Neutrino masses and superheavy dark matter in the 3-3-1-1 model

In this work, we interpret the 3-3-1-1 model when the B-L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B-L$$\end{document} and 3-3-1 breaking scales behave simultaneously as the inflation scale. This setup not only realizes the previously achieved consequences of inflation and leptogenesis, but also provides new insights in superheavy dark matter and neutrino masses. We argue that the 3-3-1-1 model can incorporate a scalar sextet, which induces both small masses for the neutrinos via a combined type I and II seesaw and large masses for the new neutral fermions. Additionally, all the new particles have large masses in the inflation scale. The lightest particle among the W-particles that have abnormal (i.e., wrong) B-L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B-L$$\end{document} number in comparison to those of the standard model particles may be superheavy dark matter as it is stabilized by W-parity. The dark matter candidate may be a Majorana fermion, a neutral scalar, or a neutral gauge boson, which was properly created in the early universe due to gravitational effects on the vacuum or thermal production after cosmic inflation.