Perturbations in Little Higgs Inflation

Little Higgs Inflation is a novel approach to relate the Higgs boson with inflaton. By treating the Higgs as a pseudo-Nambu-Goldstone (pNG) boson with a periodic potential and a quadratic Chern-Simons coupling, this framework can achieve slow-roll inflation without fine-tuning the Higgs mass and inflationary potentials. In this work, we present a full perturbation analysis of the minimal implementation of this idea: littlest Higgs inflation with a symmetry coset SU(5)/SO(5). The parameter space for the littlest Higgs inflation is constrained by the requirements of at least 60 e-folds of inflation, while measurements of the electric dipole moment of the electron stringently limit the Chern-Simons coupling constant. For the viable parameter space, tensor modes can exhibit a notably blue tilt due to an extended period of gauge field instability, leading to an exponential enhancement of left-hand gravitational waves. In conjunction with scalar perturbations, we will determine whether the tensor-to-scalar ratio and the scalar spectral index can align with the current observational data.