Cosmological surveys planned for the current decade will provide us with
unparalleled observations of the distribution of galaxies on cosmic
scales, by means of which we can probe the underlying large-scale
structure (LSS) of the Universe. This will allow us to test the
concordance cosmological model and its extensions. However, precision
pushes us to high levels of accuracy in the theoretical modelling of the
LSS observables, in order not to introduce biases in the estimation of
cosmological parameters. In particular, effects such as redshift-space
distortions (RSD) can become relevant in the computation of
harmonic-space power spectra even for the clustering of the
photometrically selected galaxies, as it has been previously shown in
literature studies. In this work, we investigate the contribution of
linear RSD, as formulated in the Limber approximation by
arXiv:1902.07226, in forecast cosmological analyses with the photometric
galaxy sample of the Euclid survey, in order to assess their impact and
quantify the bias on the measurement of cosmological parameters that
neglecting such an effect would cause. We perform this task by producing
mock power spectra for photometric galaxy clustering and weak lensing,
as expected to be obtained from the Euclid survey. We then use a Markov
chain Monte Carlo approach to obtain the posterior distributions of
cosmological parameters from such simulated observations. We find that
neglecting the linear RSD leads to significant biases both when using
galaxy correlations alone and when these are combined with cosmic shear,
in the so-called 3$\times$2pt approach. Such biases can be as large as
$5\,\sigma$-equivalent when assuming an underlying $\Lambda$CDM
cosmology. When extending the cosmological model to include the
equation-of-state parameters of dark energy, we find that the extension
parameters can be shifted by more than $1\,\sigma$.