 Goals: testing Lambda CDM model and its extensions
 Testing inflation
 Methods: redshift distance relation (SN, BAO…)
 Linear perturbations: RSD, WL…
 Consistency, complimentarity, future data sets…
2

 We wish to test Friedmann equation: redshift-distance
 Redshift-distance relation has come a long way since the days of Hubble (and people before him)
But we are celebrating CMB, so… 3

 Each initial overdensity (in DM & gas) is an overpressure that launches a spherical sound wave.
 This wave travels outwards at 57% of the speed of light.
 Pressure-providing photons decouple at recombination. CMB travels to us from these spheres.
 Sound speed plummets. Wave stalls at a radius of 147 Mpc.
 Seen in CMB as acoustic peaks
 Overdensity in shell (gas) and in the original center (DM) both seed the formation of galaxies.
Preferred separation of 147 Mpc.
4

 The acoustic oscillation scale depends on the matter-to-radiation ratio
(
W m h 2 ) and the baryon-to-photon ratio (
W b h 2 )
 The CMB anisotropies measure these and fix the oscillation scale to <1%.
 In a redshift survey, we can measure this along and across the line of sight:
 BAO along los
 BAO tranverse
 Yields H(z) and D
M
(z)

10,000 square degrees
1.5M galaxy redshifts
160k QSO Lya forest
6

7

 BAO is damped due to nonlinear evolution
Eisenstein,
Padmanabhan,
White…
 Easiest to see in Zeldovich approximation, for which we have an analytic expression for P(k): BAO is damped by
P w
/P nw
=exp(-k 2 S 2 /2) , where particles separated by 147Mpc
S is rms displacement between two
 Reconstruction: take final density and estimate a filtered displacement field, move particles back with displacements, take random (uniform) particles and displace them, add the two
 Reconstruction reduces
S for both fields (Padmanabhan, White, Cohn)
 At 2nd order in PT removes BAO shifts
 Reconstruction does not reconstruct linear density
8

Schmittful etal
Simulations: reconstruction removes BAO shifts, but those are tiny
One can achieve almost the same
S/N by adding bispectrum
9

10

Aubourg etal
(BOSS coll)
11

 SN1A are standard candles, but to get H
0 need absolute calibration
 Standard ladder: stellar calibration
(cepheids to SN host galaxies…)
 Inverse ladder: BAO is a standard ruler with a known absolute calibration, and at z=0.57 overlaps with SN1A, allowing absolute calibration of SN1A, bringing it down to z=0 gives H
0
12

 Perfect agreement with
Planck CMB
0
 Some discrepancy with direct distance ladder
13

Delubac etal 2014
Font-Ribera etal 2014
Aubourg etal 2014
2.5 sigma discrepant with Planck
No reasonable model can explain it
(need “crazy” models like tuned oscillations)
14

 Volume increase by 15%
 Lya BAO updates: many systematics checks, no issues found so far
 Small increase in errors+small shifts: current discrepancy with
Lambda CDM less than 2 sigma
 CMASS/LOWZ BAO updates: “optimal analyis” under way, not expected to yield major changes vs DR11
 Huge improvements expected in RSD/AP due to better nonlinear modeling
 SDSS-IV (eBOSS) is already underway
15

Growth of structure by gravity

Perturbations can be measured at different epochs:
1.
CMB z=1000
2.
Ly-alpha forest z=2-4
3.
Weak lensing z=0.3-2
4.
Galaxy clustering, clusters z=0-2
Sensitive to matter components, initial conditions…

Picture from
Binney & Tremaine
Nearly scaleinvariant spectrum
Suppression on small scales
Probes initial conditions
We measure redshifts and angles, and the shape is not a power law, so there are neoclassical tests in broadband measurements as well
17

Galaxy clustering in redshift space
SDSS
Measures 3-d distribution, has many more modes than projected quantities like shear from weak lensing
Easy to measure: effects of order unity, not 1%

 Galaxy clustering traces dark matter clustering
 Amplitude depends on galaxy type: galaxy bias b
P gg
(k)=b 2 (k)P mm
(k)
 To determine bias we need additional information
 Galaxy bias can be scale dependent: b(k)
 Once we know bias we know how dark matter clustering grows in time
Tegmark et al. (2006)

