Hertzberg, Kachru, Taylor, Tegmarkclaim that they can rule out all types of type IIA models that have been constructed in literature, by their violation of cosmological requirements.
The slow-roll parameter epsilon that should be small is shown to be greater than 27/13 whenever the potential V is positive. You may view this inequality as a quantitative example of our generalized "weak gravity" principle. Slow-roll inflation and de Sitter vacua therefore become impossible. Their theorem makes some assumptions - such as the absence of NS5-branes. They sketch a possible class of models with extra features that could circumvent their no-go theorem. Well, with the right ingredients to obtain mirrors of the type IIB vacua claimed to be alive and well, it should be possible. ;-)
Sociologically speaking, you may want to know that these authors have been saying that type IIB vacua - the canonical KKLT-like and KKLLMT-like landscape - are the phenomenologically more acceptable ones for quite some time.
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