Inflationary assessment of $F(\mathcal{R},\tilde{\mathcal{R}})$ Einstein-Cartan models

In the framework of $F(\mathcal{R},\tilde{\mathcal{R}})$ Einstein-Cartan gravity with an action depending both of the Ricci scalar and the so-called Holst-invariant curvature we consider models that include cubic terms of the latter in the action and study their inflationary behavior. These terms can have a considerable effect either positive or negative in relation to the agreement with present observational data, depending on parameters. In parameter regions where the quadratic models fail to produce results consistent with observational data, the presence of these additional cubic terms can lead to compatible predictions.