# Presentation: 544525

## Dark Energy and Cosmic Sound

- Daniel Eisenstein
- (University of Arizona)
- Michael Blanton, David Hogg, Bob Nichol, Nikhil Padmanabhan, Will Percival, David Schlegel, Roman Scoccimarro, Ryan Scranton, Hee-Jong Seo, Ed Sirko, David Spergel, Max Tegmark, Martin White, Idit Zehavi, 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)
*w*(*z)* is even harder.
- Need 1% distance measurements!

- 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 better than 1% from *z*=0.3 to *z*=3.
- Present the Baryon Oscillation Spectroscopic Survey and SDSS-III.
- 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 partially smears out the signature (more later).
- Clustering bias and redshift distortions alter the power spectrum but don’t create preferred scales at 150 Mpc!
- Acoustic peaks expected to survive mostly intact.

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

- z=1

## Virtues of the Acoustic Peaks

- The acoustic signature is created by physics at z=1000 when the perturbations are 1 in 104.  Linear perturbation theory is excellent.
- Measuring the acoustic peaks across redshift gives a geometrical measurement of cosmological distance.
- The acoustic peaks are a manifestation of a preferred scale. Still a very large scale today, so non-linear effects are mild and dominated by gravitational flows that we can simulate accurately.
- No known way to create a sharp scale at 150 Mpc with low-redshift astrophysics.
- Measures absolute distance, including that to *z*=1000.
- Method has intrinsic cross-check between *H*(*z*) & *D**A*(*z*), since *D**A* is an integral of *H*.

## 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

## Redshift Distribution

- 55,000 galaxies for this analysis; about 100k now available.

## 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-1).
- 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.
- Also FKP analysis in Percival et al. (2006, 2007).
- The results are highly consistent.
**m = 0.25, in part due to WMAP-3 vs WMAP-1.

- Tegmark et al. (2006)

## Power Spectrum

- We have also done the analysis in Fourier space with a quadratic estimator for the power spectrum.
- Also FKP analysis in Percival et al. (2006, 2007).
- The results are highly consistent.
**m = 0.25, in part due to WMAP-3 vs WMAP-1.

- Percival et al. (2007)

## 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)
- Require several Gpc3 of survey volume with number density few x 10-4 comoving *h*3 Mpc-3, typically a million or more galaxies!
- No heroic calibration requirements; just need big volume.
- Discuss design considerations, 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 the BAO

- The acoustic signature is carried by pairs of galaxies separated by 150 Mpc.
- Nonlinearities push galaxies around by 3-10 Mpc.  Broadens peak, making it hard to measure the scale.
- 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 <0.5%.
- Simulations confirm that theshift is <0.5%.

- Seo & DJE (2005); DJE, Seo, & White (2007)

## 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, 2007

## 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, 2007

## 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, 2007

## 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, 2007

## Seeing Sound in the Lyman  Forest

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

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

- Neutral H absorption observed
- in quasar spectrum at z=3.7

- Neutral H simulation (R. Cen)

## 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.

## Baryon Oscillation Spectroscopic Survey (BOSS)

- New program for the SDSS telescope for 2008–2014.
- Definitive study of the low-redshift acoustic oscillations. 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 1% at *z*=0.35 and *z*=0.6.
- Easy extension of current program.
- Simultaneous project to discover theBAO in the Lyman  forest.
- 160,000 quasars.  20% of fibers.
- 1.5% measurement of distance to *z*=2.3.
- Higher risk but opportunity to open the high-redshift distance scale.

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

## Cosmology with BOSS

- BOSS measures the cosmic distance scale to 1.0% at *z* = 0.35, 1.1% at *z* = 0.6, and 1.5% at *z* = 2.5.  Measures *H*(*z* = 2.5) to 1.5%.
- These distances combined with Planck CMB & Stage II data gives powerful cosmological constraints.
- Dark energy parameters *w*p to 2.8% and *w*a to 25%.
- Hubble constant *H*0 to 1%.
- Matter density* ***m to 0.01.
- Curvature of Universe **k to 0.2%.
- Sum of neutrino masses to 0.13 eV.
- Superb data set for other cosmological tests, such as galaxy-galaxy weak lensing.

