1. Dark Energy and Cosmic Sound
Daniel Eisenstein
Steward Observatory
Acknowledge Blake, Glazebrook, Linder
Eisenstein 2003 (astro-ph/ )
Seo & Eisenstein, ApJ, 598, 720 (2003)
Blake & Glazebrook (2003), Hu & Haiman (2003), Linder (2003)

2. Dark Energy is Subtle
Parameterize by equation of state, w = p/r, which controls how the energy density evolves with time.
Measuring w(z) requires exquisite precision.
Varying w assuming perfect CMB:
Fixed Wmh2
DA(z=1000)
dw/dz is even harder.
Need precise, redundant observational probes!
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.
Comparing Cosmologies

3. 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 DA(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.
For those who want their conclusions in under 5 minutes…

4. Acoustic Oscillations in the CMB
WMAP team (Bennett et al. 2003)

5. 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.

6. 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!
Possible Detection by Miller.
Detection would be a confirmation of gravitational structure formation.
It *must* be there.
Linear regime matter power spectrum

7. A Standard Ruler Yields H(z) and DA(z)!
The acoustic oscillation scale depends on the matter-to-radiation ratio (Wmh2) and the baryon-to-photon ratio (Wbh2).
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 DA(z)!
Observer
dr = (c/H)dz
dr = DAdq
The acoustic oscillations are also quantitatively useful, because they can form a standard ruler.

8. 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 (l=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).

9. A Baseline Survey at z = 3 500,000 gal. ~150 sq. deg. 5x108 h-3 Mpc3
n=1/sq. arcmin
Linear regime k<0.5h Mpc-1
4 oscillations
Similar density to Steidel LBGs.
Statistical Errors from the z=3 Survey

10. 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<0.2h Mpc-1
2-3 oscillations
Statistical Errors from the z=1 Survey

11. 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: Wmh2, Wbh2, n, T/S, Wm, plus separate distances, growth functions, b, 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.

12. Baseline Performance Distance Errors (1-s) versus Redshift
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.
Distance Errors (1-s) versus Redshift

13. Results for LCDM Data sets:
CMB (Planck)
SDSS LRG (z=0.3)
Baseline z=1
Baseline z=3
SNe (1% in Dz=0.1 bins to z=1.7)
s(Wm) = s(w)= 0.10 at z=0.8 s(dw/dz) = 0.28
SNe+CMB have s(dw/dz) = 0.23
All together has s(dw/dz) = 0.16
Redshift surveys are about a factor of 2 worse than SNAP.
Not hugely complementary, but an excellent cross-check.
Dark Energy Constraints in LCDM

14. Results for w = –2/3 Easier to measure.
s(Wm) = s(w) = 0.05 at z=0.8 s(dw/dz) = 0.08
SNe+CMB s(dw/dz) = 0.12
All data sets s(dw/dz) = 0.05!
Redshift surveys are comparable to SNAP.
This fiducial model is not favored by the data today. How secure is this?
Dark Energy Constraints in w=–2/3

15. 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 100h-1 Mpc!
Acoustic peaks expected to survive in the linear regime.
z=1
Meiksen & White (1997), Seo & DJE (2004)

16. 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.
fibers, using Echidna technology, feeding multiple bench spectrographs.
1.5 degree diameter FOV
Well ranked in Aspen process.
Detailed feasibility study in progress.
Also high-res for Galactic studies.
Contact Arjun Dey to get involved.
Am I insane? My therapist assures me that I’m not.

17. 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. sz~0.003(1+z).
But measuring DA(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 smear the acoustic oscillations.

18. 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 h3 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.

19. 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 L, then z<1 is more interesting.
Some model dependence as regards inferences from CMB.

20. Conclusions
Acoustic oscillations provide a robust way to measure H(z) and DA(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.
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.

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

23. Dark Energy is Subtle Measuring w(z) requires exquisite precision.
Varying w assuming perfect CMB:
Fixed Wmh2
DA(z=1000)
dw/dz is even harder.
w>–1 is easier.
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.
Comparing Cosmologies

24. …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 smear the acoustic oscillations.

25. 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.
Half-sky might match DA, but it doesn’t match sigma(w). Probably need 2% photo-z’s.

26. 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!

27. Distance Derivatives

28. 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.
fibers
1.5 degree diameter FOV
See poster by Dey, talk by Glazebrook,
Am I insane? My therapist assures me that I’m not.