Cosmological Physics with Redshift Surveys Martin White UCB/LBNL MS-DESI meeting, Mar 2013

Topics The CMB and MS-DESI –The “standard fluctuation spectrum” Baryon Acoustic Oscillations (BAOs) –So much success, so little time... –Ly  Redshift space distortions (RSDs) –And broad-band power. Cross-correlations and dN/dz. –The meanings of “sparse” and “big enough”, … Conclusions.

CMB cosmology Existence of CMB –One of the pillars of the hot big-bang model. Measurement of the black-body spectrum –T =  K, deviations < –Sets the temperature scale of the Universe Only cosmological parameter known to 0.01%! –Rules out significant energy injection below z~10 7. Measurement of the anisotropy –Shrunk substantially the range of viable models. –Showed the fluctuations are of the form predicted by inflation and space-time is “simple”. –Best measurement of most cosmological parameters

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A “standard fluctuation spectrum” Measurement of the anisotropy constrains the initial fluctuation spectrum over 4 orders of magnitude in length scale. –The scales most directly relevant for this talk! Within GR the growth rate of fluctuations is well determined once the constituents are known. –The same ones that are well measured by the CMB. Thus the CMB provides a “standard fluctuation spectrum”. –Like a standard candle. –More than just a standard ruler...

Galaxy clustering: BAO and Growth of Structure

Baryon Acoustic Oscillations In the early Universe radiation pressure stabilizes density perturbations, leading to oscillating “acoustic” modes. –Well measured now in CMB (acoustic scale 2 nd best known number in cosmology). When these modes “freeze” at decoupling they imprint a preferred scale in the clustering of objects. –The sound horizon (~c s t dec ~150Mpc). –Same physics as CMB, but measurable at a wide range of redshifts. This can be used as a standard ruler to probe d A (z) and H(z). –Future experiments will quote constraints on both, current experiments quote constraints on D V ~d A 2 /H.

BAO detection: Anderson++12 (BAO detected at >5  in both  and P)  We scale a template by  so that

BAO status: The method … Works on paper. –Theory very well developed now. –Effects of non-linearity, bias and redshift space distortions understood. –Reconstruction understood analytically. Works in a computer. –Analytic and numerical results agree (very well!). Works in the real Universe. –Models and data agree well. –Scale independent of tracer and analysis methodology. Path towards next generation is clear!

The distance ladder The BOSS distance scale is in slight tension with WMAP, with some SNe and H 0 measurements … will know soon if tension improves or worsens with Planck …

Friedman equation 2-parameter model3-parameter model (marginalized) 3-parameter model (marginalized)

BAO and the IGM Distance constraints become tighter as one moves to higher z –More volume per sky area & less non-linearity. Expensive if use galaxies as tracers. Any tracer will do: H I –21cm from H I in galaxies: SKA or custom expt. –Ly  from IGM as probed by QSOs. Absorption traces mass in a calculable way. A dense grid of QSO sightlines can probe BAO. BOSS has validated this technique! –First BAO detection at high-z, in matter-dominated epoch. –See expansion decelerating! –BOSS thus sees deceleration->acceleration characteristic of dark energy models.

The constraints SDSS-BAO BOSS-AP WiggleZ SNe Ly  F

What is a QSO worth? The optimal estimator for P F (k) given a quasar survey is almost analytic. Allows a simple quasar weighting scheme, with weight per quasar: – =1/[ 1+P noise / P los ] –For z~2-3 hit diminishing returns for quasars with [S/N] 1Å ≈2. This means we can design and optimize QSO surveys with some confidence. –Results born out by BOSS experience. (McDonald&Eisenstein 2007; McQuinn&White 2011)

Two dimensional clustering Anisotropy in the 2-point function due to peculiar velocities allows measurement of the growth of structure and tests of gravity on cosmological scales.

RSD status Unlike BAO, people have been measuring/interpreting RSDs in redshift surveys since the 1980’s. Linear regime less accessible. –Violations of “simple” models already large enough to be seen with high significance in early BOSS data. More constraining power at smaller, quasi-linear scales. –More gains to be had by improvements in theory. Models well developed on paper. Simulations improving dramatically. –Modeling of velocity bias is important. Good enough for BOSS, not yet good enough for NGen –Can continue to improve theory or take an “engineering” approach and develop simulations further. Or both.

Dark Energy or modified gravity? Samushia  G/G=  s a s (Not all analyses make the same assumptions or use the same priors so direct comparison is slightly tricky.)

Caveat Cosmology from measurement of redshift space distortions is more susceptible to survey systematics. –e.g. fiber collisions, survey masks, etc. The field hasn’t given this too much attention to date. –The issues are quite well known, but the impetus for a detailed, systematic, precision study has never really existed … –… or people were too busy with other things.

Cross-correlations and dN/dz (McQuinn & White 2013) Measuring dN/dz for a population of objects is a long- standing & crucial problem in cosmology/astronomy. Objects which are close on the sky tend to be close in 3D, so can use cross-correlation techniques. OQE performs well. –Largely analytic. –Naturally selects linear scales (big surveys!) –Robust iterative scheme. For “sparse” samples –  b(z)N(z)]/  b(z)N(z)] ~ √[10 2 n bin /N spec ]

What is sparse? The relevant scales in the problem are set by the power spectrum, which is set by the CMB! Sparse is fewer than several hundred objects per sq. deg. per dz. In the sparse limit, it’s only the total number of spectra that matters. A “large enough” survey is determined by the location of the peak – which is determined by MR equality.

This technique would want … Tracers which span 0<z<2. –e.g. LRG+ELG+QSOs. Wide area coverage. –Field size larger than l eq -1 (radians). –Minimize sample variance effects. Many redshifts (but bright is fine). So if anyone can think of a way to do a highly multiplexed, wide area, spectroscopic survey targeting LRGs, ELGs and QSOs they should let me know …

Conclusions The CMB provides a “standard fluctuation spectrum”. –Most robust feature is acoustic scale. –We have yet to make use of the full power of this tool. The physics of BAO is well understood and the technique works on paper, in the computer and in observations. –BOSS is exploiting this technique extremely well. –Get good constraints from both galaxies and IGM. –No show stoppers yet identified. RSDs returning good results on BOSS. –Needs continuing development to scale to NGen. Cross-correlations can inform dN/dz. –Optimal estimator naturally selects linear scales. –Robust, iterative scheme.

The End

On large scales Differences with the galaxies –Not yet a proven technique! –Signal is e - , so downweights high-  (unlike galaxies which trace high-  –Need to be slightly careful about redshift space distortions (  conserved, not n, except in line-dominated regime). –Noise comes in two forms: Noise in an individual spectrum. Projection/finite sampling: dominant for us and BigBOSS. Balance is important for optimization! Additional physics –Absorption could be affected by non-gravitational physics Fluctuations in the UV background Temperature fluctuations due to HeII reionization Your favorite astrophysical phenomenon here.

BAO at high z Signal in “theory” Slosar, Ho, White & Louis (2009) BAO feature survives in the Ly  flux correlation function, because on large scales flux traces density. Relatively insensitive to astrophysical effects. Signal in “simulations”

Aliasing Can’t tell the difference between a constant field (k x =k y =k z =0) and one varying transverse to the line-of-sight (k x >0 or k y >0)

Constraining power Survey area/(limiting flux) 2 (i.e. observing time) S/N on P F (k=0.1 Mpc -1 ) McQuinn & White (2011) BigBOSS

Skewer density