  We explore the emissions of the Gravitational Waves (GWs) from a strong
first-order ekectroweak phase transition. To this end, a dark matter model has
been investigated in Feebly Interacting Massive Particle (FIMP) scenario, where
the dark matter particles are produced through "freeze-in" mechanism in the
early Universe and due to their very small couplings they could not attain
thermal and chemical equilibrium with the Universe's thermal plasma. In this
context, we extend scalar sector of Standard Model of particle physics by two
additional scalar singlets whose stability is protected by an unbroken discrete
$Z_2 \times Z'_2$ symmetry and they are assumed to develop no VEV after
spontaneous symmetry breaking. We study the first-order phase transition within
the framework of this present model. We have done both analytical and numerical
computations to calculate the consequent production of GWs and then the
detectabilities of such GWs have been investigated at the future space based
detectors such as LISA, BBO, ALIA, DECIGO, aLIGO and aLIGO+ etc. We also find
that dark matter self coupling has a considerable influence on the GW
production in the present scenario.
