Low-z BAOs: proving acceleration and testing Neff

1. Low-z BAOs:proving acceleration and testing Neff Will Sutherland (QMUL)

2. Talk overview Cases for low-redshift BAO surveys : • Smoking-gun test of cosmic acceleration - assumes only homogeneity & isotropy, not GR. • Testing fundamental assumptions from CMB era, in particular the number of neutrino species.

3. 2005: first observation of predicted BAO feature by SDSS and 2dFGRS (Eisenstein et al 2005)

4. BAO feature in BOSS DR9 data: ~ 6 sigma (Anderson et al 2012)

5. BAO observables: transverse and radial Spherical average gives rs / DV ,

6. BAOs : strengths and weaknesses • BAO length scale calibrated by the CMB . + Uses well-understood linear physics (unlike SNe). - CMB is very distant: hard to independently verify assumptions. • BAO length scale is very large, ~ 153 Mpc: + Ruler is robust against non-linearity, details of galaxy formation + Observables very simple: galaxy redshifts and positions. - Huge volumes must be surveyed to get a precise measurement. - Can’t measure BAO scale at “ z ~ 0 ” • + BAOs can probe both DA(z) and H(z); no differentiation needed for H(z). More sensitive to “features” in H(z); enables consistency tests for flatness, homogeneity.

7. “Cosmic speed trap:”Proving cosmic acceleration with BAOs only • Assuming homogeneity, evidence for accelerating expansion is strong: SNe, CMB+low-z measurements . • SNe require acceleration independent of GR (if no evolution, and photon number conserved) • CMB + LSS : acceleration evidence very strong, but requires assumption of GR. • Possible loophole to allow non-accelerating model : • Assume SNe are flawed by evolution and/or photon non-conserving processes (peculiar dust, photon/dark sector scattering). • AND: GR not correct, so CMB inferences are misleading. • This is contrived, but we should close this loophole

8. Cosmic expansion rate: da/dt

9. Cosmic expansion rate, relative to today

10. BOSS: Busca et al 2012 Caveat: assumed flatness and standard rs

11. Speed-trap: motivations • Radial BAO scale directly measures rs H(z) / c • Ratio of two such measurements will cancel rs , and detect acceleration directly. • BUT, there is a practical problem: • very feeble acceleration at z > 0.3 • Not enough volume to measure radial BAOs at z < 0.3 . • Can’t measure rs H0 at “z ~ 0”. • Spherical-average BAOs can prove acceleration IF we assume almost-flatness, but we don’t want to rely on this. • Workaround: use radial BAO at z ~ 0.7, compare to spherical-average BAO observable at z ~ 0.2 .

12. Limit relating DV(z1) and H(z2) for any non-accelerating model: Comoving radial distance: No acceleration requires : therefore:

13. Assuming homogeneity, angular-diameter distance is : No acceleration requires : Therefore : Open curvature: ( ) > 1 Closed curvature :

14. radial BAO observable: Spherical-average BAO observable, at z1 : Divide: Use previous limit for DV :

15. Rearrange square-bracket onto LHS: now RHS becomes 1 + O(z2), depends very weakly on curvature. Define XS as “excess speed” , ratio of BAO observables: Flat models : RHS = 1 exactly . Open models : RHS < 1 … limit gets stronger. Closed models : RHS > 1 … need to constrain this. But, closed models have a maximum angular diameter distance < Rc / (1+z) , so z ~ 3 galaxy sizes eliminate “super-closed” models.

16. (Sutherland, MN 2012, arXiv:1105.3838) Blue/green: predictions for LambdaCDM / wCDM Red: upper limits for non-accelerating model, various (extreme) curvatures.

17. Speed-trap result: • If we assume • Homogeneity and isotropy • Redshift due to cosmic expansion, and constant speed of light • BAO length conserved in comoving coordinates • No acceleration after redshift z2 • Then : • Observable BAO ratio must be below red-lines above • If observed XS > 3 sigma above red-line , at least one of four statements above is false. • “Signal” ~ 10 percent: need < 3% (ideally 2%) precision on ratio of two BAO observables. Challenging, but definitely achievable.

18. Measuring the absolute scale of BAOs : • BAO length scale is essentially the sound horizon at “drag redshift” zd ~ 1020. • If we assume • Standard GR • Standard neutrino content • Standard recombination history • Nearly pure adiabatic fluctuations • Negligible early dark energy • Negligible variation in fundamental constants • Then BAO length depends on just two numbers, ωmand ωb ; both well determined by WMAP and Planck. • WMAP results give rs(zd) = 153 ± 2 Mpc (1.3 percent). Planck gives rs(zd) = 151.7 ± 0.5 Mpc(0.33 percent).

19. Measuring the absolute scale of BAOs (2): • Above assumptions are (mostly) testable from CMB acoustic peaks structure. • But there’s a risk of circular argument… a wrong assumption may be “masked” by fitting biased values of cosmological parameters – especially H0; also Ωm, w etc. • Highly desirable to actually measure the BAO length with a CMB-independent method. • “Obvious” way: measure transverse BAOs and DL(z) at same redshift; distance duality gives DA(z) and absolute BAO scale. • Would like to work at lower z , and use DV(z) • Snag: DV(z) is not directly measurable with standard distance indicators.

