Dark Energy: The Observational Challenge

1. Dark Energy: The Observational Challenge David Weinberg Ohio State University Based in part on Kujat, Linn, Scherrer, & Weinberg 2002, ApJ, 572, 1

2. The current SN Ia evidence Riess et al. 2004, astro-ph/0402512

3. Riess et al. 2004 A Robust Result • Cosmic acceleration evidence: • SN Ia Hubble diagram • CMB acoustic peak + • Dynamical evidence for low m • Age of oldest stars + H0  70 • Overall success of CDM in explaining wide range of data Bennett et al. 2003

4. A Grand Unified Model of Dark Energy

5. The Puzzles of Dark Energy • The Cosmological Constant Problem • Why is vac < 10-120 Planck ? • The Dark Energy Problem • What is causing cosmic acceleration? • The Coincidence Problem • Why are  and m comparable today? We have no good solutions to any of these problems.

6. Kinds of proposed solutions • True value of fundamental vacuum energy is vac ~ (10-3eV)4 • True value of fundamental vacuum energy is zero. Observed “dark energy” is a new scalar field or other component (quintessence, k-essence, spintessence, string network, …) • Value of fundamental vacuum energy varies throughout “multiverse”; anthropic selection requires small local value. • Back reaction causes fundamental value of vacuum energy to oscillate in time; accelerated and decelerated phases alternate. • Friedmann equation is wrong (extra dimensions?). • Any solution involves fundamental revision of physics, maybe clues to string theory, extra dimensions, etc.

7. Dark energy and cosmic expansion Dark energy changes cosmic expansion via the Friedmann eqn:

8. Dark energy and cosmic expansion Current data consistent with m=0.3, =0.7, k=0 w = –1   = constant Can we detect evidence for w  –1    constant ? Can we detect evidence for w  constant    (1+z)n ?

9. Type Ia supernovae Type IIp supernovae Radio galaxy angular diameters Cluster SZ effect + X-ray distances Volume-redshift test with high-z galaxy redshift survey (e.g., DEEP2) Characteristic scale in angular clustering of galaxy clusters or galaxies Amplitude of cluster angular correlation Amplitude of transverse Lya forest correlations Strong gravitational lensing statistics Golden lens systems Lya forest clustering scales, in km/s High-z galaxy redshift surveys: features in power spectrum, measured in km/s. Differential galaxy ages Weak lensing bispectrum Alcock-Pacyznski applied to quasars, Lyman-alpha forest, galaxies, Sloan LRGs. Evolution of cluster “mass” function Cosmic shear power spectrum. Lyman-alpha forest flux power spectrum Ages of high-redshift galaxies

10. Expansion history observables • Hubble parameter H(z) • Distance d(z) • Linear growth factor D1(z) • normalized to present-day amplitude or to CMB amplitude • Age t(z) Nearly all proposed dark energy tests measure one of these observables or some combination thereof, e.g., Volume element: V(z)  dA2(z) / H(z) Alcock-Paczynski parameter: h(z)  H(z) dA(z)

11. Expansion history observables • Hubble parameter • Distance (k=0) • Age • Linear growth factor:

12. Challenge 1: 2-parameter models Current evidence consistent with =0.7, w = –1. How well can we tighten constraints and break the degeneracy between  and w? Assume flat universe, hence m = 1 – .

20. Challenge 1: 2-parameter models • Interesting constraints on w require ~1-2% accuracy. • Different redshifts and different observables have complementary information, can break m – w degeneracy. • CMB will give high precision constraint on • m h2 / dA(z=1100) = m h3 / F(m , k , w). • Galaxy clustering gives fairly precise constraint on m h. • Galaxy clustering may yield precise constraint on m.

21. SNAP collaboration 2004 Challenge 2: Time-varying w • Recall: (z) = ,0 (1+z)3(1+w) • Demonstrating time-dependence of w requires showing that   ,0 (1+z)n for any n. • Common parameterizations: • w(z) = w0 + w1 z • w(a) = w0 + wa (1 – a) • A given combination of (w0 , w1) may be well mimicked by a constant value of w  w0 .

22. An optimistic toy model with time-variable w

23. Distance relative to best-fit constant-w model

24. Distance relative to best-fit constant-w model

25. Distance relative to best-fit constant-w model

26. Models with =const. at low z   (1+z)m at high z A single constant-w model matches well for all observables. Kujat et al. 2002

27. Challenge 2: Time-varying w • Hard to show that   ,0 (1+z)n because  usually small at high-z. Not much leverage. • Need wide redshift range to have a shot. • Not much complementarity from different observables. SNAP Collaboration 2004

28. Challenge 2: Time-varying w • Hard to show that   ,0 (1+z)n because  usually small at high-z. Not much leverage. • Need wide redshift range to have a shot. • Not much complementarity from different observables. • Easiest time-variation to detect:  scales like matter at high redshift, changes to constant at low redshift.

29. Wide Field Imaging From Space The Beyond Einstein Probes ? Essential for a healthy space science program. Join the dark side, Luke. It is your …………..

30. Joint Dark Energy Mission

31. Magnificently Useful Supernova Telescope For Learning about the Yooniverse

32. MUSTFLY as a Dark Energy Probe • Type Ia Sne – Measure d(z), high precision • Cosmic shear – Power spectrum and bispectrum, depend on d(z), D1(z), and H(z) • Type IIp Sne – d(z) • Angular galaxy clustering – d(z) ? • Redshift galaxy clustering – possible with grism? d(z) & H(z)? • Cluster correlations – shape and amplitude, d(z) • “Golden” gravitational lenses – d(z) • Cluster-mass correlations from weak lensing

33. Cluster Masses as a Dark Energy Measure • Change in growth factor shifts mass scale of cluster mass function n(M).

34. Cluster Masses as a Dark Energy Measure • Change in growth factor shifts mass scale of cluster mass function n(M). • Compensating volume effect. • Steep n(M)  good statistical precision, but sensitivity to systematic errors in mass. • For mass indicator I, accurate results require accurate knowledge of full distribution P(M|I). • Best (?) method: Use weak lensing to precisely measure average surface density profile of clusters above threshold in I.

35. w = -1 vs. w = -0.8 J. Yoo

36. Some Issues For MUSTFLY • If dark energy is primary justification, should be better than any alternative probes on the horizon. • For an “interesting” result, what confidence level will we demand? • w  – 1 : one > 3 or two > 2. OK to assume k= 0. (?) • Time-dependent w : one > 4 or two > 3. Allow k  0. • What is more likely : |w –1| ~ 0.05 or |dw/dz| ~ 1 at low z?

37. Some Issues For MUSTFLY • DESTINY version: • Without weak lensing, what could confirm an “interesting” 2-3  result? • SNAPversion: • What is right balance of SNe, weak lensing? • Do 0.1-arcsec pixels allow sufficiently accurate photometry and shape measurements? • Can necessary photometric calibration be achieved? • Is precision on w being sacrificed to take a shot at detecting dw/dz? If so, is this the right choice?

38. Conclusions • Dark energy is a theoretically important problem. • Dark energy is an observationally challenging problem. • Observational methods measure d(z), H(z), D1(z), t(z), or some combination thereof. • Many methods can achieve moderate precision. • m – w models: 1 – 2 % precision needed for interesting results. Different measures complementary. External constraints on m. • Time-varying w: Hard to detect, even going to z ~ 2. Requires ~unity change at low z, sub-percent precision. Not much complementarity of different methods.