Abstract
Axions play an tremendously important role in understanding several aspects of cosmology. From theoretical perspective, they have long been considered the leading candidate to solve the strong CP-problem in particle physics. Ultralight axions (ULAs) motivated by string theory have gained substantial attention in the last decade due to their rich and novel phenomenology. The presence of ULA field is promising to resolve several tensions and small-scale crises of the standard -cold-dark-matter model. Firstly, ULA with mass ma ' 10ô€€€22 eV, which is usually referred to as fuzzy dark matter (FDM), has long been treated as a highly promising alternative to traditional cold dark matter (CDM) regime. On large scales, FDM retains CDM prediction of cosmic microwave background and the large-scale structure of the universe. On small scales, FDM power spectrum is suppressed due to quantum pressure and its halo structure features a prominent central core, which provides a potential solution for the missing satellite and cusp-core problem of CDM. Secondly, ULA with mass ma ' 10ô€€€29 eV behaves as either dark energy or dark matter throughout the cosmic history. This axion, when being coupled to the Higgs field in the so-called axi-Higgs model, can uplift the electron mass in the early universe and alter recombination. As a result, the Hubble tension between early-time and late-time measurement is alleviated. The axi-Higgs model may also explain the 7Li puzzle in bigbang nucleosynthesis, the clustering S8 tension with weak-lensing data, and the observed isotropic cosmic birefringence. The main focus of my thesis is to particularly demonstrate the aforementioned potentials of ULAs in cosmology.