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We investigate the exoplanet candidate TOI-1422b, which was discovered by theTESS space telescope around the high proper-motion G2V star TOI-1422 ($V=10.6$mag), 155pc away, with the primary goal of confirming its planetary nature andcharacterising its properties. We monitored TOI-1422 with the HARPS-Nspectrograph for 1.5 years to precisely quantify its radial velocity variation.The radial velocity measurements are analyzed jointly with TESS photometry andwe also check for blended companions through high-spatial resolution imagesusing the AstraLux instrument. We estimate that the parent star has a radiusand a mass of $R^*=1.019_{-0.013}^{+0.014} R_{\odot}$,$M^*=0.981_{-0.065}^{+0.062} M_{\odot}$, respectively. Our analysis confirmsthe planetary nature of TOI-1422b and also suggests the presence of aNeptune-mass planet on a more distant orbit, the candidate TOI-1422c, which isnot detected in TESS light curves. The inner planet, TOI-1422b, orbits on aperiod $P_{\rm b}=12.9972\pm0.0006$ days and has an equilibrium temperature$T_{\rm eq, b}=867\pm17$ K. With a radius of $R_{\rm b}=3.96^{+0.13}_{-0.11}R_{\oplus}$, a mass of $M_{\rm b}=9.0^{+2.3}_{-2.0} M_{\oplus}$ and,consequently, a density of $\rho_{\rm b}=0.795^{+0.290}_{-0.235}$ g cm$^{-3}$,it can be considered a warm Neptune-size planet. Compared to other exoplanetsof similar mass range, TOI-1422b is among the most inflated ones and we expectthis planet to have an extensive gaseous envelope that surrounds a core with amass fraction around $10\%-25\%$ of the total mass of the planet. The outernon-transiting planet candidate, TOI-1422c, has an orbital period of $P_{\rmc}=29.29^{+0.21}_{-0.20}$ days, a minimum mass, $M_{\rm c}\sin{i}$, of$11.1^{+2.6}_{-2.3} M_{\oplus}$, an equilibrium temperature of $T_{\rm eq,c}=661\pm13$ K and, therefore, if confirmed, it could be considered as anotherwarm Neptune.

The GAPS Programme at TNG XL: A puffy and warm Neptune-sized planet and an outer Neptune-mass candidate orbiting the solar-type star TOI-1422