Emergent universe and Genesis from the DHOST cosmology

In this article, we present an emergent universe scenario that can be derived from DHOST cosmology. The starts asymptotically Minkowski in the far past just like regular Galileon Genesis, but evolves to a radiation dominated period at late stage, and therefore, has graceful exit which is absent Genesis. We analyze behavior of cosmological perturbations show both scalar tensor modes are free gradient instability problem. further primordial spectrum generated various situations discuss whether scale invariance achieved.