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.
Superheavy threshold corrections to the matching condition between matter Yukawa couplings of the effective Minimal Supersymmetric Standard Model (MSSM) and the New Minimal Supersymmetric (SO(10)) GUT(NMSGUT) provide a novel and generic mechanism for
reducing the long standing and generically problematic operator dimension 5 Baryon decay rates. In suitable regions of the parameter space strong wave function renormalization of the effective MSSM Higgs doublets due to the large number of heavy fields can take the wave function renormalization of the MSSM Higgs field close to the dissolution value ($Z_{H,overline{H}}=0$). Rescaling to canonical kinetic terms lowers the SO(10) Yukawas required to match the MSSM fermion data. Since the same Yukawas determine the dimension 5 B violation operator coefficients, the associated rates can be suppressed to levels compatible with current limits. Including these threshold effects also relaxes the constraint $ y_b-y_tausimeq y_s-y_mu$ operative between $textbf{10} -textbf{120} $ plet generated tree level MSSM matter fermion Yukawas $y_f$. We exhibit accurate fits of the MSSM fermion mass-mixing data in terms of NMSGUT superpotential couplings and 5 independent soft Susy breaking parameters specified at $10^{16.25},$ GeV with the claimed suppression of Baryon decay rates. As before, our s-spectra are of the mini split supersymmetry type with large $|A_0|,mu,m_{H,overline H} > 100,,$ TeV, light gauginos and normal s-hierarchy. Large $A_0,mu$ and soft masses allow significant deviation from the canonical GUT gaugino mass ratios and ensure vacuum safety. Even without optimization, prominent candidates for BSM discovery such as the muon magnetic anomaly, $brightarrow sgamma$ and Lepto-genesis CP violation emerge in the preferred ball park.
Supersymmetric Unified theories which incorporate a renormalizable Type I seesaw mechanism for small neutrino masses can also provide slow roll inflection point inflation along a flat direction associated with a gauge invariant combination of the Hig
gs, slepton and right handed sneutrino superfields. Inflationary parameters are related to the Majorana and Dirac couplings responsible for neutrino masses with the scale of inflation set by a right-handed neutrino mass $M_{ u^c} sim 10^6-10^{12}$ GeV. Tuning of the neutrino Dirac and Majorana superpotential couplings and soft Susy breaking parameters is required to enforce flatness of the inflationary potential. In contrast to previous inflection point inflation models the cubic term is dominantly derived from superpotential couplings rather than soft A-terms. Thus since $M_{ u^c}>>M_{Susy}$ the tuning condition is almost independent of the soft supersymmetry breaking parameters and therefore more stable. The required fine tuning is also less stringent than for Minimal SUSY Standard Model (MSSM) inflation or Dirac neutrino A-term inflation scenarios due to the much larger value of the inflaton mass. Reheating proceeds via `instant preheating which rapidly dumps all the inflaton energy into a MSSM mode radiation bath giving a high reheat temperature $T_{rh} approx M_{ u^c}^{3/4}, 10^{6}$ GeV $sim 10^{11}- 10^{15} $ GeV. Thus our scenario requires large gravitino mass $> 50 $ TeV to avoid a gravitino problem. The `instant preheating and Higgs component of the inflaton also imply a `non-thermal contribution to Leptogenesis due to facilitated production of right handed neutrinos during inflaton decay. We derive the tuning conditions for the scenario to work in the realistic New Minimal Supersymmetric SO(10) GUT and show that they can be satisfied by realistic fits.
