Abstract: The discovery of Higgs particle has ushered in a new era of particle physics. Even though the list of members of the standard theory of particle physics is now complete, the shortcomings of the theory became ever more acute. It is generally considered that the best solution to the problems is an electron-positron collider that can study Higgs particle with high precision and high sensitivity; namely, a Higgs factory. Among a few candidates for Higgs factory, the International Linear Collider (ILC) is currently the most advanced in its program. In this article, we review the physics and the project status of the ILC including its energy expandability.

Abstract: We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and FLRW backgrounds, we introduce the basic tools for the discretization of field theories, including lattice gauge invariant techniques. Following, we discuss and classify numerical algorithms, ranging from methods of O(delta t(2)) accuracy like staggered leapfrog and Verlet integration, to Runge-Kutta methods up to O(delta t(4)) accuracy, and the Yoshida and Gauss-Legendre higher-order integrators, accurate up to O(delta t(10)) We adapt these methods for their use in classical lattice simulations of the non-linear dynamics of scalar and gauge fields in an expanding grid in 3+1 dimensions, including the case of 'self-consistent' expansion sourced by the volume average of the fields' energy and pressure densities. We present lattice formulations of canonical cases of: i) Interacting scalar fields, ii) Abelian U(1) gauge theories, and iii) Non-Abelian SU(2) gauge theories. In all three cases we provide symplectic integrators, with accuracy ranging from O(delta t(2)) up to O(delta t(10)) For each algorithm we provide the form of relevant observables, such as energy density components, field spectra and the Hubble constraint. We note that all our algorithms for gauge theories always respect the Gauss constraint to machine precision, including when 'self-consistent' expansion is considered. As a numerical example we analyze the post-inflationary dynamics of an oscillating inflaton charged under SU(2) x U(1). We note that the present manuscript is meant to be part of the theoretical basis for the code CosmoLattice, a multi-purpose MPI-based package for simulating the non-linear evolution of field theories in an expanding universe, publicly available at http://www.cosrnolattice.net.

Abstract: R-parity conserving supersymmetric models with right-handed (RH) neutrinos are very appealing since they could naturally explain neutrino physics and also provide a good dark matter (DM) candidate such as the lightest supersymmetric particle (LSP). In this work we consider the next-to-minimal supersymmetric standard model (NMSSM) plus RH neutrino superfields, with effective Majorana masses dynamically generated at the electroweak scale (EW). We perform a scan of the relevant parameter space and study both possible DM candidates: RH sneutrino and neutralino. Especially for the case of RH sneutrino DM we analyse the intimate relation between both candidates to obtain the correct amount of relic density. Besides the well-known resonances, annihilations through scalar quartic couplings and coannihilation mechanisms with all kind of neutralinos, are crucial. Finally, we present the impact of current and future direct and indirect detection experiments on both DM candidates.