# Presentation: 544545

## Dark Energy andCosmic Sound

- Daniel Eisenstein
- (University of Arizona)
- Michael Blanton, David Hogg, Bob Nichol, Roman Scoccimarro, Ryan Scranton, _Hee-Jong Seo_, Ed Sirko, David Spergel, Max Tegmark, Martin White,_Idit Zehavi_, Zheng Zheng, and the SDSS.

**Notes:**
Acknowledge Blake, Glazebrook, Linder

## Dark Energy is Mysterious

- Observations suggest that the expansion of the universe is presently accelerating.
- Normal matter doesn’t do this!
- Requires exotic new physics.
- Cosmological constant?
- Very low mass field?
- Some alteration to gravity?

- We have no compelling theory for this!
- Need observational measure of the time evolution of the effect.

## A Quick Distance Primer

- The homogeneous metric is described by two quantities:
- The size as a function of time,*a*(*t).  *Equivalent to the Hubble parameter *H*(*z*) = *d *ln(*a*)/*dt.*
- The spatial curvature, parameterized by **k.
- The distance is then                         (flat)
*H*(*z*) depends on the dark energy density.

## Dark Energy is Subtle

- Parameterize by equation of state, *w* = *p*/**, which controls how the energy density evolves with time.
- Measuring *w*(*z*) requires exquisite precision.

- Varying *w* assuming perfect CMB:
- Fixed m*h*2
*D**A*(*z*=1000)
*dw*/*dz* is even harder.
- Need precise, redundant observational probes!

- Comparing Cosmologies

**Notes:**
If this picture differs from what you’re used to seeing, it’s because I’ve held the CMB fixed.
Note that DA saturates at high redshift.  H(z) is more interesting there.

## Outline

- Baryon acoustic oscillations as a standard ruler.
- Detection of the acoustic signature in the SDSS Luminous Red Galaxy sample at *z*=0.35.
- Cosmological constraints therefrom.
- Large galaxy surveys at higher redshifts.
- Future surveys could measure H(z) and DA(z) to few percent from *z*=0.3 to *z*=3.
- Assess the leverage on dark energy and compare to alternatives.

**Notes:**
For those who want their conclusions in under 5 minutes...

## Acoustic Oscillations in the CMB

**Acoustic Oscillations in the CMB**

- Although there are fluctuations on all scales, there is a characteristic angular scale.

## Acoustic Oscillations in the CMB

**Acoustic Oscillations in the CMB**

- WMAP team (Bennett et al. 2003)

## Sound Waves in the Early Universe

-   Before recombination:
- Universe is ionized.
- Photons provide enormous pressure and restoring force.
- Perturbations oscillate as acoustic waves.

-   After recombination:
- Universe is neutral.
- Photons can travel freely past the baryons.
- Phase of oscillation at trec affects late-time amplitude.

## Sound Waves

- 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 150 Mpc.
- Overdensity in shell (gas) and in the original center (DM) both seed the formation of galaxies.  Preferred separation of 150 Mpc.

## A Statistical Signal

- The Universe is a super-position of these shells.
- The shell is weaker than displayed.
- Hence, you do not expect to see bullseyes in the galaxy distribution.
- Instead, we get a 1% bump in the correlation function.

## Response of a point perturbation

- Based on CMBfast outputs (Seljak & Zaldarriaga).  Green’s function view from Bashinsky & Bertschinger 2001.

## Acoustic Oscillations in Fourier Space

- A crest launches a planar sound wave, which at recombination may or may not be in phase with the next crest.
- Get a sequence of constructive and destructive interferences as a function of wavenumber.
- Peaks are weak — suppressed by the baryon fraction.
- Higher harmonics suffer from Silk damping.

- Linear regime matter power spectrum

**Notes:**
Possible Detection by Miller.

Detection would be a confirmation of gravitational structure formation.
It *must* be there.

