Constraints On Curvature And Dark Energy From Future Surveys

With the rapid development of cosmological surveys,future high precision large sky area surveys will constrain the ΛCDM model and its alternatives tightly,and clarify many fundamental questions.In this thesis,we study the potential of future cosmological surveys to constrain cosmological curvature ΩK and dark energy.The Universe’s curvature is one of its fundamental properties,stringent constraints on curvature provide powerful probes of early Universe physics such as inflation.However,curvature constraints based on specific assumptions of dark energy may lead to unreliable conclusions when used to test inflation models.To avoid this,it is important to obtain constraints that are independent on assumptions for dark energy.On the other hand,different models of dark energy leave different signatures in the expansion rate of the Universe and the growth rate of large-scale structure.The statistics of galaxy clusters are sensitive to the geometry of Universe and structure growth,which can be used to probe the nature of dark energy.In the first work,we investigate constraints on curvature from the pure geometrical probe constructed from galaxy-lensing cross-correlations measured from the LSST and Stage Ⅳ CMB surveys.We study comprehensively the cross-correlations of galaxy with magnification,measured from type Ia supernvae’s brightnesses("gKSN"),with shear("gκg"),and with CMB lensing("gκCMB").We find for the LSST and Stage ⅣCMB surveys,"gκSN","gκg" and "gκCMB" can be detected with signal-to-noise ratio S/N=104,2291,1842 respectively.When combined with supernovae Hubble diagram("SN")to constrain curvature,we find galaxy-lensing cross-correlation becomes increasingly important with more degrees of freedom allowed in dark energy.When galaxy-lensing cross-correlations are added to the combined probe of "SN+BAO+CMB",where "BAO" stands for the Stage Ⅳ BAO survey,and "CMB" stands for Planck measurement for the CMB acoustic scale,we obtain a dark energy independent constraint on ΩK of 0.0013,which is a factor of 7 improvement from "SN+BAO +CMB".This indicates that galaxy-lensing cross-correlations help to break parameter degeneracies effectively,which is important to obtain the dark energy independent constraints on curvature.In the second work,we study the potential of the galaxy cluster sample expected from the China Space Station Telescope(CSST)survey to constrain dark energy.We construct the Fisher matrix for the cluster number counts for the CSST,and forecast constraints on dark energy parameters for models with constant(w0CDM)and timedependent(w0waCDM)dark energy equation of state.By adopting the selection threshold in the observed richness λ≥15,about 1.0 × 105 clusters in the redshift range 0≤z≤1.5 can be detected.If the selection threshold is lowered down to λ≥10,the total number of clusters rises up to about 3.0 × 105.Lower richness threshold,which corresponds to larger number of clusters,leads to tighter parameter constraints.The parameter constraints can be tightened by including priors on the richness-mass scaling relation parameters.For λ≥15,with priors on the richness-mass scaling relation parameters for the Subaru Hyper Suprime-Cam(HSC)CAMIRA cluster catalogue,the dark energy equation of state parameter w0 of w0CDM model can be constrained toΔw0=0.052.We obtain Δw0=0.14 and Δwa=0.87 for the w0waCDM model,with a Figure of Merit for(w0,wa)to be 21.9.If we assume that the richness-mass scaling relation parameters are fixed,we obtain Δw0=0.022 for w0CDM model,Δw0=0.1 and Δwa=0.43 for w0waCDM model.The dark energy Figure of Merit of(w0,wa)increases to 100.77.This indicates the importance of the calibration of the richnessmass scaling relation for photometrically selected galaxy clusters.By extending the maximum redshift of the clusters from zmax～1.5 to zmax～2,possibly achieved by joint analyses with the Euclid survey,the dark energy Figure of Merit for(w0,wa)can increase to 37.17(with HSC priors)and 142.23(with fixed richness-mass scaling relation parameters),improved by a factor of～1.7 and～1.4,respectively.We find that the impact of the photometric redshift uncertainty on the cosmological forecast is negligible as long as the photometric redshift error is better than 0.01.