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