Redshift space distortions redshift cz=aHr+v p
20

Kaiser
1984
Conservation of galaxies
Jacobian drop v/z
Go to Fourier space, assume v is irrotational
Define Q =i kv
Use continuity equation
21

On very large scales linear RSD distortions: Kaiser formula
From angular dependence we can determine velocity power proportional to f s
8
On small scales: virialized velocities within halos lead to
FoG, extending radially 10 times farther than transverse
White etal 2011 22

Nonlinear gravity
Nonlinear bias
Nonlinear velocities (FoG)
In correlation function one can get quite far with Zeldovich approximation
In P(k) standard perturbation theory+bias
Simulations vs model
Vlah, US etal 2013
23

f s
8
= 0.415 +/- 0.033 ( z =0.57)
( Reid et al 2012, Samushia et al 2013, Beutler et al 2013 ) 24

Current models go to k=0.1-0.2h/Mpc, monopole and quadrupole only
There is a lot more information at high k
Beutler etal 2014
25

Can we model quasi-linear regime and extract more information?
 Need to develop nonlinear models that are sufficiently general to allow for any reasonable nonlinear effects present in the data, while preserving as much of cosmological information as possible
 Some can be modeled by perturbation theory (PT)
 There is always more information on small scales, but most of it is hopelessly corrupted by nonlinear effects that cannot be modeled in PT
 One needs to model our ignorance that is genteel (no sharp k or r cutoffs) and obeys all symmetries (e.g. k 2 P
L
(k) at low k) and all physics (the parameters are physical, e.g. FoG is determined by halo mass…)
 In recent years a workhorse has been the halo model+PT
26

 Use PT (e.g. Zeldovich, SPT…) to describe large scales
 Use halo picture to describe small scales
 Halo description: halo profile: take moments
Expand in (even) powers of k
 P
1halo
=A
0 k 0 -A
2 k 2 +A
4 k 4 +…
 P
2halo
=P
L
(k)(1-A
2 k 2 …) (or replace P
L with PT version)
 FoG: cannot use low k expansion, need to resum the terms
 P
1halo
=A
0
G(k), P
2halo
=P
L
(k)G(k)
27

Lorentzian does a reasonable job
Low k expansion
G(k)=1-k 2 m 2 s 2 v
/2
1% valid only to k=0.1h/Mpc (this is EFT domain)
Value of s 2 v determined by the halo mass (strong prior)
Okumura etal 2015
28

Okumura etal 2015
Linear Kaiser never a good model
NL model achieves 1% to k=0.4h/Mpc by introducing many physical parameters in the PT model: central and satellite galaxies, each with a bias and FoG, 1-halo contribution from central-satellite pairs, halo exclusion…
A lot of neoclassical test information in here (AP parameter D
M
/D
H
)
29

Reid etal 2014
 2.5% determination of f s
8 in DR11 (more than
2x reduction of error) by using information from very small scales
 Needs to be tested more, marginalized…
30

Weak Gravitational Lensing: sensitive to total mass distribution (DM dominated)
Distortion of background images by foreground matter
Unlensed Lensed

convergence k =
3
W m
H
0
2
2
( r
LSS
r ) r
ò
2 F dr
= r lSS
( r
LSS
r ) r r lSS dr d a shear



1
2
( l
( l

)
)
=
=



( l
( l

)
) cos sin
2

2
 l l
Convergence shear relation in Fourier space

 Just a projection of total matter P(k)
 Need P(k) for dark+baryonic matter: a lot of information in nonlinear regime
 Dark matter is easy
 Sensitive to many cosmological parameters

Challenges:
Kiblinger et al 2013
Small scales: could be contaminated by baryonic effects
Redshift distributions not completely known
Various systematics: a lot of data removed
DES/HSC data coming soon!
34

T lensed
(
 n )
=
T unlensed
(
 n
+
 d )
 d
= -

2
  -
2

 Here
 is the convergence and is a projection of the matter density perturbation.
 Lensing creates magnification and shear
Okamoto and
Hu 2002

40 sigma in Planck 2015
36

 astrophysical effects that redistribute matter inside the halos change mass distribution (AGNs…), but not total mass
 Parametrizing ignorance with the halo model: change
1 halo term A
A
0 halo term
2
, A
4
…, but not
, there is also a small 2
 With proper modeling and marginalization these effects do not reduce information substantially
37

