Various paths to the spontaneous growth ofp-form fields

We show that $p$-form fields can go through spontaneous growth due to various couplings in gravity theories, forming a new example of spontaneous tensorization. Generalizing the spontaneous scalarization theory of Damour and Esposito-Farese where the original idea has been applied to different fields from vectors to spinors has received high levels of interest in recent years. We first review this existing literature on spontaneous growth in gravity, and then apply the known mechanisms to $p$-forms. We show that one can induce spontaneous growth in $p$-forms for each of the regularized instability mechanisms, which was not the case for other types of fields. We obtain theories with the common property that they lead to large deviations from general relativity in strong gravity as is usual in spontaneous tensorization. This is especially interesting for gravitational wave observations, a direct probe of this regime.