In this thesis, we review the current cosmological crisis in the framework of the Lambda–cold dark matter model, which is observational inconsistencies between different probes, including Hubble tension, S₈ tension, and dipole tension. In revealing the cosmic tensions, we propose a novel cosmological probe, cosmological standard timers, for a clear picture of cosmic tensions and a theoretical model, a Gpc-scale local void, as a potential solution of cosmic tensions. The cosmological standard timers can construct the redshift-time relation based on dynamical systems in the universe, and further constrain the cosmic evolution. Two kinds of standard timer candidates are proposed, which are primordial black hole (PBH) clusters and PBH binaries. By studying their intrinsic dynamics and obse...[ Read more ]

In this thesis, we review the current cosmological crisis in the framework of the Lambda–cold dark matter model, which is observational inconsistencies between different probes, including Hubble tension, S₈ tension, and dipole tension. In revealing the cosmic tensions, we propose a novel cosmological probe, cosmological standard timers, for a clear picture of cosmic tensions and a theoretical model, a Gpc-scale local void, as a potential solution of cosmic tensions. The cosmological standard timers can construct the redshift-time relation based on dynamical systems in the universe, and further constrain the cosmic evolution. Two kinds of standard timer candidates are proposed, which are primordial black hole (PBH) clusters and PBH binaries. By studying their intrinsic dynamics and observable signals, the redshift-time relation can be constructed from the early epoch to the late epoch, which gives a complete picture of cosmic expansion history. A Gpc-scale local void provides a joint reconciliation on cosmic tensions, where S₈ tension can be explained by a low value of local matter density, Hubble tension can be eased via the outward peculiar motion of distance indicators inside a Gpc-scale local void, and dipole tension is reconciled by an anisotropic spacetime induced by an off-center observer inside a Gpc-scale void. With the development of observational technologies and theoretical studies, a combination of cosmological standard timers and a Gpc-scale void cosmology with various cosmological probes and theoretical models would reveal cosmic tensions and build a novel concordance cosmological model.