Topological Defects in Beyond the Standard Models, Gravitational Waves and Pulsar Timing Data

Topological defects such as monopoles, cosmic strings, domain
walls, and various composite structures can be produced during phase
transitions in the early universe in Beyond the Standard Model (BSM)
theories. Composite structures such as monopoles connected by strings and
walls bounded by strings (WBS) can be formed in BSM theories, such as the
grand unified theories (GUTs), depending on the symmetry-breaking
patterns. We will discuss the formation of a network of `quasi-stable'
strings (QSS) in the former case. The gravitational radiation emitted in
the early universe by QSS with a dimensionless string tension $Gmusim
10^{-6}$, is compatible with the exciting evidence of low-frequency
(nanoHertz) gravitational background in PTA data, as well as the recent
LIGO-VIRGO constraints, provided the superheavy strings and monopoles
experience a certain amount of inflation. Finally, we discuss an SO(10)
model where a dimension five operator induces kinetic mixing between the
abelian subgroups at the unification scale. We discuss gauge coupling
unification and proton decay in this model, as well as the appearance of
superheavy quasi-stable strings, which can explain the PTA data.