Unitarity constraints in the standard model with a singlet scalar field

Motivated by the discovery of a new scalar field and amelioration of the electroweak vacuum stability ascribed to a singlet scalar field embedded in the standard model (SNI), we examine the implication of the perturbative unitarity in the SM with a singlet scalar field. Taking into account the full contributions to the scattering amplitudes, we derive unitarily conditions on the scattering matrix which can be translated into bounds on the masses of the scalar fields. In the case that the singlet scalar field develops vacuum expectation value (VEV), we get the upper bound on the singlet scalar mass varying with the mixing between the singlpt and Higgs scalars. On the other hand, the mass of the Higgs scalar can be constrained by the unitarity condition in the case that the VIN of the singlet scalar is not generated. Applying the upper bound on the Higgs mass to the scenario of the unitarized Riggs inflation, we discuss how the unitarily condition can constrain the Higgs inflation. The singlet scalar mass is not constrained by the unitarily itself when we impose 22 in the model because of no mixing with the :Higgs scalar. But, regarding the singlet scalar field as a cold dark matter candidate, we derive upper bound on the singlet scalar mass by combining the observed relic abundance with the uni,arity condition.