Non-parametric Reconstruction Of Cosmic Expansion History And Dark Energy Equation Of State

In the late 1990's,two teams independently discovered that our Universe is under-going an accelerated expansion from measurements of luminosity distances of type la supernovae.Later on,several other observations,for example,the cosmic microwave background radiation,large scale structure and baryonic acoustic oscillations all cor-roborate the accelerated cosmic expansion.However,until now we still do not know the physical origin of the acceleration.There are mainly two classes of explanations to the cosmic acceleration.In the first one,General Relativity is believed to be the correct theory of gravity,applicable to the largest cosmological scales,therefore a new energy component with negative pressure,i.e.,dark energy,has to be introduced.The other class of explanations attribute the acceleration to the failure of General Relativity on large scales,so that modifications to General Relativity has to be made.So far,we are not able to rule out one or the other conclusively with observations.From observational point of view,in order to solve the problem of cosmic ac-celeration,the first thing we need is to measure the history of cosmic expansion and evolution precisely.The cosmic expansion is most directly described by the Hubble parameter H(z).One direct method to measure H(z)is to numerically differentiate the age of galaxies with respect to redshift.However,the errors in the results are large,due to errors in age determinations and that numerical differentiation is sensitive to the ran-dom errors.BAOs could also provide direct measurements of H(z),but there are only very limited number of results currently.Besides direct measurements,one could also choose to reconstruct H(z)from data using non-parametric methods.The first work we present in this thesis is non-parametric reconstruction of the cosmic expansion history from type ?a supernovae.We introduce a mono tonicity prior on the cosmic expansion history.Using simulated mock samples,we show that the monotonicity prior could greatly improve the reconstructions,without introducing bias into the results.We then apply the monotonicity prior to real supernovae samples to reconstruct the cosmic ex-pansion history.The obtained results are consistent with predictions of the Planck2015 CMB data best-fit ACDM model and those derived from galaxy ages.We also apply the monotonicity prior to forecast the ability of using supernovae of future WFIRST survey to constrain the cosmic expansion history.We find that WFIRST is higly complemen-tary to DESI(using BAO+LSS)and LSST(using BAO+WL)at low redshifts(z ? 0.5),and that the three surveys could cross check with each other at higher redshifts.Regardless of the underlying mechanism that derives the cosmic acceleration,we can always measure an effevtive EoS of "dark energy",which can be used to test dif-ferent dark energy models as well as modified gravity models.Until now,there is still no way to measure the equation of state directly,many works instead are trying to reconstruct the dark energy EoS from various observations non-parametrically.A problem with non-parametric reconstructions is that the results are dominated by high frequency modes,which weakens the overall constraints.In order to reduce or control errors in the reconstructions,one could choose to filter out the high frequency modes in the reconstructed results or apply a continuity prior,which retains only low frequency modes,during the reconstructions.The second work we present here is a study of the effect of the continuity prior on dark energy reconstructions.By using simulated mock type ?a supernovae and mock CMB distance prior,we find that although the continuity prior helps to reduce the errors,the results are often biased.Using principal component analysis,we indentify the cause of the biases.Based on the findings in this work,we suggest that the continuity prior(or any other similar prior)should be examined more closely to avoid potential biases.