Cosmography with the Einstein Telescope (0906.4151v1)

Abstract: Einstein Telescope (ET) is a 3rd generation gravitational-wave (GW) detector that is currently undergoing a design study. ET can detect millions of compact binary mergers up to redshifts 2-8. A small fraction of mergers might be observed in coincidence as gamma-ray bursts, helping to measure both the luminosity distance and red-shift to the source. By fitting these measured values to a cosmological model, it should be possible to accurately infer the dark energy equation-of-state, dark matter and dark energy density parameters. ET could, therefore, herald a new era in cosmology.

• The paper introduces how gravitational-wave standard sirens from the Einstein Telescope can bypass the cosmic distance ladder to measure luminosity distances.
• It rigorously simulates compact binary mergers to project precise estimates of key cosmological parameters, including dark energy equation-of-state.
• The study highlights the synergy between gravitational-wave and optical observations, offering a transformative method for cosmological measurements.

Exploring Cosmography with the Einstein Telescope

The paper, "Cosmography with the Einstein Telescope," provides an in-depth analysis of the potential implications of the third-generation gravitational-wave (GW) detector, the Einstein Telescope (ET), on the field of cosmology. The work outlines how ET's capacity to detect compact binary mergers across vast distances could refine our understanding of key cosmological parameters, notably the dark energy equation-of-state and both dark matter and dark energy density parameters.

One of the pivotal aspects of this research is ET's ability to detect millions of compact binary mergers up to redshifts ranging from 2 to 8. A fraction of these events might correlate with gamma-ray bursts, offering a dual way to measure both the luminosity distance and redshift of the event sources. This dual measurement could circumvent traditional step-wise methods of cosmic distance determination, known as the "cosmic distance ladder," which relies on successive "standard candles" with varying reach.

In the domain of cosmology, one of the primary objectives is to understand the geometric and dynamic nature of the universe by associating observed parameters with theoretical cosmological models. The universe at large scale can be assumed to be homogeneous and isotropic, and its large-scale properties can be characterized by the scale factor $a(t)$ and the curvature of spatial sections $k$. In this framework, the Friedman equation stands central, relating the cosmic scale factor $a(t)$ to the energy makeup of the universe.

The research meticulously explores how ET's high sensitivity could allow for a new approach to cosmography through "standard sirens." GW events such as those from chirping signals of binary coalescences enable the measurement of intrinsic properties like amplitude and mass ratio, bypassing errors inherent in the cosmic distance ladder approach. Although gravitational waves provide the luminosity distance, they don't inherently yield redshift. Thus, optical identification remains crucial, portraying the significant synergy needed between gravitational and electromagnetic observations.

The simulations within the paper underscore the impressive capabilities of ET. Through a simulated array of binary neutron star mergers, the paper illustrates substantial promise in determining cosmological parameters with remarkable precision. For instance, the fractional 1-$\sigma$ errors projected for parameters such as $\Omega_{\Lambda}$, $\Omega_{\rm M}$, and $w$ suggest a degree of accuracy that could potentially refine existing models of the universe's expansion, especially if weak lensing corrections are applied.

The implications of this research stretch beyond mere academic curiosity, potentially influencing observational strategies in cosmology. With advancements in GW detection technologies like ET, the traditional reliance on a cosmic distance ladder could be supplanted by more reliable and wide-ranging GW standard sirens. This offers a new frontier for both theoretical and observational cosmology.

This paper plausibly sets the stage for future inquiries into the synergistic use of GW and EM observations in cosmology. Continued refinement of these methodologies, including accounting for rotational effects in black hole and neutron star mergers or diversifying the masses in compact binary system simulations, could provide even further enhancements in parameter accuracy. Ultimately, the work underscores a promising avenue not just for understanding the cosmos but also for redefining the methodologies by which cosmological insights are garnered.