Fisher Matrix Analysis of the Weak Lensing Spectrum Manuel Rabold Institute for Theoretical Physics, University of Zurich
Fisher Matrix Analysis of the Weak Lensing Spectrum Manuel Rabold Aarhus University, Denmark ( Steen Hannestad) ( Institute for Theoretical Physics, University of Zurich )
1. Introduction Observables: Theory: Universe in 1. order: Einstein - Boltzmann equations for CDM, Baryons, Photons, Neutrinos, Grav. Potentials Parameters:
1. Introduction Spectrum of Cosmological Weak Gravitational Lensing (cosmic shear, lensing spectrum) :
2. Cosmological Weak Lensing Statistics / cosmological principle: CMB: Matter power spectrum: Lensing Spectrum at a fixed redshift:
2. Cosmological Weak Lensing Statistics / cosmological principle: CMB: Matter power spectrum: Lensing Spectrum at a fixed redshift:
2. Cosmological Weak Lensing
2. Cosmological Weak Lensing WEAK LENSING power spectrum: 2- or 3-dimensional quantity? 2-dimensional spectrum for every value of the radial distance χ or likewise for each value of the redshift z where the source galaxies whose, images are under consideration, are located Using bins in z-space of size Δz? Cosmological WEAK LENSING with the application of TOMOGRAPHIC BINNING
2. Cosmological Weak Lensing N bins N autocorrelation spectra ½ N(N-1) crosscorrelation spectra (symmetry in I and J) Example 2 bins:
3. Statistics Principle of the cosmic variance Inherent in quantities which represent position or direction in the universe e.g. non-zero
3. Statistics Gaussian likelihood distribution for obtaining the data d given the theoretical value of observables w Systematic covariance matrix for angular power spectra Observables and covariance matrix depend on the parameters θ:
3. Statistics Which parameter values maximize the Likelyhood function? FISHER INFORMATION MATRIX By analogy 1 - σ - standard deviation
Overview Analysis through the Fisher matrix method quantification of the parameter uncertainties through the 1-σ-standard deviations Testing of correlations between parameters in spectra, by checking the 1-σ-ellipses
4. Experiments Uncertainties arising from: 1. Cosmological Principle 2. Experimental / Observational limitations Experiments under consideration: WEAK LENSING: Wide Surveys like LSST (Large Synoptic Survey Telescope) or the Euclid space probe (maximum multipole moment l=3000)
4. Expectations Main expectation on cosmological WEAK LENSING: 1) Distribution of all mass (including dark matter) is probed, instead of only the one of luminous matter 2) Complementary information source to the CMB, since weak lensing takes place at a different era 3) Information about parameters that influence the time evolution of the cosmic structures like the ones of the dark energy or the ones of neutrinos Can the degeneracy between both be broken
4. Results CMB only, WEAK LENSING without binning only and both combined For all parameters the uncertainties are reduced, if the information from WEAK LENSING is added to the one of the CMB. Most dramatic decrease for H0 and w
4. Results Ratio between the 1 - σ - standard deviations and the default values of the 8 cosmological parameters under consideration. The table shows the results with the highest sensitivities, which were obtained by using 5 equally sized tomographic bins, and combining the information from Weak Lensing, with the one from the CMB.
4. Results Summary: H0 : Severe reduction of the uncertainty by two orders of magnitude, compared to the CMB only case; correlation between H 0 and w can be reduced w : parameter whos uncertainty descreases most dramatic, by a factor of 414 compared to the CMB case; correalations with H0, n, Ωνh² and S which are inherent in the CMB spectrum do not exist in the case of 5 bin WEAK LENSING
4. Results Summary: Ωνh² : Reduction of the uncertainty by a factor of 40, degeneracy between Ωνh² and w, inherent in the CMB spectrum, is decreased.
4. Results Summary: The uncertainty on the neutrino energy density translates into the one on sum of the neutrino masses: Ωch² : High sensitivity of the WEAL LENSING spectrum on CDM has not been confirmed Ωbh² : Only minor decrease in the uncertainty compared to CMB only case