Parameters “ and “ characterizing modified gravity theory are given by

1. Principal Component Analysis of Modified Gravity using Cosmological Measurements ShinsukeAsaba(Nagoya University) email: asaba.shinsuke@j.mbox.nagoya-u.ac.jp Collaborator: Chiaki Hikage1, Kazuya Koyama2, Gong-Bo Zhao2,3, Alireza Hojjati4, Levon Pogosian2,5,6 1 Nagoya University, 2 University of Portsmouth, 3 Chinese Academy of Science, 4 EwhaWomans University, 5 Simon Fraser University, 6 University of Cambridge Results Introduction & Motivation We suppose the experiments are PLANCK CMB survey Euclid( ) Tomography survey Euclid( ) +BOSS( ) 2-dimensional forecasted confidence contours of cosmological parameters We calculate by using temperature and polarization modes of CMB, and 2D contain CMB, WL, GC and cross correlations (CMB×WL, CMB×GC, WL×GC). MG mean after marginalizing over the parameters of modified gravity. The errors of the eigenmodes of (Red) and (blue) Lines are the results calculated from data of CMB and tomography survey. Dots are the results after adding data of spectroscopic redshift survey. The eigenmodes of (left) and (right) by using all data Spectroscopic redshift survey Recent observations detect the accelerating expansion of the Universe. Which is the reason for the accelerating expansion We show the constraints on modified gravity theory by using CMB survey and near future tomography and spectroscopic redshift survey. Parameters Dark Energy or Modified Gravity Theory ? Parameters “ and “ characterizing modified gravity theory are given by : Space curvature perturbation, : Gravitational potential We do not determine the function forms of and , but bin and on the grid in the space, so that the number of parameters is 2 × 15 × 15. Observables Angular power spectra (2D) : Primordial curvature power spectra, : Angular transfer function Weak lensing (WL) ( : lens potential) Galaxy number counts (GC) ( : density contrast) Integrated Sachs-Wolfe (ISW) effect of CMB Observed power spectra in redshift space (3D) ( ) : galaxy power spectrum : peculiar velocity power spectrum is the time derivative of the solution to The observations of GC and the power spectra constrain . The observations of WL and CMB constrain . We can constrain by using all observations. Method of analysis We do a principal component analysis of and in the space, so that we obtain principal components constrained efficiently from observations without losing the information, namely the modes having higher S/N. The principal components are the eigenmodes of the covariance matrix, and the error of the principal components is given by the square roots of the eigenvalues associated with the eigenmodes. Covariance matrix We use the inverse of the Fisher matrix as the lower limit of the covariance matrix (Cramér-Rao inequality). Fisher matrix from angular power spectra Fisher matrix from observed power spectra in redshift space Discussion & Conclusion We performed a principal component analysis of and by using PLANCK and near future tomography and spectroscopic redshift survey, and obtained well-constrained modes. We found thatspectroscopic redshift survey improve the constraints on and by about 5 times compared to the constraints from tomography survey + CMB survey. We found the information of lens potential obtained mainly from tomography survey and the information of density contrast obtained from spectroscopic survey. We can discuss the constraint on the eigenmodes of the parameters of modified gravity and with high precision , because we can constrain the cosmological parameters by using the data of CMB independently of the parameters of modified gravity. We will be able todecide the property of the accelerating expansion of the Universe in detail by constraining the eigenmodes.