# Presentation: 116032

## Dark Energy andCosmic Sound

- Daniel Eisenstein
- Steward Observatory

- Eisenstein 2003 (astro-ph/0301623)
- Seo & Eisenstein, ApJ, 598, 720 (2003)
- Blake & Glazebrook (2003), Hu & Haiman (2003), Linder (2003)

**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.

- Riess et al. (2004)

## 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
- DA(*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.

## Punchlines

- CMB calibrates baryon acoustic oscillations in the galaxy power spectrum as a standard ruler.
- This can be measured in large (~million galaxy) surveys at high redshift.
- Can measure *H*(*z*) and *D*A(*z*) to few percent from *z*=0.5 to *z*=3.
- Leverage on dark energy is comparable to future SNe experiments.  Systematics are completely different.

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

## Acoustic Oscillations in the CMB

**Acoustic Oscillations in the CMB**

- WMAP team (Bennett et al. 2003)

## Sound Waves from 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.

## Acoustic Oscillations in the Matter Power Spectrum

- Peaks are weak; suppressed by a factor of the baryon fraction.
- Higher harmonics suffer from Silk damping.
- 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 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.

## Large Galaxy Redshift Surveys

- By performing large spectroscopic surveys, we can measure the acoustic oscillation standard ruler at a range of redshifts.
- Higher harmonics are at *k*~0.2h Mpc-1 (=30 Mpc).
- Measuring 1% bandpowers in the peaks and troughs requires about 1 Gpc3 of survey volume with number density ~10-3 galaxy Mpc-3.  ~1 million galaxies!
- SDSS Luminous Red Galaxy Survey provides this at *z*=0.3.
- We have studied possible future surveys at *z*=1 and *z*=3.
- See related works by Blake & Glazebrook (2003), Hu & Haiman (2003), Linder (2003), Amendola et al. (2004).

## A Baseline Survey at z = 3

- 500,000 gal.
- ~150 sq. deg.
- 5x108 *h*-3 Mpc3
*n*=1/sq. arcmin
- Linear regime *k*<0.5*h* Mpc-1
- 4 oscillations

- Statistical Errors from the *z*=3 Survey

**Notes:**
Similar density to Steidel LBGs.

## A Baseline Survey at z = 1

- 900,000 gal. *z *= 0.5 to 1.3 in 4 slices.
- 1000 sq. deg.
- 0.25/sq. arcmin
- Linear regime *k*<0.2*h* Mpc-1
- 2-3 oscillations

- Statistical Errors from the *z*=1 Survey

## Methodology

- Fisher matrix treatment of statistical errors.
- Full three-dimensional modes including redshift and cosmological distortions.
- Flat-sky and Tegmark (1997) approximations.
- Large CDM parameter space: mh2, bh2, n, T/S, m, plus separate distances, growth functions, , and anomalous shot noises for all redshift slices.
- Planck-level CMB data
- Supernovae: 1% distances in 16 redshift slices, 0.3 to 1.7 plus 0.05, with 5% overall distance scale uncertainty.
- Combine some or all data; predict statistical errors on w(z) = w0 + w1z.

## Baseline Performance

- Distance Errors (1-) 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.

## Results for CDM

- Data sets:
- CMB (*Planck*)
- SDSS LRG (z=0.3)
- Baseline *z*=1
- Baseline *z*=3
- SNe (1% in *z*=0.1 bins to *z*=1.7)
- (m) = 0.037(*w*)= 0.10 at *z*=0.8(*dw*/*dz*) = 0.28
- SNe+CMB have (*dw*/*dz*) = 0.23
- All together has (*dw*/*dz*) = 0.16

- Dark Energy Constraints in CDM

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

Not hugely complementary, but an excellent cross-check.

## Results for w = –2/3

- Easier to measure.
- (m) = 0.025(*w*) = 0.05 at *z*=0.8(*dw*/*dz*) = 0.08
- SNe+CMB(*dw*/*dz*) = 0.12
- All data sets(*dw*/*dz*) = 0.05!

- Dark Energy Constraints in *w*=–2/3

**Notes:**
Redshift surveys are comparable to SNAP.

This fiducial model is not favored by the data today.  How secure is this?

