[Paper Review] Prospects of testing late-time cosmology with weak lensing of gravitational waves and galaxy surveys

Anna Balaudo, Alice Garoffolo+3 more|arXiv (Cornell University)|Oct 12, 2022

Pulsars and Gravitational Waves Research4 citations

TL;DR

This paper investigates the potential of combining weak lensing of gravitational waves (GW-WL) with galaxy surveys to test late-time cosmology, particularly modified gravity and dark energy models. It shows that GW-WL can double the accuracy on non-$\Lambda$CDM parameters, achieving sub-percent-level constraints in optimal scenarios, offering a complementary probe to standard sirens and large-scale structure surveys.

ABSTRACT

We investigate the synergy of upcoming galaxy surveys and gravitational wave (GW) experiments in constraining late-time cosmology, examining the cross-correlations between the weak lensing of gravitational waves (GW-WL) and the galaxy fields. Without focusing on any specific GW detector configuration, we benchmark the requirements for the high-precision measurement of cosmological parameters by considering several scenarios, varying the number of detected GW events and the uncertainty on the inference of the source luminosity distance and redshift. We focus on $Λ$CDM and scalar-tensor cosmologies, using the Effective Field Theory formalism as a unifying language. We find that, in some of the explored setups, GW-WL contributes to the galaxy signal by doubling the accuracy on non-$Λ$CDM parameters, allowing in the most favourable scenarios to reach even percent and sub-percent level bounds. Though the most extreme cases presented here are likely beyond the observational capabilities of currently planned individual GW detectors, we show nonetheless that - provided that enough statistics of events can be accumulated - GW-WL offers the potential to become a cosmological probe complementary to LSS surveys, particularly for those parameters that cannot be constrained by other GW probes such as standard sirens.

Motivation & Objective

• To assess the synergistic potential of upcoming galaxy surveys and gravitational wave (GW) experiments in constraining late-time cosmology.
• To evaluate how cross-correlations between weak lensing of gravitational waves (GW-WL) and galaxy fields improve constraints on cosmological parameters.
• To investigate the impact of varying GW event statistics and distance/redshift uncertainty on cosmological parameter estimation.
• To test the effectiveness of GW-WL as a complementary probe to standard sirens and large-scale structure surveys, especially for parameters unconstrained by other GW methods.
• To determine the viability of GW-WL in constraining scalar-tensor theories and $\Lambda$CDM extensions using the Effective Field Theory formalism.

Proposed method

• Uses the Effective Field Theory (EFT) of dark energy to unify and analyze scalar-tensor gravity models, including Horndeski theories.
• Models the cross-correlation between weak lensing of gravitational waves and galaxy overdensity fields to extract cosmological information.
• Varying the number of detected GW events and the uncertainty in luminosity distance and redshift inference to benchmark cosmological constraints.
• Performs Fisher matrix forecasts to estimate the precision of cosmological parameter estimation under different scenarios.
• Compares cosmological constraints across different redshift distributions of GW sources (e.g., $z_0 = 0.5, 1.0, 1.5$) to assess sensitivity to source distribution.
• Evaluates the contribution of GW-WL to constraining parameters like $w_0$, $w_a$, $\Omega_0$, and $\gamma_2^0$ in $\Lambda$CDM and scalar-tensor models.

Experimental results

Research questions

• RQ1 How does the cross-correlation between GW weak lensing and galaxy surveys improve constraints on non-$\Lambda$CDM parameters compared to galaxy surveys alone?
• RQ2 What level of GW event statistics and distance accuracy is required for GW-WL to achieve sub-percent-level bounds on cosmological parameters?
• RQ3 How sensitive are cosmological constraints to the redshift distribution of GW sources, particularly in comparison to standard sirens?
• RQ4 In what scenarios does GW-WL outperform or complement other GW-based cosmological probes, such as standard sirens?
• RQ5 To what extent can GW-WL break degeneracies in modified gravity models that are difficult to constrain with electromagnetic surveys?

Key findings

• In favorable scenarios, GW-WL can double the accuracy on non-$\Lambda$CDM parameters, enabling constraints at the percent and even sub-percent level.
• The most significant improvement in cosmological constraints occurs when there is substantial overlap between the redshift distributions of GW sources and galaxies, with $z_0 = 1.5$ yielding the strongest performance due to higher high-redshift source statistics.
• The case $z_0 = 0.5$ leads to significantly looser constraints due to poor overlap with galaxy distributions, especially at high redshift.
• For $\sigma_{d_L} = 1\%$, GW-WL contributes significantly to constraining $\Omega_0$ and $\gamma_2^0$ across all numbers of GW events, indicating robustness even at low event counts.
• The impact of source distribution is more pronounced in Model I than in Model II, with differences in bounds on $w_a$ and $\Omega_0$ reaching up to 10% for $z_0 = 0.5$ compared to $z_0 = 1.5$.
• While 3rd-generation detectors (e.g., ET, CE) may not achieve sufficient statistics for GW-WL to be competitive, future 4th-generation detectors could make it a viable and complementary cosmological probe.