1. Large-scale structure and matter in the universe John Peacock Royal Society January 2003

2. 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?

3. Redshift surveys Inverting v = cz = Hd gives an approximate distance. Applied to galaxies on a strip on the sky, gives a ‘slice of the universe’

4. Inflationary origin of structure? Assume early universe dominated by scalar-field V(  ) at GUT energies Predicts small fluctuations in metric. Scalar fluctuations (= Newtonian potential) have nearly flat spectrum - also expect tensor modes (gravity waves)

5. Spectrum of inhomogeneities  x Primordial power-law spectrum (n=1?) Transfer function

6. Key scales: * Horizon at z eq : 16 (  m h 2 ) -1 Mpc (observe  m h) * Free-stream length : 80 (M/eV) -1 Mpc (  m h 2 = M / 93.5 eV) * Acoustic horizon : sound speed < c/3 1/2 * 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

7. Limiting WDM m > 0.75 keV from the Ly-alpha forest (Narayanan et al. 2000) Galaxies at z>6 need <100 kpc damping length

8. The CDM power spectrum growth:  a  a f(  [a]) Break scale relates to  (density in units of critical density): In practice, get shape parameter  almost =  h 

9. Tilt, COBE and cluster normalization

10. The universe according to CDM Bright galaxies today were assembled from fragments at high redshift

11. 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)

12. 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

13. 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

14. 2dFGRS input catalogue  Galaxies: b J  19.45 from revised APM  Total area on sky ~ 2000 deg 2  250,000 galaxies in total, 93% sampling rate  Mean redshift ~ 0.1, almost all with z < 0.3

15. 2dFGRS geometry NGP SGP NGP 75  x7.5  SGP 75  x15  Random 100x2  Ø ~70,000 ~140,000 ~40,000 ~2000 sq.deg. 250,000 galaxies Strips+random fields ~ 1x10 8 h -3 Mpc 3 Volume in strips ~ 3x10 7 h -3 Mpc 3

17. The 2dF site Prime Focus

18. 2dF on the AAT

19. Final 2dFGRS Sky Coverage NGP SGP Final redshift total: 221,283

20. 2dFGRS Redshift distribution  N(z) Still shows significant clustering at z < 0.1  The median redshift of the survey is = 0.11  Almost all objects have z < 0.3.

21. Cone diagram: 4-degree wedge

22. Fine detail: 2-deg NGP slices (1-deg steps) 2dFGRS: b J < 19.45 SDSS: r < 17.8

23. 2dFGRS power-spectrum results Dimensionless power: d (fractional variance in density) / d ln k Percival et al. MNRAS 327, 1279 (2001)

24. Effects of baryons

25. 2dFGRS power spectrum - detail Ratio to  h=0.25 CDM model (zero baryons) nonlinearities, fingers of God, scale-dependent bias...

26. Power spectrum and survey window  Window sets power resolution and maximum scale probed: P obs (k) = P(k) * |W(k)| 2  Full survey  more isotropic, compact window function.

27. CDM Model fitting Essential to include window convolution and full data covariance matrix

28. Confidence limits ‘Prior’: h = 0.7 ± 10% & n = 1  m h = 0.20 ± 0.03 Baryon fraction = 0.15 ± 0.07

29. Consistency with other constraints Cluster baryon fraction Nucleo- synthesis

30. Comparison with other data All-sky PSCz:  = 0.20  0.05SDSS EDR:  = 0.19  0.04 2dFGRS:  = 0.16  0.03

31. Power spectrum: Feb 2001 vs ‘final’

32. Model fits: Feb 2001 vs ‘final’  m h = 0.20 ± 0.03 Baryon fraction = 0.15 ± 0.07  m h = 0.18 ± 0.02 Baryon fraction = 0.17 ± 0.06 (if n = 1)

33. 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 )

34. Tests on mock data

35. Recovering  CDM

36. Redshift-space distortions (Kaiser 1987) z obs = z true +  v / c  v prop. to  0.6  0.6 b -1  n/n Apparent shape from below linearnonlinear (bias)

37. Redshift-space clustering  z-space distortions due to peculiar velocities are quantified by correlation fn  ( ,  ).  Two effects visible: –Small separations on sky: ‘Finger-of- God’; –Large separations on sky: flattening along line of sight r  

38.  and   Fit quadrupole/monopole ratio of  ( ,  ) as a function of r with model having    0.6 /b and  p (pairwise velocity dispersion) as parameters  Best fit for r > 8 h -1 Mpc (allowing for correlated errors) gives:  =  0.6 /b = 0.43  0.07  p = 385  50 km s -1  Applies at z = 0.17, L =1.9 L* (significant corrections) Model fits to z- space distortions  = 0.3,0.4,0.5;  p = 400  = 0.4,  p = 300,500  99%

39. 2dFGRS in COLOUR passive active R magnitudes from SuperCosmos Rest-frame colour gives same information as spectral type,  but to higher z

42. Redshift-space distortions and galaxy type Passive:  =  0.6 /b = 0.46  0.13  p = 618  50 km s -1 Active:  =  0.6 /b = 0.54  0.15  p = 418  50 km s -1

43. Power spectrum and galaxy type shape independent of galaxy type

44. Meaning of clustering Neyman Scott & Shane (1953): random clump model  r  (r < R) ”  r  obs:  r   ”  = 2.4? Modern view: gravitational instability of (C)DM - sheets, pancakes, filaments, voids...

45. Dark-matter haloes and bias Moore et al:  = [ y 3/2 (1+y 3/2 ) ] -1 ; y = r/r c

46. Correlations from smooth haloes PS++ mass function and NFW++ halo profile gives correct clustering  CDM  CDM Lin NL APM

47. Halo occupation numbers depend on mass PS++ mass function wrong shape for cluster/group LF Correct weighting of low-mass haloes predicts antibias  CDM

48. Relation to CMB results Combining LSS & CMB breaks degeneracies: LSS measures  m h only if power index n is known CMB measures n and  m h 3 (only if curvature is known) curvature total density baryons

49. The CMB geometrical degeneracy

50. 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)

51. The CMB peak degeneracy

52. 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)

53. 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

54. Effect of neutrinos Free-stream length: 80 (M/eV) -1 Mpc (  m h 2 = M / 93.5 eV) M ~ 1 eV causes lower power at almost all scales, or a bump at the largest scales  =0.05

55. 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)

56. Vacuum equation of state (P = w  c 2 ) 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

57. Extra relativistic components? Matter-radiation horizon scale depends on matter density (  m h 2 ) and relativistic density (=1.68  CMB for 3 light neutrinos). Suppose  rel = X (1.68  CMB ) so apparent  m h =  m h X -1/2 and  m =1 h=0.5 works if X=8 But extra radiation affects CMB too. Maintaining peak location needs h=0.5X 1/2 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)

58. the equation of state of the vacuum energy w < - 0.54 the CMB angular power spectra (top panel) compared to expected MAP errors (lower panel) Further constraints from combining 2dFGRS and CMB P(k) for flat cosmologies

59. 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 h 3.4 = 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