20. Effect of non-standard radiation density Definition of Neff : Matter density: Sound horizon in terms of rad. density and zeq : Define and use base parameter set :

21. (WMAP7: Komatsu et al 2010)

22. WMAP7 likelihood contours: Strong degeneracy between Neff and ωm ; but zeq is basically unaffected.

23. WMAP7 likelihood contours:

24. Not exact, but accurate summary : • If we drop the assumption of standard Neff, then: • WMAP still tells us redshift of matter-radiation equality ~ 3200, (Planck ~ 3350) , but the physical matter and radiation densities are much less precise. • Keeping CMB acoustic angle constant requires physical dark energy density to scale in proportion to matter & radiation. • best-fit inferred H0 scales as √(Xrad) • Sound horizon rs scales as 1/ √(Xrad) . • The BAO observables don’t change: inferred Ωm , w are nearly unbiased (Eisenstein & White 2004). • If a 4th neutrino species, equivalent to 13.4% increase in densities, 6.5% increase in H (e.g. 70 to 74.5) and 6.1% reduction in cosmic distances/ages. Substantial effect !

25. Neff affects all dimensionful parameters : • Nearly all our WMAP+ SNe + BAO observables are actually dimensionless (apart from photon+baryon densities) : • redshift of matter-radiation equality • CMB acoustic angle • SNe give us distance ratios or H0 DL /c . • BAOs also give distance ratios. • All these can give us robust values for Ω’s , w, E(z) etc ; almost independent of Neff . • But: there are 3 dimensionful quantities in FRW cosmology ; • Distances, times, densities. • Two inter-relations : distance/time via c ,and Friedmann equation relates density + timescale, via G. • This leaves one short, i.e. any number of dimensionless distance ratios can’t determine overall scale. • Usually, scales are (implicitly) anchored to the standard radiation density, Neff ~ 3.04 . But if we drop this, then there is one overall unknown scale factor.

26. Neff , continued… • Photon and baryon densities are determined in absolute units… but these don’t appear separately in Friedmann eq., only as partial sums. • Rescaling total radiation, total matter and dark energy densities by a common factor leaves WMAP, BAO and SNe observables (almost) unchanged; but changes dimensionful quantities e.g. H. • Potential source of confusion: use of h and ω’s. These are unitless but they are not really dimensionless, since they involve arbitrary choice of H = 100 km/s/Mpc , and corresponding density.

27. What BAOs really measure : • Standard rule-of-thumb is “CMB measures ωm , and the sound horizon; then BAOs measure h ” : only true assuming standard radiation density. • Really, CMB measures zeq ; adding a low-redshift BAO ratio measures (almost) Ωm. These two tell us H0 / √(Xrad) , but not an absolute scale. • Thus, measuring the absolute BAO length provides a strong test of standard early-universe cosmology, especially the radiation content (Neff). • Measuring just H0 is less good, since it mixes Neff, w and curvature. The absolute BAO scale probes only the early universe.

28. Measuring the absolute BAO scale (3) : • Need two observations: a relative BAO ratio at some redshift, and an absolute distance measurement to a matching redshift. • It is generally easier to measure cosmic distances at lower z ~ 0.25, which favours BAOs at moderate redshift. • For SNe, the issue is evolution, so shorter time lever arm is favourable. • SNe are better in near-IR (Barone-Nugent et al 2012); sweet spot at z~0.3 where rest-frame J, H appear in observed H,K. • For lens time delays, degeneracy with cosmology: zl << zs is favourable for absolute distances. • The “ideal” distance indicators long-term may be gravitational wave standard sirens; precision limited by SNR , favours lower z. • It is feasible to reach 1.5% precision on BAO ratio at z ~ 0.25 ; this is probably better than medium-term distance indicators.

29. Measuring the absolute scale of BAOs (4): • Most robust quantity from a BAO survey is rs / DV(z) ; this is (almost) theory-independent. • DV is related to comoving volume per unit redshift… • Could measure DV exactly if we had a population of “standard counters” of known comoving number density. But prospects don’t look good – galaxy evolution. • At very low z, DV≈ c z / H0 . But error is 6% at z ~ 0.2 : much too inaccurate. • Next we’ll find much better approximations for DV(z)…

30. Pretty good approximations (< 0.5 percent at z < 0.4): Suitable choice of z’s can eliminate H and gives :

31. Relative accuracy of approximation : 1 percent

32. Relative accuracy of approximation : 1 percent

33. Better approximation: 1 percent Accuracy < 0.2 percent at z < 0.5

34. An easy route to Ωm h becomes a derived parameter: Define ε as error in approximation : BAO ratio is : This is exact (apart from non-linear shifts in rs ) and fully dimensionless: all H and ω’s cancelled.

35. An easy route to Ωm For WMAP baryon density, the above simplifies to the following , to 0.4 percent : • This is all dimensionless, and nicely splits z-dependent effects: • Zeroth-order term is just Ωm-0.5 (strictly Ωcb , without neutrinos) • Leading order z-dependence is E(2z/3) • The εV is second-order in z, usually ~ z2 / 25 and almost negligible • at z < 0.5

36. An easy route to Ωm Repeat approximation from previous slide : Substituting in the WMAP range for zeq , and the BAO measurement at z = 0.35 from Padmanabhan et al (2012), and discarding the sub-percent εV , this gives And just square and rearrange to :

37. Why DV approximation is good: post-hoc explanation using Taylor series Deceleration and Jerk parameters: For “reasonable” models, abs [ ] < 4 … leading order error < z2 / 27

38. Conclusions : • BAOs are a gold standard for cosmological standard rulers. Very well understood; observations huge in scope but clean. • Most planned BAO surveys are targeting z > 0.7, to exploit the huge available volume and sensitivity to dark energy w. • However, there are still two good cases for optimal low-z BAO surveys at z ~ 0.25 (e.g. extending BOSS to South and lower galactic latitude) : • A third direct test of cosmic acceleration, without GR assumption. (arXiv:1105.3838) • In conjunction with precision distance measurements, can provide a test of the CMB prediction rs ~ 151 Mpc, and/or a clean test for extra “dark radiation”, independent of DE and curvature. (arXiv:1205.0715)

39. Thank you !