## DETF Figure of Merit

| Experiment | DETF FOM |
| --- | --- |
| Stage II + Planck | 67 |
| + BOSS LRG BAO | 97 |
| + BOSS QSO BAO | 144 |
| + BOSS Galaxy power spectrum | 270 |

- Powerful Stage III data set.
- High complementarity with future weak lensing and supernova data sets.

## BOSS in Context

- DETF reports states that the BAO method is “less affected by astrophysical uncertainties than other techniques.” Hence, BOSS forecasts are more reliable.
- BOSS is nearly cosmic-variance limited (quarter-sky) in its *z *< 0.7 BAO measurement.
- Will be the data point that all higher redshift BAO surveys use to connect to low redshift.  Cannot be significantly superceded.
- BOSS will be the first dark energy measurement at *z *> 2.
- Moreover, BOSS complements beautifully the new wide-field imaging surveys that focus on weak lensing, SNe, and clusters.
- BAO adds an absolute distance scale to SNe and extends to *z *> 1.
- BAO+SNe are a purely *a*(*t*) test, whereas WL and Clusters include the growth of structure as well.  Crucial opportunity to do consistency checks to test our physical assumptions.

## BOSS Instrumentation

**BOSS Instrumentation**

- 1000 small-core fibers to replace existing
- (more objects, less sky contamination)

- LBNL CCDs + new gratings improve throughput
- Update electronics + DAQ

-  Straightforward upgrades to be  commissioned in summer 2009

- SDSS telescope + most systems unchanged

## SDSS-III

- BOSS is the flagship program for SDSS-III, the next phase of the SDSS project.
- SDSS-III will operate the telescope from summer 2008 to summer 2014.
- Other parts of SDSS-III are:
- SEGUE-2: Optical spectroscopic survey of stars, aimed at structure and nucleosynthetic enrichment of the outer Milky Way.
- APOGEE: Infrared spectroscopic survey of stars, to study the enrichment and dynamics of the whole Milky Way.
- MARVELS: Multi-object radial velocity planet search.
- Extensive re-use of existing facility and software.
- Strong commitment to public data releases.
- Collaboration is now forming.
- Seeking support from Sloan Foundation, DOE, NSF, and over 20 member institutions.

- 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.

## Photometric Redshifts?

- Can we do this without spectroscopy?
- Measuring H(z) requires detection of acoustic oscillation scale alongthe line of sight.
- Need ~10 Mpc accuracy.  z~0.003(1+z).
- Measuring *D*A(*z*) from transverse clustering requires only 4% in 1+*z*.
- Need 10x more sky than spectroscopy.  Less robust, but likely feasible.
- First work by Padmanabhan et al (2006) and Blake et al (2006).6% distance to *z *= 0.5.

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

## 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.

## 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.
- What if the radiation density were different, i.e. more/fewer neutrinos or something new?
- Sound horizon would shift in scale.  LSS inferences of ***m*, ***k*, *w*(*z*), etc, would be correct, but ***m**h*2 and *H*0 would shift.
- Minor changes in baryon fraction and CMB anisotropic stress.
- So comparison of *H*0 from direct measures to CMB-based inferences are a probe of “dark radiation”.
- 1 neutrino species is roughly 5% in *H*0.
- We could get to ~1%.

- DJE & White (2004)

## 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 *D*A(*z*).
- Clean signature in the galaxy power spectrum.
- Can probe high redshift.
- Can probe *H*(*z*) directly.
- Independent method with good precision.
- SDSS LRG sample uses the acoustic signature to measure *D**A*(*z*=0.35)/*D**A*(*z*=1000) to 4%.
- Larger galaxy surveys are feasible in the coming decade, push to 1% across a range of redshift.

**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.

## Slide 56

## Distances to Acceleration

## Distances to Acceleration

## Distances to Acceleration