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Euclid is poised to survey galaxies across a cosmological volume ofunprecedented size, providing observations of more than a billion objectsdistributed over a third of the full sky. Approximately 20 million of thesegalaxies will have their spectroscopy available, allowing us to map the 3Dlarge-scale structure of the Universe in great detail. This paper investigatesprospects for the detection of cosmic voids therein and the unique benefit theyprovide for cosmology. In particular, we study the imprints of dynamic andgeometric distortions of average void shapes and their constraining power onthe growth of structure and cosmological distance ratios. To this end, we madeuse of the Flagship mock catalog, a state-of-the-art simulation of the dataexpected to be observed with Euclid. We arranged the data into four adjacentredshift bins, each of which contains about 11000 voids and estimated thestacked void-galaxy cross-correlation function in every bin. Fitting alinear-theory model to the data, we obtained constraints on $f/b$ and $D_M H$,where $f$ is the linear growth rate of density fluctuations, $b$ the galaxybias, $D_M$ the comoving angular diameter distance, and $H$ the Hubble rate. Inaddition, we marginalized over two nuisance parameters included in our model toaccount for unknown systematic effects. With this approach, Euclid will be ableto reach a relative precision of about 4% on measurements of $f/b$ and 0.5% on$D_M H$ in each redshift bin. Better modeling or calibration of the nuisanceparameters may further increase this precision to 1% and 0.4%, respectively.Our results show that the exploitation of cosmic voids in Euclid will providecompetitive constraints on cosmology even as a stand-alone probe. For example,the equation-of-state parameter $w$ for dark energy will be measured with aprecision of about 10%, consistent with previous more approximate forecasts.

Euclid: Forecasts from redshift-space distortions and the Alcock-Paczynski test with cosmic voids