We study the collider, astrophysical and cosmological constraints on the dark matter sector of a conformal model within the framework of both the freeze out as well as the freeze in mechanism. The model has a dark sector with strong self interactions. This sector couples weakly with the Standard Model (SM) particles via a scalar messenger. The lightest dark sector particle is a pion-like fermion anti-fermion bound state. We find that the model successfully satisfies the constraints coming from the Higgs decay to the visible as well as the invisible sector. We have used the results of the dark matter direct detection experiments, such as, XENON1T in order to impose bounds on the parameters of the model. The model satisfies the indirect detection constraints of gamma ray from the galactic center and Dwarf spheroidal galaxies. We also determine the parameter range for which it satisfies the astrophysical constraints on the dark matter self coupling.

24 pages, 6 figures, major changes, to be published in Physical Review D