BAO & RSDNikhil Padmanabhan

Essential Cosmology for the Next Generation

December, 2017

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 (DA 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.

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

Distances

Define an angle averaged distance.

Measure shifts in the BAO scale. Note the scaling with the sound horizon

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?

A quick review of RSD

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.

The limitations of Kaiser

M. White

The limitations of PT

Reid & White 2011

The Challenge of RSDWrite the correlation function in redshift space

Note that v12 is function of y

If we expand the exponential, we get all powers of v – a nonlinear expression

Reid & White 2011

If velocities are uncorrelated with densities, average is separable.

The Gaussian limitIf δ and v are Gaussian distributed, we can do the average (Fisher 1995)

Expand around y=Z

Reid & White 2011

Recovering the Kaiser limit

v12 depends on density-velocity correlations

Fisher, 1995

A Streaming Ansatz

Re-sum terms back into exponential assuming P is Gaussian

Make an ansatz

The Gaussian limit

The streaming model

Reid & White 2011

BiasConsider Lagrangian Space

White 2014

Eulerian treatments are also possible; may be advantages to Lagrangianformulation though

Write the correlation function

Partially expand out terms in exponential in K

White 2014

Even more bias terms

Vlah, Castorina, White 2017

Halo-Zeldovich

Constant accounts for small scale configuration space structure

Fourier transforming to correlation function moves constant to zero lag term

Halo-Zeldovich

Vlah, Castorina, White 2017

Fit to simulations

Vlah, Castorina, White 2017

Forecasting

Seo & Eisenstein, 2007

The Fisher Matrix

Wikipedia

Define the Fisher matrix in terms of derivatives of the log-likelihood

Assuming the likelihood is Gaussian

The Fisher matrix

• Assuming a Gaussian likelihood, and a diagonal covariance matrix• Large number of modes, central-limit theorem

Seo & Eisenstein, 2007

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, low-number density surveys

Seo & Eisenstein, 2007

BOSS pushes out to higher redshift

… and surveys a larger volume

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

Seo & Eisenstein, 2007

A Quick Survey of (e)BOSS Results

Anderson et al, 2014

Alam et al, 2016

Aubourg et al, 2014

Ata et al, 2017

A Sharper Feature, More Oscillations

Anderson et al, 2014

Alam et al, 2016

Alam et al, 2016

BOSS measures DA and H

Alam et al, 2016

A BAO Hubble diagram

Alam et al, 2016

BAO measure the expansion history

Alam et al, 2016

BAO measure the expansion history

Alam et al, 2016

BAO measure the growth history

Alam et al, 2016

A BAO Hubble diagram

Anderson et al, 2014

BAO constrains cosmology

Anderson et al, 2014

Measuring Dark Energy

Aubourg et al, 2014

Measuring Dark Energy

Ata et al, 2017

The Cosmic Fire Escape

Aubourg et al, 2014

Tensions in the Hubble Constant?

Aubourg et al, 2014

A Glimpse of the Future

BOSS

20292027202520232021201720152013 2019

Dark Energy Experiments: 2013 - 2031

Dark Energy Survey (DES)

Extended BOSS (eBOSS)

HSC imaging PFS spectroscopy

Dark Energy Spec. Instrument (DESI)

Large Synoptic Survey Telescope (LSST)

Euclid

WFIRST-AFTA

BOSS

HETDEX

2031

Blue = imagingRed = spectroscopy

Weinberg et al, Snowmass 2013… and many others (JPAS,PAU, KIDS, CHIME..)

B. Flaugher

The DESI Survey

• 2019-2024

• 14000 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

DESI is BIG

• SDSS covered ~ 2h-3Gpc3

• BOSS is covering ~ 6h-3Gpc3

• DESI will cover ~ 50h-3Gpc3

• unprecedented volume

DESI Targets

B. Flaugher

The expansion rate in the DESI era

14 December 2017DESI CDR

DESI measures the growth of structure

0 0.5 1 1.5Redshift z

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Gro

wth

rate

= d

lnD

/ d

lna

DGP

f(R)k=0.02

CDM

f(R)k=0.1

DESI CDR

Neutrino measurements

Abazajian et al, 2013

The power of galaxy surveys