Large-scale structure and matter in the universe

John Peacock Royal Society January 2003

The distribution of the galaxies

1930s:

Hubble proves galaxies have a non-random distribution

1950s:

Shane & Wirtanen spend 10 years counting 1000,000 galaxies by eye

- filamentary patterns?

Redshift surveysInverting v = cz = Hd gives an approximate distance.

Applied to galaxies on a strip on the sky, gives a ‘slice of the universe’

Spectrum of inhomogeneities

x

Primordial power-law spectrum (n=1?)

Transfer function

Transfer function Key scales:

* Horizon at zeq :

16 (mh2)-1 Mpc

(observe mh)

* Free-stream length : 80 (M/eV)-1 Mpc

(m h2 = M / 93.5 eV)

* Acoustic horizon : sound speed < c/31/2

* Silk damping

M sets damping scale - reduced power rather than cutoff if DM is mixed

Generally assume adiabatic

Parameters: d b v neutrino h w n M

Limiting WDM

m > 0.75 keV from the Ly-alpha forest

(Narayanan et al. 2000)

Galaxies at z>6 need <100 kpc damping length

The universe

according to CDM

Bright galaxies today were assembled from fragments at high redshift

Nonlinear evolution and bias

Linear

NL

Benson et al. (2000):

galaxies tend to be antibiased on small scales in

numerical simulations

= autocorrelation = FT (power spectrum)

Results from the 2dF Galaxy Redshift Survey

Target: 250,000 redshifts to B<19.45

(median z = 0.11)

250 nights AAT 4m time

1997-2002

The 2dFGRS Team Australia

Joss Bland-Hawthorn Terry Bridges Russell Cannon Matthew Colless Warrick Couch Kathryn Deeley Roberto De Propris Karl Glazebrook Carole Jackson Ian Lewis Bruce Peterson Ian Price Keith Taylor

Britain Carlton Baugh Shaun Cole Chris Collins Nick Cross Gavin Dalton Simon Driver George Efstathiou Richard Ellis Carlos Frenk Ofer Lahav Stuart Lumsden Darren Madgwick Steve Maddox

Stephen Moody Peder Norberg John Peacock Will Percival Mark Seaborne Will Sutherland Helen Tadros

33 people at 11

institutions

2dFGRS input catalogue Galaxies: bJ 19.45 from revised APM

Total area on sky ~ 2000 deg2

250,000 galaxies in total, 93% sampling rate Mean redshift <z> ~ 0.1, almost all with z < 0.3

2dFGRS geometry

NGP

SGP

NGP 75x7.5 SGP 75x15 Random 100x2Ø ~70,000 ~140,000 ~40,000

~2000 sq.deg.250,000 galaxies

Strips+random fields ~ 1x108 h-3 Mpc3

Volume in strips ~ 3x107 h-3 Mpc3

The 2dF site

Prime Focus

2dF on the AAT

Final 2dFGRS Sky Coverage

NGP

SGP

Final redshift total: 221,283

2dFGRS Redshift distribution

N(z) Still shows significant clustering at z < 0.1

The median redshift of the survey is <z> = 0.11

Almost all objects have z < 0.3.

Cone diagram: 4-degree wedge

Fine detail: 2-deg NGP slices (1-deg steps)

2dFGRS: bJ < 19.45

SDSS: r < 17.8

2dFGRS power-spectrum results

Dimensionless power:

d (fractional variance in density) / d ln k

Percival et al. MNRAS 327, 1279 (2001)

2dFGRS power spectrum - detail

Ratio to h=0.25CDM model (zero baryons)

nonlinearities, fingers of God, scale-dependent bias ...

CDM Model fitting

Essential to include window convolution and full data covariance matrix

Confidence limits

‘Prior’:

h = 0.7 ± 10%

&

n = 1

mh = 0.20 ± 0.03

Baryon fraction = 0.15 ± 0.07

Consistency with other constraints

Cluster baryon fraction

Nucleo-synthesis

Comparison with other data

All-sky PSCz: = 0.20 0.05 SDSS EDR: = 0.19 0.04

2dFGRS: = 0.16 0.03

Power spectrum: Feb 2001 vs ‘final’

Model fits: Feb 2001 vs ‘final’

mh = 0.20 ± 0.03

Baryon fraction = 0.15 ± 0.07

mh = 0.18 ± 0.02

Baryon fraction = 0.17 ± 0.06

(if n = 1)

Initial conclusions

• Lack of oscillations. Must have collisionless component

• CDM models work

• Low density if n=1 and h=0.7 apply

• possibilities for error:

• Isocurvature?

• =1 plus extra ‘radiation’?

• Massive neutrinos?

• Scale-dependent bias? (assumed gals mass)

Power spectrum and galaxy type

shape independent of galaxy type

Relation to CMB results

Combining LSS & CMB breaks degeneracies:

LSS measures mh only if power index n is known

CMB measures n and mh3 (only if curvature is known)

curvature

total density

baryons

2dFGRS + CMB: Flatness

CMB alone has a geometrical degeneracy: large curvature is not ruled out

Adding 2dFGRS power spectrum forces flatness:

| 1 - tot | < 0.04

Efstathiou et al. MNRAS 330, L29 (2002)

The CMB peak degeneracy

Detailed constraints

for flat models

(CMB + 2dFGRS only: no priors)

Preferred model is scalar-dominated and very nearly scale-invariant

Percival et al. MNRAS 337, 1068 (2002)

The tensor CMB degeneracy

Degeneracy: compensate for high tensors with high n and high baryon density

scalar

plus tensors

tilt to n = 1.2

raise b to 0.03

Effect of neutrinos

Free-stream length: 80 (M/eV)-1 Mpc

(m h2 = M / 93.5 eV)

M ~ 1 eV causes lower power at

almost all scales, or a bump at the largest

scales

=0.05

Neutrino mass limit

Elgaroy et al. PRL 89, 061301 (2002)

Degeneracy: higher neutrino mass resembles lower h, so true h can be higher

Needs a prior:

for < 0.5, limit is f< 0.13, or

M < 1.8 eV (sum of

eigenvalues)

Vacuum equation of state (P = w c2)

w shifts present horizon, so different m

needed to keep CMB peak

location for given h

w < -0.54

similar limit from

Supernovae: w < -0.8 overall

2dFGRS

Extra relativistic components?

Matter-radiation horizon scale depends on matter density (mh2) and relativistic density (=1.68 CMB for 3 light neutrinos).

Suppose rel = X (1.68 CMB ) so apparent mh = mh X-1/2 and m=1 h=0.5 works if X=8

But extra radiation affects CMB too. Maintaining peak location needs h=0.5X1/2 if m=1

If w=-1, 2dFGRS+CMB measure h X-1/2 = 0.71 +- 5% with HST h = 0.72 +- 11%, hence

1.68X = 1.70 +- 0.24 (3.1 +- 1.1 neutrinos)

Summary >10 Mpc clustering in good accord with CDM

– power spectrum favours m h= 0.18 & 17% baryons

CMB + 2dFGRS implies flatness– CMB + Flatness measures m h3.4 = 0.078

– hence h = 0.71 ± 5%, m = 0.26 ± 0.04

No evidence for tilt (n = 0.96 +- 0.04) or tensors– But large tensor fractions not yet strongly excluded

Neutrino mass <1.8 eV if m =1 excluded

w < -0.54 by adding HST data on h (agrees with SN) Boosted relativistic density cannot save m =1

– Neutrino background detected if w=-1

And 2dFGRS has much to say about galaxy formation