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Register a new userNonparametric reconstruction of the cosmic expansion with local regression smoothing and simulation extrapolation
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In this work we present a nonparametric approach, which works on minimal assumptions, to reconstruct the cosmic expansion of the Universe. We propose to combine a locally weighted scatterplot smoothing method and a simulation-extrapolation method. The first one (Loess) is a nonparametric approach that allows to obtain smoothed curves with no prior knowledge of the functional relationship between variables nor of the cosmological quantities. The second one (Simex) takes into account the effect of measurement errors on a variable via a simulation process. For the reconstructions we use as raw data the Union2.1 Type Ia Supernovae compilation, as well as recent Hubble parameter measurements. This work aims to illustrate the approach, which turns out to be a self-sufficient technique in the sense we do not have to choose anything by hand. We examine the details of the method, among them the amount of observational data needed to perform the locally weighted fit which will define the robustness of our reconstruction. In view of our results, we believe that our proposal offers a promising alternative for reconstructing global trends of cosmological data when there is little intuition on the relationship between the variables and we also think it even presents good prospects to generate reliable mock data points where the original sample is poor.
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We discuss nonparametric tests for parametric specifications of regression quantiles. The test is based on the comparison of parametric and nonparametric fits of these quantiles. The nonparametric fit is a Nadaraya-Watson quantile smoothing estimator. An asymptotic treatment of the test statistic requires the development of new mathematical arguments. An approach that makes only use of plugging in a Bahadur expansion of the nonparametric estimator is not satisfactory. It requires too strong conditions on the dimension and the choice of the bandwidth. Our alternative mathematical approach requires the calculation of moments of Nadaraya-Watson quantile regression estimators. This calculation is done by application of higher order Edgeworth expansions.
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We test Einstein gravity using cosmological observations of both expansion and structure growth, including the latest data from supernovae (Union2.1), CMB (WMAP7), weak lensing (CFHTLS) and peculiar velocity of galaxies (WiggleZ). We fit modified gravity parameters of the generalized Poisson equations simultaneously with the effective equation of state for the background evolution, exploring the covariances and model dependence. The results show that general relativity is a good fit to the combined data. Using a Pad{e} approximant form for the gravity deviations accurately captures the time and scale dependence for theories like $f(R)$ and DGP gravity, and weights high and low redshift probes fairly. For current observations, cosmic growth and expansion can be fit simultaneously with little degradation in accuracy, while removing the possibility of bias from holding one aspect fixed.
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