Information in Galaxy Surveys Beyond the Power Spectrum

Transcription

1 Information in Galaxy Surveys Beyond the Power Spectrum Non-linear Transformations for Cosmology István Szapudi Institute for Astronomy University of Hawaii FMOS Workshop, March 2, 2011

2 Outline 1 2

3 Why is survey volume important Each shell in k-space has 4πk 2 dk modes The error of P(k) in Gaussian field roughly 1/ N modes Why not use more k? Non-linear evolution and shot noise Understand non-linearities However, even if one were to control non-linear evolution completely, information about the initial conditions leaks out from P(k) Therefore P(k) can be used only up to non-linear k s, and the total number of useful modes is proportional to the volume Standard solution is higher order statistics (complex). We propose an alternative that can be understood as increasing the effective volume of a survey like FastSound by factor of 5 or more

4 Extra variance in non-linear scales Neyrinck, Szapudi, & Rimes 2006

5 Fisher Information z =127 P P log(1 + ) P Gauss global mean z =127 z =1.2 z = S/N k max [h/mpc]

6 )*%+,-)"%%$../*0"1-, Covariance Matrix

7 Logarithmic Mapping Szapudi & Kaiser (2003) From the Schrödinger Equation Ȧ = 1 [ 2 B + 2 A B] 2ma 2 Ḃ = 2 [ 2 A+ A 2 ] 1 B 2 mv 2ma 2 2ma 2 2 V = 4πG ρa 2 (e 2A 1) where A = 1 2 log(1 + δ). Tree level perturbation theory in A corresponds to infinite partial loop summation.

8 nslational, rotational Non-linear evolution is similar to exponential map l conditions

9 nslational, rotational Non-linear evolution is similar to exponential map l conditions

10 Densities Neyrinck, Szapudi, & Szalay 2009 δ δinitial log(1+δ) δgauss

11 Lognormality P[(x x)/ (x)] log(1 + ) Gaussian (x x >)/ (x)

12 Theoretical Calculations of the Bias A Perturbative and a Non-Perturbative Result P log(1+δ) (k) ξ lim = 2 [ ( ) s k 0 P δ (k) 4 + ξ l 1 + ξs 2 C1,2 + ( )] + ξs 2 7 2S 3 4C 1,2 + 2C 1,3 3 + C 2,2 4 + O(ξs 3 ) e Var[log(1+δ cell)]

13 Bias P log(1 + ) (k 0)/P (k 0) First-order Second-order exp( Var[log(1 + )]) P log(1 + ) bias P Gauss bias z s = < 2 cell >

14 Powerspectrum Amplitude 4 2 z =4.2 z =0.69 z =0 P z =127 P log(1 + ) P Gauss P init /P nowig k [h/mpc]

15 Information z =127 P P log(1 + ) P Gauss global mean z =127 z =1.2 z = S/N k max [h/mpc]

16 Simulated Galaxy Survey (Millennium)

17 Simulated Galaxy Survey (Millennium)

18 Still substantial gain Similar results in redshift space

19 Los Alamos Coyote Universe

20 All Cosmological Parameters

21 Focussing on w

22 Summary High Precision Cosmology With Non-linear Transformations Non-linear transformations (log, Gauss) appear to pump cosmological information leaked to higher order back into two-point. Because the technique renders the covariance matrix diagonal, errorbars can be simply scaled with volume show that about factor of 5 information gain is persists with non-linear transformations: log + and Gaussianization Discreteness, bias, and redshift distortion are all included

23 Summary High Precision Cosmology With Non-linear Transformations were at z = 0, for FastSound more simulations are needed to take into account redshift range and geometry Initial calculations suggest that our technique is unlikely to help with BAO But half the constraint on w is from the power spectrum This part of the constraint expected to increase by about factor of 5, Thus the total constraint for FastSound is expected to be about about half of a 1Gpc 3 BAO survey Combining this with the redshift distortion results should provide a great baseline for distinguishing between models Other possibilities, more notably constraining primordial non-gaussianity