Swampland conjectures in hybrid metric-Palatini gravity

In this paper, we study a hybrid combination of Einstein-Hilbert action with curvature scalar $R$, and a function $f(\mathcal{R})$ in Palatini gravity within the context of inflationary scenario, from the Swampland conjecture point of view. This hybrid model has been paid attention in recent cosmological studies, and its applications have been widely studied in the literature. In this regard, using the Swampland conjecture (using ($ C_ {1} $) as the first component of dS swampland conjecture, which is obtained from the first derivative of the potential upon the potential and ($ C_ {2} $) as the second component which is acquired from the second derivative of the potential upon the potential), we investigate the cosmological implications of the present gravity theory, with a suitable potential, in the framework of inflationary scenario to obtain cosmological quantities such as slow-roll parameter, scalar spectral index $(n_{s})$, tensor-to-scalar ratio ($r_{s}$), and then compare them with the cosmological observations. Moreover, we compare the compatibility or incompatibility of the model with observable data, such as Planck, by applying Swampland conjecture to $r_{s}-n_{s}$ , $C_{1,2}-n_{s}$ and $C_{1,2}-r_{s}$ plots.