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Illuminating the Dark Sector: Understanding Modified Gravity Signatures with Cross-Correlations of Gravitational Waves and Large-Scale Structure

Chiara De Leo, Guadalupe Cañas-Herrera, Anna Balaudo, Matteo Martinelli, Alessandra Silvestri, Tessa Baker

Abstract

We investigate the synergy between large-scale structure (LSS) observations and gravitational wave (GW) events for testing modified gravity. In particular, we forecast the LSS $\times$ GW cross-correlation signal using Stage-IV LSS surveys, such as Euclid, in combination with future detections from the Einstein Telescope. This cross-correlation provides a novel probe of fundamental physics, potentially revealing deviations from the $Λ$CDM paradigm that may not be accessible through electromagnetic observations alone. We describe the considered modified gravity scenarios, the relevant LSS and GW observables, and the synthetic forecast methodology. Our results demonstrate that combining LSS and GWs can significantly enhance constraints on departures from General Relativity, opening a new window for multi-messenger cosmology. We further assess the observational requirements GW experiments must meet to improve upon constraints obtainable from LSS alone.

Illuminating the Dark Sector: Understanding Modified Gravity Signatures with Cross-Correlations of Gravitational Waves and Large-Scale Structure

Abstract

We investigate the synergy between large-scale structure (LSS) observations and gravitational wave (GW) events for testing modified gravity. In particular, we forecast the LSS GW cross-correlation signal using Stage-IV LSS surveys, such as Euclid, in combination with future detections from the Einstein Telescope. This cross-correlation provides a novel probe of fundamental physics, potentially revealing deviations from the CDM paradigm that may not be accessible through electromagnetic observations alone. We describe the considered modified gravity scenarios, the relevant LSS and GW observables, and the synthetic forecast methodology. Our results demonstrate that combining LSS and GWs can significantly enhance constraints on departures from General Relativity, opening a new window for multi-messenger cosmology. We further assess the observational requirements GW experiments must meet to improve upon constraints obtainable from LSS alone.
Paper Structure (19 sections, 34 equations, 11 figures, 2 tables)

This paper contains 19 sections, 34 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Beyond-LambdaCDM: phenomenological framework
  3. Description of the cosmological observables
  4. Photometric Large-Scale Structure observables
  5. Gravitational Waves observables
  6. Cross-correlation of photometric large-scale structure surveys with gravitational waves
  7. Methodology
  8. Evaluation of the posterior probability distribution
  9. Synthetic data generation
  10. Photometric Large-Scale Structure survey
  11. Gravitational Wave sources
  12. Data, models and sampled parameters
  13. Results
  14. $\Lambda$CDM
  15. $\mu\Sigma$CDM
  16. ...and 4 more sections

Figures (11)

  • Figure 1: Representative redshift distributions of galaxies and gravitational waves for the specifics in \ref{['N_gal']} and \ref{['eq:n_gw']} with $z_0=\frac{0.9}{\sqrt{2}}$ and $z_0=1.5$ respectively. The galaxy one is divided in $10$ redshift bins as in EuclidPreparationForecast, while the gravitational waves one into $6$.
  • Figure 2: Contribution to the angular power spectra for LSS$\times$GW in 3 redshift bins $i=[1,3,6]$, evaluated taking the observables distribution shown above in a $\Lambda$CDM scenario. The plot displays 9 spectra corresponding to galaxy observables (blue), GW observables (purple), and their cross-correlation (green), we do not show the GW-NC$\times$GW-WL term. However, the full $10 \times 2$pt is considered in the analysis.
  • Figure 3: Impact of the cosmological model on the angular power spectra coefficients for galaxies (blue), from GWs (purple), and their cross-correlation (green). The figure shows the relative difference in $C_{ij}^{\rm AB}(\ell)$, as defined in Eq. \ref{['eq:C_ls']}, between a standard $\Lambda$CDM cosmology and a $\mu\Sigma$CDM model. The source distributions used are the same as in \ref{['fig:Cls_plot']}. The $\mu\Sigma$CDM model corresponds to a $\Lambda$CDM background with modified growth and lensing parameters, characterized by $\mu_0= 0.64$ and $\Sigma_0 =0.61$. These values are the upper limits of DESY3 Table IV.
  • Figure 4: Relative change in the forecast error on $\Sigma_0$ when combining LSS and GW data, compared to using LSS alone. Each subplot shows the effect of varying two parameters while keeping the third fixed at the reference value used in the final configuration. The relative error is computed with Eq. \ref{['eq:rel_err']} and in the plot it is shown in percentage.
  • Figure 5: Forecast of the constraints for the $\Lambda$CDM model for the cosmological parameters $H_0,\,\Omega_ch^2,\,\sigma_8$ using LSS only -3 $\times$ 2 pt- (pink shaded) and LSS and GW probes -10 $\times$ 2 pt- (bordeaux-dashed).
  • ...and 6 more figures