Abstract In this paper. the electroweak phase transition. the gravitational waves and the dark matter issues are investigated in two scalar singlet extension of the standard model. The detectability of the gravitational wave signals are discussed by comparing the results with the sensitivity curves of $$\mathbf {eLISA}$$ eLISA . https://countryscenesaddleryandpetsuppliers.shop/product-category/fender-hobbles/