1. Some bonus cosmological applications of BigBOSS ZHANG, Pengjie Shanghai Astronomical Observatory BigBOSS collaboration meeting, Paris, 2012 Refer to related talks by Shao, Jiawei on the SZ tomography with BigBOSS, Oct. 10 Yang, Xinjuan on mapping dark matter with BigBOSS, Oct. 10

2. What BigBOSS can do BAO, redshift space distortion (RSD), primordial non-Gaussianity, small scale power/neutrino mass/dark matter properties What else BigBOSS can do for free, but with tremendous gains: 3D peculiar velocity reconstruction at cosmological distance (ZPJ et al. 2012; Zheng Yi, ZPJ, et al. 2012, in preparation) 2D dark matter mapping with cosmic magnification (ZPJ & Pen 2005; Yang Xinjuan & ZPJ, 2011; Yang, ZPJ, et al. 2012) – Not galaxy-galaxy lensing! – Refer to the talk By Yang Xinjuan on Oct. 10 The kinetic SZ tomography (ZPJ 2010; Shao, ZPJ, et al. 2011; ZPJ & Stebbins, 2011; Li, ZPJ, Chen, 2012) – probe (1) missing baryons and (2) horizon scale inhomogeneities (dark flow, etc.) – Refer to the talk by Shao Jiawei on Oct. 10

3. KIAS cosmology 20083 Matter distribution in our universe is inhomogeneous Gravitational attraction arising from inhomogeneity perturbs galaxies and causes deviation from the Hubble flow v r v r peculiar velocity v=Hr What is peculiar velocity?

4. 4 What makes peculiar velocity special and important to probe the dark universe? At scales larger than galaxy clusters, only respond to gravity In linear regime, honest tracer of matter distribution Necessary for the complete phase-space description of the universe

5. 5 How to measure peculiar velocity? Traditional method v r Subtract the Hubble flow to obtain the peculiar velocity v=Hr Measure the recession velocity from the redshift Measure the distance through FP,TF,FJ,SN, etc. Error increases at least linearly with distance. Can not apply at cosmological distances

6. 6 New probes of large scale peculiar velocity which do not rely on distance indicators These new probes of large scale peculiar velocity do not rely on subtracting the Hubble flow, so are applicable to z~1 3D velocity reconstruction in redshift surveys (this talk) The kinetic Sunyaev Zel'dovich effect – Galaxy clusters (e.g. Kashlinsky et al. 2008--; Hand et al. 2012) – The diffuse IGM (Ho et al. 2009; Shao et al. 2011) – Dark flow and horizon scale flows in general (ZPJ 2010; ZPJ & Stebbins, 2011) Type Ia supernovae at z<~0.5

7. From the galaxy distribution to the velocity distribution A number of key assumptions/uncertainties/errors Our works: (1) single out the velocity component that can be reconstructed, (2) set up a viable methodology for the reconstruction, (3) eliminate uncertainties in f and b_g, in light of redshift distortion. Assuming linear evolution. Complicated by nonlinearity Unknown. Incomputable from first principle Real space density. Complicated by redshift distortion What velocity is it?

8. The velocity decomposition Only grows after orbit crossing Completely correlated with the density Uncorrelated with the density. Caused by nonlinearity ZPJ, Zheng Yi & Pan Jun, 2012

9. The three velocity eigen-modes: different origins, different scales v_delta dominates at large scale v_S grows with nonlinearities v_B grows after v_S, after orbit crossing Zheng Yi, et al. 2012, in preparation

10. The three velocity modes have different impacts on RSD v_S causes a u^4 distortion v_delta is the source of the usual Kaiser effect, but with complicated corrections! V_B only causes damping (FOG), virtually speaking. Redshift space power spectrum

11. A potentially severe source of systematical errors for RSD cosmology RSD measures instead of f, so there is a systematical error there: already 10% at k=0.1! Perturbation theory: ZPJ, Zheng Yi & Pan Jun, 2012 Numerical simulations: Zheng Yi, et al. 2012

12. What velocity can be reconstructed? By the consideration of information budget, a redshift survey can at best reconstrucut 3D v_delta. – Some statistics of v_S and v_B may be recovered Now the reconstruction of a stochastic 3D vector field (v_delta) becomes the reconstruction of a deterministic window function W Velocity divergence

13. Redshift distortion---Noise or signal? We do not directly measure the real space density http://www.astr.ua.edu/keel/galaxies/hamcollapse.gif

14. Real space to redshift space In reality, we only have the redshift space density. So we have to seek for an estimator like this: We can show that The key is to infer W(k) and r(k)

15. Redshift distortion as a source of information instead of noise(1 ) W can be inferred from analyzing the redshift space power spectrum With W, r can be calculated

16. Redshift distortion as a source of information instead of noise(2) From the redshift space distortion, one can measure W^s in even more model independent ways. The bottom line is, ONLY the correct W^s can undo the redshift distortion caused by v_delta. By tuning W^s such that the RSD consistent with the one with v_delta=0, we obtain W^s. Advantages: Less assumptions on cosmology/gravity/DE, with nonlinearity evolution automatically taken into account Less dependence on galaxy bias (free of deterministic bias)

17. To do list Evaluate relevant statistics with N-body simulations (Zheng Yi, et al. 2012a,b, in preparation) Evaluate its applicability to BigBOSS, against mock catalogs Applications to explore: mapping dark matter, the thermal and kinetic SZ tomography, testing gravity, etc.