Non-standard Cosmology: Modified Gravity And Dark Energy Models

It is widely believed that our universe is undergoing an accelerated expansion.In the standard ?CDM model,this acceleration is driven by a cosmological constant.While favored by the observations,this standard model is suffering some theoretical problems,e.g.the cosmological constant problem and the coincidence problem,and recently it also faces some challenges due to tensions in the observational data.Many attempts have been made to find a more natural non-standard cosmological model to describe our universe,such as dark energy model and modified gravity.In this thesis,we will investigate the cosmological imprints and observational constraints on two alternative cosmological models: interacting dark matter and dark energy model,f(R)modified gravity with non-minimal gravitational coupling to matter.We first focus on the discordance problem in the standard ?CDM model between Kilo Degree Survey(Ki DS)weak lensing measurements and Planck cosmic microwave background(CMB)measurements.Confronting the phenomenological interacting dark matter and dark energy models to the same measurements,we find that interaction models can effectively alleviate the tension between Ki DS and Planck datasets,and they are more favored than the ?CDM model by the data.Then we put our attention on the weak lensing bispectrum and forecast how well it can constrain the interactions between dark sectors,as well as other cosmological parameters.The results show that bispectrum is a sensitive probe to constrain the interaction models and it may shed light on the mechanism of the interactions between dark sectors.After low redshift observational examinations,we extend the effect of the interaction to larger redshifts,namely the epoch of reionization.We use a semi-analytical reionization model to investigate the evolution of ionized fraction and the 21 cm radiation power spectrum in the interaction models,and find that certain types of interactions can significantly affect the reionization history.This result tells us that 21 cm observations can be helpful for us to investigate different cosmological models in the future.N-body simulations have been widely adopted to study the nonlinear evolution of the large scale structure of the universe.We build a fully self-consistent simulation pipeline for the first time to study nonlinear structure formation in the phenomenological interacting dark matter and dark energy models.We find that the nonlinear effect at low redshift can further refine and constrain the interaction models.Confronting our simulation results with the SDSS galaxy-galaxy weak lensing measurements,we point to plausible improvements on the constraints of interaction strength by using small-scale information from weak lensing comparing with previous studies using linear examinations or non-linear corrections.This new simulation pipeline opens a new window to study the nonlinear structure formation in general interacting dark matter and dark energy models,and it can be further improved to investigate more non-standard cosmological models.Then we perform the observational examinations and N-body simulation tests for a quintessence model with Yukawa interaction.We find that this model is compatible with observational data,and can moderately alleviate the discordance between weak lensing measurements and CMB measurements as previously inferred from the standard?CDM model,as well as the coincidence problem.By performing self-consistent Nbody simulations,we confirm the validity of the observational examinations and find that small scale observations are plausible to improve the constraints significantly in the future.Besides dark energy,another promising way to explain the accelerated expansion is to assume that at large scales Einstein gravity breaks down and more general actions are needed to describe the gravitational field.We perform a dynamical analysis of a generalized f(R)modified gravity theory with non-minimal gravitational coupling to matter and confront it with observations.We find that this non-minimally coupled theory of gravity is a viable model to describe the late time universe acceleration.