We calculate the proton lifetime and discuss topological defects in a wide class of non-supersymmetric (non-SUSY) SO(10) and E(6) Grand Unified Theories (GUTs), broken via left-right subgroups with one or two intermediate scales (a total of 9 different scenarios with and without D-parity), including the important effect of threshold corrections. By performing a goodness of fit test for unification using the two-loop renormalisation group evolution equations (RGEs), we find that the inclusion of threshold corrections significantly affects the proton lifetime, allowing several scenarios, which would otherwise be excluded, to survive. Indeed we find that the threshold corrections are a saviour for many non-SUSY GUTs. For each scenario we analyse the homotopy of the vacuum manifold to estimate the possible emergence of topological defects.

We consider magnetic monopoles and strings that appear in non-supersymmetric SO(10) and E6 grand unified models paying attention to gauge coupling unification and proton decay in a variety of symmetry breaking schemes. The dimensionless string tension parameter Gμ spans the range 10−6− 10−30, where G is Newton’s constant and μ is the string tension. We show how intermediate scale monopoles with mass ∼ 1013− 1014 GeV and flux ≲ 2.8 × 10−16 cm−2s−1sr−1, and cosmic strings with Gμ ∼ 10−11− 10−10 survive inflation and are present in the universe at an observable level. We estimate the gravity wave spectrum emitted from cosmic strings taking into account inflation driven by a Coleman-Weinberg potential. The tensor-to-scalar ratio r lies between 0.06 and 0.003 depending on the details of the inflationary scenario.

We perform a detailed study of the grand unified theories SO (10) and E(6) with left-right intermediate gauge symmetries of the form SU (N ) L ⊗ SU (N ) R ⊗ G. Proton decay lifetime constrains the unification scale to be 10 16 GeV and, as discussed in this paper, unwanted cosmological relics can be evaded if the intermediate symmetry scale is 10 12 GeV. With these conditions, we study the renormalisation group evolution of the gauge couplings and do a comparative analysis of all possible left-right models where unification can occur. Both the D-parity conserved and broken scenarios as well as the supersymmetric (SUSY) and Non-supersymmetric (Non-SUSY) versions are considered. In addition to the fermion and scalar representations at each stage of the symmetry breaking, contributing to the β-functions, we list the intermediate left-right groups which successfully meet these requirements. We make use of the dimension-5 kinetic mixing effective operators for achieving unification and large intermediate scale. A significant result in the supersymmetric case is that to achieve successful unification for some breaking patterns, the scale of SUSY breaking needs to be at least a few TeV. In some of these cases, intermediate scale can be as low as ∼ 10 12GeV, for SUSY scale to be ∼ 30 TeV. This has important consequences in the collider searches for SUSY particles and phenomenology of the lightest neutralino as dark matter. *

No abstract

We estimate the stochastic gravitational wave spectrum emitted from a network of cosmic strings in which the latter are effectively stable against breaking by monopole pair creation. The monopoles are produced at a higher scale from an earlier symmetry breaking and experience significant inflation before reentering the horizon. This gives rise to monopole-antimonopole pairs connected by string segments and the string loop formation essentially ceases. As a consequence, the lower frequency portion of the gravitational wave spectrum is suppressed relative to the no-inflation case with stable strings, which evades the stringent PPTA bound on the dimensionless string tension Gμ. We display the modified spectrum, accessible in the ongoing and future experiments, for Gμ values in the range 10-10–10-15. We show how this 'quasi-stable' string network is realized in realistic grand unified theories.