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.
Positron excess upto energies $sim$350 GeV has been observed by AMS-02 result and it is consistent with the positron excess observed by PAMELA upto 100 GeV. There is no observed excess of anti-protons over the expected CR background. We propose a lep
tophilic dark matter with an $U(1)_{L_{mu}-L_{tau}}$ gauge extension of MSSM. The dark matter is an admixture of the $L_{mu}-L_{tau}$ gaugino and fermionic partners of the extra $SU(2)$ singlet Higgs boson, which break the $L_{mu}-L_{tau}$ symmetry. We construct the SM$otimes U(1)_{ L_{mu}-L_{tau}}$ SUSY model which provides the correct relic density of dark matter and is consistent with constrain on $Z$ from LHC. The large dark matter annihilation cross-section into $mu^{+}mu^{-}$ and $tau^{+}tau^{-}$, needed to explain PAMELA and AMS-02 is achieved by Breit-Wigner resonance.
If a Higgs field is conformally coupled to gravity, then it can give rise to the scale invariant density perturbations. We make use of this result in a realistic inert Higgs doublet model, where we have a pair of Higgs doublets conformally coupled to
the gravity in the early universe. The perturbation of the inert Higgs is shown to be the scale invariant. This gives rise to the density perturbation observed through CMB by its couplings to the standard model Higgs and the subsequent decay. Loop corrections of this conformally coupled system gives rise to electroweak symmetry breaking. We constrain the couplings of the scalar potential by comparing with the amplitude and spectrum of CMB anisotropy measured by WMAP and this model leads to a prediction for the masses of the lightest Higgs and the other scalars.
We study the generation of magnetic field in Higgs-inflation models where the Standard Model Higgs boson has a large coupling to the Ricci scalar. We couple the Higgs field to the Electromagnetic fields via a non- renormalizable dimension six operato
r suppressed by the Planck scale in the Jordan frame. We show that during Higgs inflation magnetic fields with present value $10^{-6}$ Gauss and comoving coherence length of $100 kpc$ can be generated in the Einstein frame. The problem of large back-reaction which is generic in the usual inflation models of magneto-genesis is avoided as the back-reaction is suppressed by the large Higgs-curvature coupling.
We show that a non-minimal coupling of electromagnetism with background torsion can produce birefringence of the electromagnetic waves. This birefringence gives rise to a B-mode polarization of the CMB. From the bounds on B-mode from WMAP and BOOMERa
nG data, one can put limits on the background torsion at $xi_{1}T_{1}=(-3.35 pm 2.65) times 10^{-22} GeV^{-1}$.
