Abstract
We consider the minimal supersymmetric grand unified model (MSGUT) based on the group $\mathrm{SO}(10)$, and study conditions leading to possible domain wall (DW) formation. It has been shown earlier that the supersymmetry preserving vacuum expectation values (vev's) get mapped to distinct but degenerate set of vev's under action of $D$ parity, leading to formation of domain walls as topological pseudo-defects. The metastability of such walls can make them relatively long lived and contradict standard cosmology. Thus we are led to consider adding a nonrenormalisable Planck scale suppressed operator, that breaks $\mathrm{SO}(10)$ symmetry but preserves Standard Model symmetry. For a large range of right handed breaking scales $M_R$, this is shown to give rise to the required pressure difference to remove the domain walls without conflicting with consistent big bang nucleosynthesis (BBN) while avoiding gravitino overproduction. However, if the walls persist till the onset of weak (thermal) inflation, then a low $\sim 10 - 100$ TeV $M_R$ becomes problematic.
Highlights
All the elegant features of both SO(10) grand unified theory (GUT) and supersymmetric models can be incorporated in a minimal supersymmetric GUT (MSGUT)
While no signatures of low energy supersymmetry have been found at the LHC so far, supersymmetry continues to be an appealing mechanism for a consistent UV completion for the Standard Model (SM) and justifies the considerations here which relate to the effects of this model in the very early Universe
We calculate the conditions for successful domain wall removal during the three stated cosmological periods in our extended MSGUT model, leading to constraints on the scale of right-hand symmetry breaking characterized by mass scale MR
Summary
All the elegant features of both SO(10) grand unified theory (GUT) and supersymmetric models can be incorporated in a minimal supersymmetric GUT (MSGUT). We argue that adding such SO(10) preserving terms to the superpotential will not lead to a pressure difference across any domain wall that can arise, and cannot contribute to the required instability This forces us to go beyond the cherished principle of exact SO(10) gauge symmetry, in particular sacrifice some of its features related to ultraviolet (UV) completion. We calculate the conditions for successful domain wall removal during the three stated cosmological periods in our extended MSGUT model, leading to constraints on the scale of right-hand symmetry breaking characterized by mass scale MR It results in upper bounds on MR, forcing it to remain small compared to generic GUT scale.
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