adequate choices of the relevant parameters [@Lattanzi:2007ux; @Lattanzi:2013uza; @Audren:2014bca], the Majoron decay lifetime constraints ranging from $\tau_J > 50-160\,\mathrm{Gyr}$. Using N-body simulations one can show that Majoron as a dark matter leads to a viable alternative to the $\Lambda$CDM scenario, with predictions that can differ substantially on small scales [@Kuo:2018fgw].

Finally we mention that, in addition to dark matter, the Majoron picture may also provide a solution to other cosmological drawbacks of the Standard Model, such as inflation. The role of the Majoron has also been discussed in the context of leptogenesis [@Sierra:2014sta]. Moreover, in Ref. [@Boucenna:2014uma], it was shown that in seesaw Majoron models, inflation and dark matter can have a common origin, connected to the neutrino mass generation scheme.

The Minimal Scotogenic Seesaw {#sec:scoto}
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The minimal scotogenic seesaw model proposed in Ref. [@Rojas:2018wym] is based on the combination of the simplest (3,1) version of the seesaw mechanism [@Schechter:1980gr] with the minimal scotogenic model [@Ma:2006km]. The scotogenic seesaw model has a viable WIMP dark matter candidate and can also account for the observed neutrino masses, both features being closely related. For example, the “atmospheric” mass scale arises at the tree level from the (3,1) seesaw mechanism, while the 