4D models of de Sitter uplift

It was shown in [1] that the modified 4D version of the Kachru, Kallosh, Linde, and Trivedi (KKLT) model proposed in [2] is inconsistent for large values of the parameter c advocated in [2], since there is a point in the moduli space where vertical bar DSW vertical bar(2) vanishes. The authors responded with yet another modification of the 4D KKLT model [3]. However, for large c, this model suffers from an even worse problem: not only is there a point in the moduli space where vertical bar DSW vertical bar(2) vanishes, there is also a region in the moduli space where vertical bar DSW vertical bar(2) is negative. Meanwhile, for small c these models have de Sitter (dS) vacua. We construct improved models, which are fully consistent for all values of parameters, just as the original version of the KKLT model, using a nilpotent superfield. These models have a family of dS vacua for a broad range of parameter values. Thus, the results of the analysis of all presently available consistent generalizations of the 4D KKLT model, in the domain of their validity, confirm the existence of dS vacua in the KKLT scenario.