Finding bright $z \geq 6.6$ Lyman-$\alpha$ emitters with lensing:
  prospects for Euclid
  We model the $z \geq 6.6$ Ly$\alpha$ luminosity function to estimate the
number of lensed high$-z$ Ly$\alpha$ emitters that may be detected by the
Euclid Deep Survey. To span the whole range of possible predictions we exploit
two Ly$\alpha$ luminosity function models and two strong gravitational lensing
models from the literature. We show that the planned Euclid Deep Survey
observing 40 deg$^2$ over the 920-1850 nm wavelength range down to a flux limit
of $F_{lim}=5\times10^{-17}\,$erg s$^{-1}\,$cm$^{-2}$ will enable us to find
between $\sim 0.85$ and $\sim 1.82$ deg$^{-2}$ lensed Ly$\alpha$ emitters at $z
\geq 6.6$ depending on the adopted Ly$\alpha$ luminosity function and strong
gravitational lensing model. The obvious [OII], [OIII] and H$\beta$
contaminants of the Ly$\alpha$ lensed population will be identified with the
help of Euclid's spectral resolving power, while the SKA will enable the
identification of the interloper population of H$\alpha$ emitters. By combining
Euclid and the SKA, we will thus be able to identify, for the first time, a
sample of $\sim 34$ to $\sim 73$ lensed Ly$\alpha$ emitters at $z \geq 6.6$.
