We construct concrete supersymmetric grand unified theories based on the Pati-Salam gauge group SU (4) c × SU (2) L × SU (2) R which naturally lead to a moderate violation of 'asymptotic' Yukawa unification and thus can allow an acceptable b-quark mass even with universal boundary conditions. We consider the constrained minimal supersymmetric standard model which emerges from one of these theories with a deviation from Yukawa unification which is adequate for µ > 0. We show that this model possesses a wide and natural range of parameters which is consistent with the data on b → sγ, the muon anomalous magnetic moment, the cold dark matter abundance in the universe, and the Higgs boson masses. The lightest supersymmetric particle can be as light as about 107 GeV.

The cosmological relic density of the lightest supersymmetric particle of the minimal supersymmetric standard model is calculated under the assumption of gauge and Yukawa coupling unification. We employ radiative electroweak breaking with universal boundary conditions from gravitymediated supersymmetry breaking. Coannihilation of the lightest supersymmetric particle, which turns out to be an almost pure bino, with the next-to-lightest supersymmetric particle (the lightest stau) is crucial for reducing its relic density to an acceptable level. Agreement with the mixed or the pure cold (in the presence of a nonzero cosmological constant) dark matter scenarios for large scale structure formation in the universe requires that the lightest stau mass is about 2−8% larger than the bino mass, which can be as low as 222 GeV. The smallest allowed value of the lightest stau mass turns out to be about 232 GeV.

We analyze the cosmological implications of F -term hybrid inflation with a subdominant FayetIliopoulos D-term whose presence explicitly breaks a D-parity in the inflaton-waterfall sector. This scenario of inflation, which is called F D -term hybrid model for brevity, can naturally predict lepton number violation at the electroweak scale, by tying the µ-parameter of the MSSM to an SO(3)-symmetric Majorana mass m N , via the vacuum expectation value of the inflaton field. We show how a negative Hubble-induced mass term in a next-to-minimal extension of supergravity helps to accommodate the present CMB data and considerably weaken the strict constraints on the theoretical parameters, resulting from cosmic string effects on the power spectrum P R .The usual gravitino overabundance constraint may be significantly relaxed in this model, once the enormous entropy release from the late decays of the ultraheavy waterfall gauge particles is properly considered. As the Universe enters a second thermalization phase involving a very low reheat temperature, which might be as low as about 0.3 TeV, thermal electroweak-scale resonant leptogenesis provides a viable mechanism for successful baryogenesis, while thermal righthanded sneutrinos emerge as new possible candidates for solving the cold dark matter problem.In addition, we discuss grand unified theory realizations of F D -term hybrid inflation devoid of cosmic strings and monopoles, based on the complete breaking of an SU(2) X subgroup. The F D -term hybrid model offers rich particle-physics phenomenology, which could be probed at highenergy colliders, as well as in low-energy experiments of lepton flavour or number violation.

A novel realization of the Starobinsky inflationary model within a moderate extension of the Minimal Supersymmetric Standard Model (MSSM) is presented. The proposed superpotential is uniquely determined by applying a continuous R and a Z 2 discrete symmetry, whereas the Kähler potential is associated with a no-scale-type SU (54, 1)/SU (54)×U (1) R × Z 2 Kähler manifold. The inflaton is identified with a Higgs-like modulus whose the vacuum expectation value controls the gravitational strength. Thanks to a strong enough coupling (with a parameter c T involved) between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton with c T ≥ 76 and the corresponding effective theory being valid up to the Planck scale. The inflationary observables turn out to be in agreement with the current data and the inflaton mass is predicted to be 3 · 10 13 GeV. At the cost of a relatively small superpotential coupling constant, the model offers also a resolution of the µ problem of MSSM. Supplementing MSSM by three right-handed neutrinos we show that spontaneously arising couplings between the inflaton and the particle content of MSSM not only ensure a sufficiently low reheating temperature but also support a scenario of non-thermal leptogenesis consistently with the neutrino oscillation parameters for gravitino heavier than about 10 4 GeV.

The decoupling of a cold relic, during a decaying-particle-dominated cosmological evolution is analyzed, the relic density is calculated both numerically and semi-analytically and the results are compared with each other. Using plausible values (from the viewpoint of supersymmetric models) for the mass and the thermal averaged cross section times the velocity of the cold relic, we investigate scenaria of equilibrium or non-equilibrium production. In both cases, acceptable results for the dark matter abundance can be obtained, by constraining the reheat temperature of the decaying particle, its mass and the averaged number of the produced cold relics. The required reheat temperature is, in any case, lower than about 20 GeV.