[Paper Review] Mapping the cosmic expansion history from LIGO-Virgo-KAGRA in synergy with DESI and SPHEREx

Cristina Cigarrán Díaz, Suvodip Mukherjee|arXiv (Cornell University)|Jul 27, 2021

Pulsars and Gravitational Waves Research146 references59 citations

TL;DR

This paper proposes a multi-messenger approach to measure the cosmic expansion history using gravitational wave (GW) sources detected by LIGO-Virgo-KAGRA (LVK) in synergy with spectroscopic galaxy surveys DESI and SPHEREx. By cross-correlating the 3D spatial distribution of dark GW sources (unassociated with electromagnetic counterparts) with galaxy redshift surveys, it achieves ~1.5% precision on the Hubble constant H₀ and ~8% precision on the dark energy equation of state w₀ within five years of observation, with SPHEREx outperforming DESI due to its wider sky coverage.

ABSTRACT

The measurement of the expansion history of the Universe from the redshift unknown gravitational wave (GW) sources (dark GW sources) detectable from the network of exttt{LIGO-Virgo-KAGRA} ( exttt{LVK}) detectors depends on the synergy with the galaxy surveys having accurate redshift measurements over a broad redshift range, large sky coverage, and detectability of fainter galaxies. In this work, we explore the possible synergy of the LVK with the spectroscopic galaxy surveys such as exttt{DESI} and exttt{SPHEREx} to measure the cosmological parameters which are related to the cosmic expansion history and the GW bias parameters. We show that by using the three-dimensional spatial cross-correlation between the dark GW sources and the spectroscopic galaxy samples, we can measure the value of Hubble constant with about $2\%$ and $1.5\%$ precision from exttt{LVK+DESI} and exttt{LVK+SPHEREx} respectively within the five years of observation time with $50\%$ duty-cycle. Similarly, the dark energy equation of state can be measured with about $10\%$ and $8\%$ precision from exttt{LVK+DESI} and exttt{LVK+SPHEREx} respectively. We find that due to the large sky coverage of exttt{SPHEREx} than exttt{DESI}, performance in constraining the cosmological parameters is better from the former than the latter. By combining exttt{Euclid} along with exttt{DESI} and exttt{SPHEREx}, a marginal gain in the measurability of the cosmological parameters is possible from the sources at high redshift ($z\geq 0.9$).

Motivation & Objective

• To develop a robust method for measuring cosmological parameters using dark gravitational wave sources (without electromagnetic counterparts).
• To assess the synergy between LIGO-Virgo-KAGRA (LVK) GW detectors and upcoming spectroscopic surveys DESI and SPHEREx.
• To improve constraints on the Hubble constant H₀ and dark energy equation of state w₀ using cross-correlation of GW sources with galaxy redshift distributions.
• To evaluate the impact of survey sky coverage and redshift depth on cosmological parameter estimation.

Proposed method

• Uses 3D spatial cross-correlation between LVK-detected dark GW sources and galaxy samples from DESI and SPHEREx to infer the clustering redshift of GW sources.
• Applies Bayesian parameter estimation with the Bilby package to model GW signal parameters, including luminosity distance and sky localization, while accounting for non-Gaussian posteriors and parameter degeneracies.
• Implements a cross-correlation likelihood framework that links the spatial distribution of GW events to the redshift distribution of galaxies, enabling redshift inference without direct EM counterparts.
• Models GW bias parameters to account for selection effects and the fact that GW sources may not perfectly trace the underlying dark matter distribution.
• Assumes a 5-year observation period with 50% duty cycle and uses mock GW data based on realistic merger rate densities and detector sensitivities.
• Performs marginalization over GW bias parameters to isolate cosmological constraints on H₀ and w₀, with Ωₘ fixed.

Experimental results

Research questions

• RQ1 Can the Hubble constant H₀ be measured with sub-2% precision using only dark GW sources and galaxy redshift surveys?
• RQ2 How does the performance of H₀ and w₀ estimation depend on the sky coverage and redshift depth of the galaxy survey?
• RQ3 Can the cross-correlation technique robustly infer the redshift of dark GW sources without electromagnetic counterparts?
• RQ4 What is the relative advantage of SPHEREx over DESI in constraining cosmological parameters via GW-galaxy cross-correlation?
• RQ5 How do systematics from waveform modeling and instrument calibration affect the final cosmological constraints?

Key findings

• The combination of LVK with SPHEREx achieves a Hubble constant measurement precision of approximately 1.5% after five years of observation with 50% duty cycle.
• The LVK+DESI combination achieves a Hubble constant precision of about 2%, slightly less precise than SPHEREx due to its smaller sky coverage.
• The dark energy equation of state w₀ can be constrained with approximately 8% precision using LVK+SPHEREx and 10% using LVK+DESI.
• SPHEREx outperforms DESI in cosmological parameter estimation due to its significantly larger sky coverage, which enhances the signal-to-noise of the cross-correlation function.
• The inclusion of Euclid with DESI and SPHEREx provides a marginal improvement in constraining parameters for high-redshift sources (z ≥ 0.9), indicating potential for future multi-survey synergy.
• The method enables the first direct measurement of the GW bias parameter and its redshift dependence, offering a new probe of how GW sources trace the dark matter distribution.