BAO & RSD. Nikhil Padmanabhan Essential Cosmology for the Next Generation December, 2017

Transcription

1 BAO & RSD Nikhil Padmanabhan Essential Cosmology for the Next Generation December, 2017

2 BAO vs RSD BAO uses the position of a large-scale feature; RSD uses the shape of the power spectrum/correlation function RSD measurements can be used to measure distances as well as growth AP effect (D A H). Note that the shape of the power spectrum can be used as a standard ruler. Loss of robustness though. Not limited to large scales work to as small a scale as possible (Reid et al 2014 worked to 2.5 Mpc) Issues Velocities Bias There are many different formulations we will simply consider one.

3 An (very) incomplete list of references Kaiser 1987 Fisher 1995 Reid & White 2011 Okumura et al 2015 Uhlemann et al 2015 Bianchi et al 2017 Vlah et al 2017 and various references within

4 Distances Define an angle averaged distance. Measure shifts in the BAO scale. Note the scaling with the sound horizon

5 The Alcock-Paczynski (AP) effect Corrections to the cosmology involve alpha (dilations) and warping (epsilon). Alpha=1, epsilon=0 => true cosmology How do these effect the BAO feature?

6 A quick review of RSD

7 RSD vs FoG vs Redshift Errors FoG = Fingers of God require modeling for precision on small scales. Model as a convolution with an exponential/gaussian (exponentials appear to work better) Velocities correlated with density/position for RSD, not for FoG/redshift errors.

8 The limitations of Kaiser M. White

9 The limitations of PT Reid & White 2011

10 The Challenge of RSD Write the correlation function in redshift space Note that v 12 is function of y If we expand the exponential, we get all powers of v a nonlinear expression If velocities are uncorrelated with densities, average is separable. Reid & White 2011

11 The Gaussian limit If δ and v are Gaussian distributed, we can do the average (Fisher 1995) Expand around y=z Reid & White 2011

12 Recovering the Kaiser limit v 12 depends on density-velocity correlations Fisher, 1995

13 A Streaming Ansatz The Gaussian limit Make an ansatz Re-sum terms back into exponential assuming P is Gaussian

14 The streaming model Reid & White 2011

15 Bias Consider Lagrangian Space Eulerian treatments are also possible; may be advantages to Lagrangian formulation though White 2014

16 Write the correlation function Partially expand out terms in exponential in K White 2014

17 Even more bias terms Vlah, Castorina, White 2017

18 Halo-Zeldovich Constant accounts for small scale configuration space structure Fourier transforming to correlation function moves constant to zero lag term

19 Halo-Zeldovich Vlah, Castorina, White 2017

20 Fit to simulations Vlah, Castorina, White 2017

21 Forecasting Seo & Eisenstein, 2007

22 The Fisher Matrix Define the Fisher matrix in terms of derivatives of the log-likelihood Assuming the likelihood is Gaussian Wikipedia

23 The Fisher matrix Assuming a Gaussian likelihood, and a diagonal covariance matrix Large number of modes, central-limit theorem Seo & Eisenstein, 2007

24 Effective Volume Trade-off between number density and amplitude of fluctuations; characterized by np np > ~ a few, no gains from increasing number density This is a k-dependent statement BAO and LSS surveys usually favor large volume, lownumber density surveys Seo & Eisenstein, 2007

25 BOSS pushes out to higher redshift

26 and surveys a larger volume

27 The BAO Fisher matrix Isolate oscillation when taking derivatives Effective volume uses full power spectrum Reconstruction reduces non-linear damping Photo-zs increase damping along the line-of-sight A 1D example - can be extended to 2D x Seo & Eisenstein, 2007

28 Seo & Eisenstein, 2007

29 A Quick Survey of (e)boss Results Anderson et al, 2014 Aubourg et al, 2014 Alam et al, 2016 Ata et al, 2017

30 A Sharper Feature, More Oscillations Anderson et al, 2014

31 Alam et al, 2016

32 Alam et al, 2016

33 BOSS measures DA and H Alam et al, 2016

34 A BAO Hubble diagram Alam et al, 2016

35 BAO measure the expansion history Alam et al, 2016

36 BAO measure the expansion history Alam et al, 2016

37 BAO measure the growth history Alam et al, 2016

38 A BAO Hubble diagram Anderson et al, 2014

39 BAO constrains cosmology Anderson et al, 2014

40 Measuring Dark Energy Aubourg et al, 2014

41 Measuring Dark Energy Ata et al, 2017

42 The Cosmic Fire Escape Aubourg et al, 2014

43 Tensions in the Hubble Constant? Aubourg et al, 2014

44 A Glimpse of the Future

45 Dark Energy Experiments: BOSS 2031 Dark Energy Survey (DES) BOSS HETDEX HSC imaging PFS spectroscopy Extended BOSS (eboss) Dark Energy Spec. Instrument (DESI) Euclid Large Synoptic Survey Telescope (LSST) Blue = imaging Red = spectroscopy WFIRST-AFTA and many others (JPAS,PAU, KIDS, CHIME..) Weinberg et al, Snowmass 2013

46 B. Flaugher

47 The DESI Survey sq. deg. Tracers Bright galaxy survey (r < 19.5, z < 0.2) Red galaxies (z < 1) Emission line galaxies (z < 1.7) Tracer QSOs (1 < z < 3) Lyman-alpha forest Designed to have multiple possible cross correlations Imaging DECam data (dec < 30) : 9000 sq.deg --- these data will be made public over the next ~4 years Bok, Mosaic data (dec > 30) WISE data

48 DESI is BIG SDSS covered ~ 2h -3 Gpc 3 BOSS is covering ~ 6h -3 Gpc 3 DESI will cover ~ 50h -3 Gpc 3 unprecedented volume

49 DESI Targets B. Flaugher

50 The expansion rate in the DESI era 14 December 2017 DESI CDR

51 Growth rate = dlnd / dlna DESI measures the growth of structure f(r) k= f(r) k=0.02 CDM DGP Redshift z DESI CDR

52 Neutrino measurements Abazajian et al, 2013

53 The power of galaxy surveys