Although the Standard Model has been a successful description of observedparticles and interactions, there exist open questions and observations which
motivate physics beyond its framework. Of particular importance are the need
for new particles and interactions to explain the origins of the observed baryon
asymmetry, the nature of dark matter, and generation of neutrino mass. This
work is motivated by the coincidental similarity between the baryon asymmetry
and abundance of dark matter which, when taken together with their mysterious
origins, constitutes a cosmological triple puzzle. In this thesis, unique mecha-
nisms which propose new interactions and symmetries between quarks and dark
matter candidates are used to unambiguously address this triple puzzle. These
models predict interesting experimental signatures such as induced proton de-
cay. Additionally, new frameworks which generate neutrino masses such as
gauged $U(1)_{B-L}$ and Dirac leptogenesis, utilize new interactions for neutrinos
which would lead to additional, measurable contributions to $N_\text{eff}$ and $\sum m_\nu$
Motivated by these imprints, this thesis also includes a new mechanism to test
the Dirac nature of the neutrino by correlating variables used by cosmological
and terrestrial probes.