## Acoustic Oscillations, Reprise

- Divide by zero-baryon reference model.
- Acoustic peaks are 10% modulations.
- Requires large surveys to detect!

- Linear regime matter power spectrum

**Notes:**
Possible Detection by Miller.

Detection would be a confirmation of gravitational structure formation.
It *must* be there.

## A Standard Ruler

- The acoustic oscillation scale depends on the sound speed and the propagation time.
- These depend on the matter-to-radiation ratio (***m**h*2) and the baryon-to-photon ratio (***b**h*2).
- The CMB anisotropies measure these and fix the oscillation scale.
- In a redshift survey, we can measure this along and across the line of sight.
- Yields *H*(*z*) and *D**A*(*z*)!

**Notes:**
The acoustic oscillations are also quantitatively useful, because they can form a standard ruler.

## Galaxy Redshift Surveys

- Redshift surveys are a popular way to measure the 3-dimensional clustering of matter.
- But there are complications from:
- Non-linear structure formation
- Bias (light ≠ mass)
- Redshift distortions
- Do these affectthe acousticsignatures?

- SDSS

## Nonlinearities & Bias

- Non-linear gravitational collapse erases acoustic oscillations on small scales.  However, large scale features are preserved.
- Clustering bias and redshift distortions alter the power spectrum, but they don’t create preferred scales at 100*h*-1 Mpc!
- Acoustic peaks expected to survive in the linear regime.

- Meiksen & White (1997), Seo & DJE (2005)

- z=1

## Virtues of the Acoustic Peaks

- Measuring the acoustic peaks across redshift gives a purely geometrical measurement of cosmological distance.
- The acoustic peaks are a manifestation of a preferred scale.
- Non-linearity, bias, redshift distortions shouldn’t produce such preferred scales, certainly not at 100 Mpc.
- Method should be robust, but in any case the systematic errors will be very different from other schemes.
- However, the peaks are weak in amplitude and are only available on large scales (30 Mpc and up).  Require huge survey volumes.

## Introduction to SDSS LRGs

- SDSS uses color to target luminous, early-type galaxies at 0.2<*z*<0.5.
- Fainter than MAIN (*r*<19.5)
- About 15/sq deg
- Excellent redshift success rate
- The sample is close to mass-limited at *z*<0.38.  Number density ~ 10-4 *h*3 Mpc-3.

- Science Goals:
- Clustering on largest scales
- Galaxy clusters to z~0.5
- Evolution of massive galaxies

- 200 kpc

## 55,000 Spectra

## Intermediate-scale Correlations

- Subtle luminosity dependence in amplitude.
- 8 = 1.80±0.03 up to 2.06±0.06 across samples
- r0 = 9.8*h*-1 up to 11.2*h*-1 Mpc
- Real-space correlation function is not a power-law.

- Zehavi et al. (2004)

- Real-space

- Redshift-space

## On to Larger Scales....

## Large-scale Correlations

**Large-scale Correlations**

## Another View

- CDM with baryons is a good fit:        2 = 16.1 with 17 dof.Pure CDM rejected at 2 = 11.7

## A Prediction Confirmed!

- Standard inflationary CDM model requires acoustic peaks.
- Important confirmation of basic prediction of the model.
- This demonstrates that structure grows from z=1000 to z=0 by linear theory.
- Survival of narrow feature means no mode coupling.

## Two Scales in Action

**Two Scales in Action**

## Parameter Estimation

- Vary ***m**h*2 and the distance to *z *= 0.35, the mean redshift of the sample.
- Dilate transverse and radial distances together, i.e., treat *D**A*(*z*) and *H*(*z*) similarly.
- Hold ***b**h*2 = 0.024, *n* = 0.98 fixed (WMAP).
- Neglect info from CMB regarding ***m**h*2, ISW, and angular scale of CMB acoustic peaks.
- Use only *r*>10*h*-1 Mpc.
- Minimize uncertainties from non-linear gravity, redshift distortions, and scale-dependent bias.
- Covariance matrix derived from 1200 PTHalos mock catalogs, validated by jack-knife testing.

