Low scale trinification symmetry through effects of dimension-5 operators in $E_6$ grand unified theory with and without supersymmetry

We examine $E_6$ GUT models (both SUSY and non-SUSY) with D-parity violating intermediate trinification symmetry $\left(SU(3)_C\otimes SU(3)_L\otimes SU(3)_R\right)(g_{3L}\neq g_{3R})$ where the D-parity breaking is achieved by quantum gravity effect through dimension-5 operators. Inclusion of the gravitational effect significantly lowers the intermediate scale, being as low as $10$ TeV. However with a given choice of the intermediate mass $M_I$, the gauge unification mass $M_U$ as well as the GUT coupling constant are unaffected by the effects. The predicted value of $M_U$ is shown to be compatible with the accessible limit of the proton lifetime in presence of additional particles i.e. color octet scalars like $(8,2,\frac{1}{2})$ or $(8,1,0)$ and electroweak triplet fermion $(1,3,0)$ at the lower scales. The presence of color octet scalar with mass of the order of TeV may suppress the production of the Higgs boson through gluon fusion. The $SU(2)_L$ triplet fermion may behave like a stable dark matter. With reference to cosmological issue, it is expected that no strings or walls bounded by strings associated with D are generated, since the discrete D-parity is broken at the GUT scale.