We review the paradigm of early-universe cosmology, and investigate gravitational theories in the very early universe. The work is motivated by the fact that, the strong presence of gravitational field in the early universe provides a testground to explore gravitational theories beyond General Relativity (GR). We start by investigating the initial singularity problem in the early universe cosmology, which persists as long as the universe undergoes eternal expansions within the framework of GR.

We firstly study a cosmological model derived from quantum gravity theories, where the universe is created by some quantum gravity effects, so the initial singularity is replaced by a period of quantum universe. We use the Euclidean Quantum Gravity formalism for describing the state of a quantum u...[ Read more ]

We review the paradigm of early-universe cosmology, and investigate gravitational theories in the very early universe. The work is motivated by the fact that, the strong presence of gravitational field in the early universe provides a testground to explore gravitational theories beyond General Relativity (GR). We start by investigating the initial singularity problem in the early universe cosmology, which persists as long as the universe undergoes eternal expansions within the framework of GR.

We firstly study a cosmological model derived from quantum gravity theories, where the universe is created by some quantum gravity effects, so the initial singularity is replaced by a period of quantum universe. We use the Euclidean Quantum Gravity formalism for describing the state of a quantum universe, and find that the universe can be properly prepared for certain underlying UV-complete gravitational theory, such as the Horava-Lifshitz gravity.

We also study the possibility if a singularity-free universe can exists without introducing quantum gravity effects. This requires the universe to have at least one non-expansion stage, which results in either a bouncing cosmology, where our universe undergoes a period of contraction before the big bang expansion; or a Genesis cosmology, where the universe is asymptotically Minkowskian in the past and transit to an expansion configuration at a certain time. Generically, such scenarios are plagued by ghost degree of freedom(s) or the gradient instability, where the sound speed squared is negative. We investigate the existence of a healthy realization of the above scenarios, and find a healthy cosmological model from Degenerate Higher Order Scalar Tensor (DHOST) theory.

Finally, we study the phenomenological applications of the above cosmological models. We find that all of the models can generate a near scale-invariant scalar power spectrum, agreeing with astrophysical observations. Besides, the tensor power spectrum of the above models would be highly blue, which contradicts with the prediction of inflationary cosmology, that results in a nearly scale-invariant tensor spectrum. Hence, our models have a chance to be verified by future experiments. The verification of the models, then, can be used to examine the underlying gravitational theories.