## Cosmological Constraints

**Cosmological Constraints**

- 1**

- 2**

## A Standard Ruler

- If the LRG sample were at *z*=0, then we would measure *H*0 directly (and hence **m from **m*h*2).
- Instead, there are small corrections from *w* and ***K* to get to *z*=0.35.
- The uncertainty in **m*h*2 makes it better to measure (**m*h*2)1/2 *D.*  This is independent of *H*0.

-   We find **m = 0.273 ± 0.025 + 0.123(1+*w*0) + 0.137***K*.

## Essential Conclusions

- SDSS LRG correlation function does show a plausible acoustic peak.
- Ratio of *D*(*z*=0.35) to *D*(*z*=1000) measured to 4%.
- This measurement is insensitive to variations in spectral tilt and small-scale modeling.  We are measuring the same physical feature at low and high redshift.
***m**h*2 from SDSS LRG and from CMB agree.  Roughly 10% precision.
- This will improve rapidly from better CMB data and from better modeling of LRG sample.
**m = 0.273 ± 0.025 + 0.123(1+*w*0) + 0.137***K*.

## Constant w Models

- For a given *w* and ***m**h*2, the angular location of the CMB acoustic peaks constrains ***m* (or *H*0), so the model predicts *D**A*(*z*=0.35).
- Good constraint on ***m*, less so on *w* (–0.8±0.2).

##  + Curvature

- Common distance scale to low and high redshift yields a powerful constraint on spatial curvature:            **K = –0.010 ± 0.009   (*w *= –1)

## Power Spectrum

- We have also done the analysis in Fourier space with a quadratic estimator for the power spectrum.
- The results are highly consistent.
**m = 0.25, in part due to WMAP-3 vs WMAP-1.
- Also FKP analysis in Percival et al. (2006).

- Tegmark et al. (2006)

## Beyond SDSS

- By performing large spectroscopic surveys at higher redshifts, we can measure the acoustic oscillation standard ruler across cosmic time.
- Higher harmonics are at *k*~0.2*h* Mpc-1 (**=30 Mpc)
- Measuring 1% bandpowers in the peaks and troughs requires about 1 Gpc3 of survey volume with number density ~10-3 comoving *h*3 Mpc-3 = ~1 million galaxies!
- Discuss survey optimization then examples.

## Non-linearities Revisited

- Non-linear gravitational collapse and galaxy formation partially erases the acoustic signature.
- This limits our ability to centroid the peak and could in principle shift the peak to bias the answer.

- Meiksen & White (1997), Seo & DJE (2005)

## Nonlinearities in (r)

- The acoustic signature is carried by pairs of galaxies separated by 150 Mpc.
- Nonlinearities push galaxies around by 3-10 Mpc.  Broadens peak, erasing higher harmonics.
- Moving the scale requires net infall on 100 *h*–1 Mpc scales.
- This depends on the over-density inside the sphere, which is about *J*3(*r*) ~ 1%.
- Over- and underdensities cancel, so mean shift is <<1%.
- Simulations show no evidencefor any bias at 1% level.

- Seo & DJE (2005); DJE, Seo, & White, in press

## Nonlinearities in P(k)

- How does nonlinear power enter?
- Shifting P(k)?
- Erasing high harmonics?
- Shifting the scale?
- Acoustic peaks are more robost than one might have thought.
- Beat frequency difference between peaks and troughs of higher harmonics still refers to very large scale.

- Seo & DJE (2005)

## Where Does Displacement Come From?

- Importantly, most of the displacement is due to bulk flows.
- Non-linear infall into clusters "saturates".  Zel'dovich approx. actually overshoots.
- Bulk flows in CDM are created on large scales.
- Looking at pairwise motion cuts the very large scales.
- The scales generating the displacements are exactly the ones we're measuring for the acoustic oscillations.

