.