Power law Starobinsky model of inflation from no-scale SUGRA

We consider a power law $\frac{1}{M^2}R^{\beta}$ correction to Einstein gravity as a model of inflation. The interesting feature of this form of generalization is that small deviations from the Starobinsky limit $\beta=2$ can change the value of tensor to scalar ratio from $r \sim \mathcal{O}(10^{-3})$ to $r\sim \mathcal{O}(0.1)$. We find that in order to get large tensor perturbation $r\approx 0.1$ as indicated by BKP measurements, we require the value of $\beta \approx 1.83$ thereby breaking global Weyl symmetry. We show that the general $R^\beta$ model can be obtained from a SUGRA construction by adding a power law $(\Phi +\bar \Phi)^n$ term to the minimal no-scale SUGRA K\"ahler potential. We further show that this two parameter power law generalization of the Starobinsky model is equivalent to generalized non-minimal curvature coupled models with quantum corrected $\Phi^{4}$- potentials i.e. models of the form $\xi \Phi^{a} R^{b} + \lambda \Phi^{4(1+\gamma)}$ and thus the power law Starobinsky model is the most economical parametrization of such models.Comment: 6 pages, 4 figures, Matches version to appear in Phys. Lett.

Plateau Inflation in RR-parity Violating MSSM

Inflation with plateau potentials give the best fit to the CMB observables as they predict tensor to scalar ratio stringently bounded by the observations from Planck and BICEP2/Keck. In supergravity models it is possible to obtain plateau potentials for scalar fields in the Einstein frame which can serve as the inflation potential by considering higher dimensional Planck suppressed operators and by the choice of non-canonical K\"ahler potentials. We construct a plateau inflation model in MSSM where the inflation occurs along a sneutrino-Higgs flat direction. A hidden sector Polonyi field is used for the breaking of supersymmetry after the end of the inflation. The proper choice of superpotential leads to strong stabilization of the Polonyi field, $m_{Z}^2\gg m_{3/2}^2$, which is required to solve the cosmological moduli problem. Also, the SUSY breaking results in a TeV scale gravitino mass and scalar masses and gives rise to bilinear and triliear couplings of scalars which can be tested at the LHC. The sneutrino inflation field can be observed at the LHC as a TeV scale diphoton resonance like the one reported by CMS and ATLAS.Comment: 7 pages, 3 figures. Version accepted for publication in Physics Letters

Kaon processes in general 2HDM

We discuss new physics (NP) contributions to kaon mixing parameter $\varepsilon_K$, direct CP violation parameter $\varepsilon^\prime/\varepsilon$ of $K\to \pi\pi$, and rare decays $K^+\to \pi^+\nu\bar\nu$, $K_L\to \pi^0\nu\bar\nu$ and $K_{L, S}\to \mu^+ \mu^-$ in the context of general two Higgs doublet model. We focus on contributions of top quark related exotic couplings, and show that simultaneous presence of flavor conserving and flavor violating interactions can lead to large NP effects in kaon sector, while being consistent with the stringent constraints from B physics observables such as $B_{s(d)}$-$\bar B_{s(d)}$ mixing, $B_s\to \mu^+ \mu^-$, and $b\to s\gamma$. We stress on the importance of correlations between $\varepsilon_K$, $K^+\to \pi^+\nu\bar\nu$ and $B_s\to \mu^+ \mu^-$ that can be exploited to distinguish the parameter space corresponding to a light (sub-TeV) or heavy (TeV) scale charged Higgs boson.Comment: Talk given at the KAON 2022 conference, September 13-16, 2022, Osaka (Japan); submission to Journal of Physics: Conference Serie

Supergravity Model of Inflation and Explaining IceCube HESE Data via PeV Dark Matter Decay

We construct an unified model of inflation and PeV dark matter with an appropriate choice of no-scale K\"ahler potential, superpotential and gauge kinetic function in terms of MSSM fields and hidden sector Polonyi field. The model is consistent with the CMB observations and can explain the PeV neutrino flux observed at IceCube HESE. A Starobinsky like Higgs-sneutrino plateau inflation is obtained from the $D$-term SUGRA potential while $F$-term being subdominant during inflation. To get PeV dark matter, SUSY breaking at PeV scale is achieved through Polonyi field. This sets the scale for soft SUSY breaking parameters $m_0, m_{1/2}, A_0$ at the GUT scale in terms of the parameters of the model. The low energy particles spectrum is obtained by running the RGEs. We show that the $\sim$125 GeV higgs and the gauge coupling unification can be obtained in this model. The $6$ PeV bino-type dark matter is a subdominant fraction ($\sim 11\%$) of the relic density and its decay gives the PeV scale neutrino flux observed at IceCube by appropriately choosing the couplings of the $R$-parity violating operators. Also we find that there is a degeneracy in scalar field parameters $(\gamma, \beta)$ and coupling $\zeta$ value in producing the correct amplitude of CMB power spectrum. However the value of parameter $\tan(\beta)=1.8$, which is tightly fixed from the requirement of PeV scale SUSY breaking, removes the degeneracy in the values of the scalar field parameters to provide a unique solution for inflation. In this way it brings the explanation for dark matter, PeV neutrinos and inflation within the same framework.Comment: 26 pages, 6 figures, 2 tables. Accepted for publication in 'AHEP (Advances in High Energy Physics)