suppressed scalar interaction with the risk of becoming weaker than gravity. Here we list four important applications leaving a more detailed account for a future publication.

Inflation
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We already mentioned that among polynomial potentials, the linear case is the only one that allows for trans-Planckian excursions. So among chaotic inflation models [@chaotic] the linear one is singled out as the unique class which can lead to sufficient inflation. As is well known, linear potentials may yield 50-60 e-folds of inflation with tensor perturbations with $r\simeq 0.07$. This relatively large value will soon be experimentally tested. Note that instead of a purely linear potential one may consider e.g. the potential in examples ii) or iii) above which behave linearly for $|\phi|>M_{\text{p}}$. It is interesting to note that linear potentials do appear in string theory realizations of monodromy inflation, see [@Silverstein:2008sg; @McAllister:2008hb; @McAllister:2014mpa; @Dong:2010in; @Marchesano:2014mla]. There the stability of the potentials against corrections is guaranteed due to shift symmetries. One type of potentials in this class has the form [@McAllister:2008hb] V(b) =  A(1 + B b\^2)\^[1/2]{} where $b$ is a Type IIB (monodromic) axionic field and we set $M_{\text{p}}=1$. A simple way to check the validity of the Strong SWGC, Eq 