- DJE, Seo, Sirko, &
- Spergel, in press

## Fixing the Nonlinearities

- Because the nonlinear degradation is dominated by bulk flows, we can undo the effect.
- Map of galaxies tells us where the mass is that sources the gravitational forces that create the bulk flows.
- Can run this backwards.
- Restore the statistic precision available per unit volume!

- DJE, Seo, Sirko, & Spergel, in press

## Cosmic Variance Limits

- Errors on *D*(*z*) in *z*=0.1 bins.  Slices add in quadrature.
- Black: Linear theory
- Blue: Non-linear theory
- Red: Reconstruction by 50% (reasonably easy)

- Seo & DJE, submitted

## Cosmic Variance Limits

- Errors on *H*(*z*) in *z*=0.1 bins.  Slices add in quadrature.
- Black: Linear theory
- Blue: Non-linear theory
- Red: Reconstruction by 50% (reasonably easy)

- Seo & DJE, submitted

## Seeing Sound in the Lyman  Forest

- The Ly forest tracks the large-scale density field as well, so a grid of sightlines should show the acoustic peak.
- This may be a cheaper way to measure the acoustic scale at *z*>2.
- Bonus: the sampling is better in the radial direction, so favors H(z).
- Require only modest resolution (R=250) and low S/N.  UV coverage is a big plus.

- White (2004); McDonald & DJE (2006)

- Green line is S/N=2 Å–1 at g=22.5

## Chasing Sound Across Redshift

- Distance Errors versus Redshift

**Notes:**
H(z) does a little worse than Da(z) just because there’s only 1 dimension of radial modes as opposed to 2 dimensions of transverse modes.

## APO-LSS

- New program for the SDSS telescope for the period 2008–2014.  10,000 deg2 of new spectroscopy from SDSS imaging.
- 1.5 million LRGs to *z*=0.8, including 4x more density at *z*<0.5.
- 7-fold improvement on large-scale structure data from entire SDSS survey, measure the distance scale to better than 1%.
- Lyforest from grid of 100,000 *z*>2.2 quasars.
- Mild upgrades to the spectrographs to reach 1000 fibers per shot and more UV coverage.
- Other aspects of the program include stellar spectroscopic survey for galactic structure and a multi-fiber radial-velocity planet search.
- Collaboration now forming.

**Notes:**
Am I insane?  My therapist assures me that I’m not.

## New Surveys

- WiggleZ: Survey of z~0.8 emission line galaxies at AAT with new AAOmega upgrade.
- FMOS: *z*~1.5 Subaru survey with IR spectroscopy for H.
- HETDeX: Ly emission galaxy survey at 1.8<*z*<3.8 with new IFU on HET.
- New WFMOS spectrograph for Gemini/Subaru could do major *z*~1 and *z*~2.5 surveys in ~100 nights each.
- Well ranked in Aspen second-generation instruments plan.  Currently entering a competitive design study.
- 1.5 degree diameter FOV, 4000-5000 fibers, using Echidna technology, feeding multiple bench spectrographs.
- Also high-res for Galactic studies.

**Notes:**
Am I insane?  My therapist assures me that I’m not.

- Concept proposed for the Joint Dark Energy Mission (JDEM).
- 3/4-sky survey of 1<*z*<2 from a small space telescope, using slitless IR spectroscopy of the H line.  SNe Ia to *z*~1.4.
- 100 million redshifts; 20 times more effective volume than previous ground-based surveys.
- Designed for maximum synergy with ground-based dark energy programs.

## Breaking the w-Curvature Degeneracy

- To prove *w* ≠ –1, we should exclude the possibility of a small spatial curvature.
- SNe alone, even with space, do not do this well.
- SNe plus acoustic oscillations do very well, because the acoustic oscillations connect the distance scale to *z*=1000.

