Supersymmetric GUTs based on SO(10) gauge group are leading contenders to describe particle physics beyond the Standard Model. Among these the New minimal supersymmetric SO(10) grand unified theory (NMSGUT) based on Higgs system 10+120+210+126+$overl
ine{126}$ has been developing since 1982. It now successfully fits the whole standard Model gauge coupling, symmetry breaking and fermion mass-mixing data as well as the neutrino mass and mixing data in terms of NMSGUT parameters and just 6 soft supersymmetry breaking parameters defined at the GUT scale. In this thesis we study the phenomenology of NMSGUT, its implications for inflationary and Cold Dark matter cosmology and develop Renormalization group(RG) equations for the flow of NMSGUT couplings in the extreme ultraviolet. In the first part we show that superheavy threshold effects can drastically lower the SO(10) yukawa couplings required for realistic unification and this cures the long standing problem of fast proton decay in Susy GUT. Then we propose a novel Supersymmetric Seesaw inflection(SSI) scenario based upon a SU(2)_L x U(1)_R x U(1)_{B-L} invariant model, where the inflation mass is controlled by the large conjugate sneutrino mass. We show that it is much less fine-tuned and more stable than Dirac sneutrino based MSSM inflation. NMSGUT can embed SSI, and even provide a large tensor scalar ratio, but obstacles in achieving enough inflation remain. The NMSGUT Bino LSP is a good dark matter candidate when it can co-annihilate with a nearly degenerate sfermion as in fits with a light smuon. We also calculate two loop NMSGUT gauge-Yukawa Renormalization Group(RG) beta functions and show that GUT scale negative Higgs mass squared parameters required by NMSGUT fits can arise by RG flows from positive values at the Planck scale.
We show that a supersymmetric renormalizable theory based on gauge group SO(10) and Higgs system {bf {10 $oplus$ 210 $oplus$ 126 $oplus$ $overline{bf 126}$}} with no scale supergravity can lead to a Starobinsky kind of potential for inflation. Succes
sful inflation is possible in the cases where the potential during inflation corresponds to $SU(3)_C times SU(2)_L times SU(2)_R times U(1)_{B-L}$, $SU(5)times U(1)$ and flipped $SU(5)times U(1)$ intermediate symmetry with a suitable choice of superpotential parameters. The reheating in such a scenario can occur via non perturbative decay of inflaton i.e. through preheating. After the end of reheating, when universe cools down, the finite temperature potential can have a minimum which corresponds to MSSM.