## 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 (2004)

- z=1

## Feasibility?

- How to survey a million galaxies at *z* = 1 over 1000 sq. deg?  Or half a million at *z *= 3 over 150 sq. deg?
- This is a large step over on-going surveys, but it is a reasonable goal for the coming decade.
- KAOS spectrograph concept for Gemini could do these surveys in a year.
- 4000-5000 fibers, using Echidna technology, feedingmultiple bench spectrographs.
- 1.5 degree diameter FOV
- _[http://www.noao.edu/kaos](http://www.noao.edu/kaos)_
- Well ranked in Aspen process.
- Detailed feasibility study in progress.
- Also high-res for Galactic studies.
- Contact Arjun Dey to get involved.

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

## 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.

## Sound in Space?

- Ground can do well up to *z*~1.4 and can pick up again at *z*~2.  Improvements are shrinking this range (but at what cost in exposure times?).
- Space-based spectroscopy may be preferred for 1.5<*z*<2.
- Wide-field IR imaging is important for efficient pre-selection at 1.3<*z*<2.3.
- Not obvious that spatial resolution is crucial for photo-z’s or spectroscopy.
- Don’t need all galaxies; ok to pick the easy ones.
- Only need *n *= 10-3 *h*3 Mpc-3 comoving.
- 1.5<z<2 is likely useful for the study of dark energy.  A good place to put constraints on the redshift evolution.

## 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).
- Is not supernova method.

- Disadvantages:
- Raw statistical precision (of surveys of quoted size) lags SNe (SNAP) and lensing/clusters (LSST).
- But is this the right comparison?
- If dark energy is close to , then *z*<1 is more interesting.
- Some model dependence as regards inferences from CMB.

## Conclusions

- Acoustic oscillations provide a robust way to measure *H*(*z*) and *D*A(*z*).
- Can probe high redshift.
- Clean signature in the galaxy power spectrum.
- Large high-*z* galaxy surveys are feasible in the coming decade.
- Space may be desired to probe dark energy at *z*~2.
- Independent method with competitive precision.

**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 22

## Higher Redshifts Perform Better

- Nonlinear gravitational clustering erases the acoustic oscillations.
- This is less advanced at higher redshifts.
- Recovering higher harmonics improves the precision on distances.
- Leverage improves from *z*=0 to *z*=1.5, then saturates.

- Errors versus non-linear cutoff scale

**Notes:**
Easier to measure the period of a wave with 4 harmonics instead of 1.

## Dark Energy is Subtle

- Measuring *w*(*z*) requires exquisite precision.

- Varying *w* assuming perfect CMB:
- Fixed m*h*2
*D*A(*z*=1000)
*dw*/*dz* is even harder.
*w*>–1 is easier.

- 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.

## ...but one can measure transverse clustering

- Slices from photometric redshifts have sufficiently uniform DA that the acoustic peaks persist in the angular power spectrum.
- Can measure DA(z) from large multicolor imaging surveys.

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

## Photo-z Surveys

- Need much more sky coverage in order to compensate for the loss of modes.
- Half-sky survey could give comparable performance on DA(z).
- Need 4% in (1+z)
- Reasonably shallow:L* is overkill.
- Not measuring H(z) directly.
- Performance on w(z) lags.

**Notes:**
Half-sky might match DA, but it doesn’t match sigma(w).  Probably need 2% photo-z’s.

## Clustering Bias

- Small-scale segregation of light and mass does create bias in clustering on large scales.
- However, on large scales, bias is simple: scale-independent form.
- Hence, large-scale galaxy clustering is a window into the early universe!

## Distance Derivatives

## Feasibility?

- How to survey a million galaxies at *z* = 1 over 1000 sq. deg?  Or half a million at *z *= 3 over 150 sq. deg?
- This is a large step over on-going surveys, but it is a reasonable goal for the coming decade.
- KAOS spectrograph concept for Gemini could do these surveys in a year.
- 4000-5000 fibers
- 1.5 degree diameter FOV
- See poster by Dey, talk by Glazebrook,http://www.noao.edu/kaos

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