## Abstract

We have investigated the cosmological constraints that can be expected
from measurement of the cross-correlation of galaxies with cosmic voids
identified in the *Euclid* spectroscopic survey, which will include spectroscopic information for tens of millions of galaxies over 15 000 deg^{2} of the sky in the redshift range 0.9 ≤ *z* < 1.8. We have done this using simulated measurements obtained from the Flagship mock catalogue, the official *Euclid*
mock that closely matches the expected properties of the spectroscopic
dataset. To mitigate anisotropic selection-bias effects, we have used a
velocity field reconstruction method to remove large-scale
redshift-space distortions from the galaxy field before void-finding.
This allowed us to accurately model contributions to the observed
anisotropy of the cross-correlation function arising from galaxy
velocities around voids as well as from the Alcock–Paczynski effect, and
we studied the dependence of constraints on the efficiency of
reconstruction. We find that *Euclid* voids will be able to constrain the ratio of the transverse comoving distance *D*_{M} and Hubble distance *D*_{H} to a relative precision of about 0.3%, and the growth rate *fσ*_{8}
to a precision of between 5% and 8% in each of the four redshift bins
covering the full redshift range. In the standard cosmological model,
this translates to a statistical uncertainty ΔΩ_{m} = ±0.0028 on the matter density parameter from voids, which is better than what can be achieved from either *Euclid*
galaxy clustering and weak lensing individually. We also find that
voids alone can measure the dark energy equation of state to a 6%
precision.

Original language | English |
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Article number | A78 |

Journal | Astronomy and Astrophysics |

Volume | 677 |

Number of pages | 20 |

ISSN | 0004-6361 |

DOIs | |

Publication status | Published - 2023 |

## Keywords

- Cosmological parameters
- Cosmology: observations
- Large-scale structure of Universe
- Surveys