## Constraining w(z)

- Data sets:
- CMB (*Planck*)
- SNe: 1% in D from z=0.05 to z=0.95 in *z*=0.1 bins.
- Current SDSS (red)
- APO-LSS (black)
- +WFMOS (blue)
- +ADEPT (magenta).
*w*(*z*) as cubic polynomial, including spatial curvature.
- BAO can add *w*(*z*) measurement at *z*>1.

- Dark Energy Constraints around CDM

- 95% contours

**Notes:**
Redshift surveys are about a factor of 2 worse than SNAP.

Not hugely complementary, but an excellent cross-check.

## Opening Discovery Spaces

- With CMB and galaxy surveys, we can study dark energy out to z=1000.
- SNe should do better at pinning down *D*(*z*) at *z*<1.  But acoustic method opens up *z*>1 and H(z) to find the unexpected.
- Weak lensing, clusters also focus on *z*<1.  These depend on growth of structure.  We would like both a growth and a kinematic probe to look for changes in gravity.

## Photometric Redshifts?

- Can we do this without spectroscopy?
- Measuring H(z) requires detection of acoustic oscillation scale along the line of sight.
- Need ~10 Mpc accuracy.  z~0.003(1+z).
- But measuring *D*A(*z*) from transverse clustering requires only 4% in 1+*z*.
- Need ~half-sky survey to match 1000 sq. deg. of spectra.
- Less robust, but likely feasible.

- 4% photo-z’s don’t smearthe acoustic oscillations.

## What about H0?

- Does the CMB+LSS+SNe really measure the Hubble constant?  What sets the scale in the model?
- The energy density of the CMB photons plus the assumed a neutrino background gives the radiation density.
- The redshift of matter-radiation equality then sets the matter density (***m**h*2).
- Measurements of ***m* (e.g., from distance ratios) then imply *H*0.
- Is this good enough?

## What about H0?

- What if the radiation density were different, (more/fewer neutrinos or something new)?
- Sound horizon would be shifted in scale.  LSS inferences of ***m*, ***k*, *w*(*z*), etc, would be correct, but ***m**h*2 and *H*0 would be shifted.
- Baryon fraction would be changed (***b**h*2 is fixed).
- Anisotropic stress effects in the CMB would be different.  This is detectable with Planck.
- So *H*0 is either a probe of “dark radiation” or dark energy (assuming radiation sector is simple).
- 1 neutrino species is roughly 5% in *H*0.
- We could get to ~1%.

- DJE & White (2004)

## Pros and Consof the Acoustic Peak Method

- Advantages:
- Geometric measure of distance.
- Robust to systematics.
- Individual measurements are not hard (but you need a lot of them!).
- Can probe *z*>2.
- Can measure *H*(*z*) directly (with spectra).
- Built-in cross-check.

- Disadvantages:
- Raw statistical precision at *z*<1 lags SNe and lensing/clusters.
- Full sky helps.
- Dark energy is more important at *z*<1.
- Calibration of standard ruler requires inferences from CMB.
- But this doesn’t matter for relative distances.

## We’ve Only Just Begun

- SDSS LRG has only surveyed only 10–3 of the volume of the Universe out to *z*~5.
- Only 10–4 of the modes relevant to the acoustic oscillations.
- Fewer than 10–6 of the linear regime modes available.
- There is an immense amount more information about the early Universe available in large-scale structure.

- Spergel

## Conclusions

- Acoustic oscillations provide a robust way to measure H(z) and DA(z).
- Clean signature in the galaxy power spectrum.
- Can probe high redshift.
- Can probe H(z) directly.
- Independent method with similar precision to SNe.
- SDSS LRG sample uses the acoustic signature to measure *D**A*(*z*=0.35)/*D**A*(*z*=1000) to 4%.
- Large high-*z* galaxy surveys are feasible in the coming decade.

**Notes:**
Given the abysmal record of theoretical predictions and prejudices about dark energy, it seems unwise to design experiments on the assumptions of a cosmological constant.