WL Method B: galaxy-shear correlations
Cross-correlation proportional to bias b
Galaxy auto-correlation proportional to b 2

Baldauf, Smith, US, Mandelbaum (2009)
Nonlinear linear
Cross-correlation coefficient r nearly unity

Mandelbaum etal,
2013
LENSES SOURCES
70,000 M*-1 galaxies (z<0.15), 10M, well calibrated photozs
62,000 low z LRGs (0.16<z<0.3), using spectroscopic surveys
35,000 high z LRGs (0.36<z<0.47)

Science complementarity: f vs
W m
, tests of modified gravity…
41

 WL: theoretical uncertainties (almost) under control
 WL+RSD: many redundancy tests can be done: higher order correlations, scale dependence of the signal…
 RSD and WL B: many different ways to slice the data (e.g. remove close pairs, split by luminosity or color…), and to analyze the data (e.g. remove line of sight pairs)
 in the end they all have to agree to believe the results
 Cluster abundance methods will be covered by others: measure one number, redundancy checks?
42

Some tension with Planck, issues related to IGM simulations limit the accuracy
43

Neutrino mass can be measured by LSS
 Neutrino free streaming inhibits growth of structure on scales smaller than free streaming distance
 If neutrinos have mass they contribute to the total matter density, but since they are not clumped on small scales dark matter growth is suppressed
 Minimum signal at 0.06eV level makes 4% suppression in power, mostly at k<0.1h/Mpc
 SDSS coud reach this at 1sigma, DESI at 2-3 sigma
 LSS: weak lensing of galaxies and
CMB, galaxy clustering m=0.15x3, 0.3x3, 0.6x3, 0.9x1 eV

To break this degeneracy we need BAO+CMB:
W m
=0.31+/-0.02
Probes: CFHTLS WL,
BOSS RSD, SDSS-III WL, cluster abundance, tSZ
At the moment LSS, even if combining all data sets, has a larger error on amplitude than Planck CMB lensing
But LSS+Planck is more sensitive to neutrino mass
45

Reasonable consensus between
Planck+BAO and
LSS zero neutrino mass becoming disfavored at 2sigma, cannot distinguish between normal and inverted hierarchy
46

A powerful combination: CMB+BAO+LSS (lensing…) adding Planck lensing and BAO to Planck reduces error on curvature by 12!
47

Future imaging surveys: DES, HSC, Euclid, LSST, Wfirst,
(Spherex ?)…
Plan: 10 8 -10 9 galaxies (without redshifts)
Future spectroscopic surveys: DESI, PFS, Euclid, Wfirst …
Plan: 10 7 galaxies (with redshifts)
Future CMB lensing (S3, S4)
New technique: 21cm, both for BAO (Chime…) and reionization
(Hera, SKA…)

Font-Ribera etal 2014…
 Curvature
W k to 0.07%: could be improved with CMB lensing, but still a long way from cosmic variance limit
 n s
, dn s
/dlnk to 0.0015 with Lya forest P
1d
, otherwise 0.005,
Spherex can also reach 0.001: test inflation?
 f nl to 1, possibly to 0.2 with
Spherex
 M n to 0.02eV, limited by
Planck optical depth uncertainty: can we do better
(21cm?)
49

 Better modeling of the ignorance
 Higher order correlations (including primordial nongaussianities etc.)
 Other types of analysis (peaks, voids…)
 Covariance matrix modeling with and without simulations
 No mode left behind: extract all the linear modes up to the noise using forward or backward modeling
50

 BAO+SN+CMB: a winning combination of neoclassical tests
 LSS: RSD and WL have a lot of promise, lots of redundancy, best results come from CMB lensing
 Amplitude of fluctuations at z<1 determined by several probes: 3-
10% precision (CMB WL, RSD, clusters, tSZ C l
)
 Some are high, some are low, some consensus at s
8 this lower than Planck lensing?
=0.78-0.80. Is
 No evidence of neutrino mass yet:
S m n
<
0.20eV (95%), but likelihood not peaking at m n
=0 anymore (at 1-2sigma)
 No evidence of curvature, despite 1 order of magnitude improvement in last year
 Future LSS probes will do a lot better
51