The Nature of Dark Energy David Weinberg Ohio State University Based in part on Kujat, Linn, Scherrer, & Weinberg 2002, ApJ, 572, 1

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

Is dark energy here to stay? Four lines of evidence: 1.Type Ia Supernova Hubble diagram Inconsistent with  m =0,   =0 (~0.15 mag) More inconsistent with  m =0.3,   =0 (~0.25 mag) Strongly inconsistent with  m =1,   =0 (~0.4 mag) Local observations suggest evolutionary effects unimportant at 0.1 mag level

Is dark energy here to stay? Four lines of evidence: 1.Type Ia Supernova Hubble diagram CMB acoustic peak implying  tot  , combined with 2. Age of globular clusters and H 0  70 km s -1 Mpc -1 or 3. Dynamical evidence that  m < 0.5

Is dark energy here to stay? Four lines of evidence: 1. Type Ia Supernova Hubble diagram 2. CMB + age of globular clusters and H 0  70 km s -1 Mpc CMB + dynamical evidence that  m < Overall success of  CDM Cosmological model with inflation, CDM,  m  0.3,    0.7, agrees with wide range of CMB and large scale structure observations, in addition to above.

Is dark energy here to stay? Four lines of evidence: 1. Type Ia Supernova Hubble diagram 2. CMB + age of globular clusters and H 0  70 km s -1 Mpc CMB + dynamical evidence that  m < Overall success of  CDM Likely answer: YES.

Why is dark energy so surprising? The Cosmological Constant Problem “Naïve” calculation predicts  vac ~ M Planck / l 3 Planck ~  m Only “natural” number ~ is zero The Dark Energy Problem Observations suggest that  vac ~ (10 -3 eV) 4 ~ erg cm -3 No known physics naturally yields this energy scale; all current models of dark energy are ad hoc The Coincidence Problem For a cosmological constant,   /  m  a 3. Why are   and  m comparable today?

Kinds of proposed solutions True value of fundamental vacuum energy is  vac ~ (10 -3 eV) 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.

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

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 ?

Expansion history observables Hubble parameter Distance Age Linear growth factor:

Expansion history observables Hubble parameter H(z) Distance d A (z) Age t(z) Linear growth factor D 1 (z) normalized to present-day amplitude or to CMB amplitude Nearly all proposed dark energy tests measure one of these observables or some combination thereof, e.g., Volume element: V(z)  d A 2 (z) / H(z) Alcock-Paczynski parameter: h(z)  H(z) d A (z)

Measurement overview Parameter space:  m,, w, w’,  k For given observable and redshift,  m and w are degenerate Multiple redshifts or observables can break degeneracy Other LSS & CMB methods can also constrain  m Interesting w constraints require ~2% precision (& accuracy) Demonstrating non-zero w’ very difficult. Requires showing    (1+z) n. Not much complementarity of different observables.

Measurement methods: distance Type Ia supernovae Type IIp supernovae Radio galaxy angular diameters Cluster Sunyaev-Zel’dovich effect + X-ray Volume-redshift test with galaxy redshift survey (e.g. DEEP2) Characteristic scale in angular clustering – e.g., turnover, baryon wiggles Amplitude of cluster angular correlation function Amplitude of transverse Lyman-alpha forest correlations Strong gravitational lensing statistics Properties of well understood gravitational lenses Angular scale of first acoustic peak in CMB

Measurement methods: Hubble parameter Lyman-alpha forest: width and separation of features, curvature scale of power spectrum, measured in km/s. High-z galaxy redshift surveys: features in power spectrum, measured in km/s. Differential galaxy ages between neighboring redshifts: yields dz/dt = – (1+z) H(z). Weak lensing bispectrum: sensitive to  m (z). Combining with  m,0 yields  c (z) = 3H 2 (z) / 8  G. Alcock-Pacyznski test measures d A (z) H(z), can be applied to quasars, Lyman-alpha forest, galaxies, Sloan LRGs.

Measurement methods: linear growth factor Evolution of cluster “mass” function, via X-ray, SZ, weak lensing, mass-calibrated richness. Systematic uncertainty in masses is the key issue. Cosmic shear power spectrum. Lyman-alpha forest flux power spectrum. CMB anisotropy amplitude. Require (or at least benefit from) good measurement of fluctuation amplitude at z=0 (i.e.,  8,matter )

What has HST contributed? Improved determination of H 0. Light curves of some ground-based SN detections. Template images of host galaxies of ground-based SN. Discovery and light curves of supernovae at z > 1.

What more could HST contribute? More template images of ground-based SN hosts. More light curves of ground-based SN. More discovery and light curves of supernovae at z > 1. Distance measurements from cluster multiple arc systems. Cosmic shear surveys to measure w via growth factor evolution. Weak lensing cluster masses to measure w via growth factor.

What more should HST contribute? Support of ground-based SN if improved precision is substantial. Cosmic shear surveys to measure w via growth factor evolution. Weak lensing cluster masses to measure w via growth factor. Not competitive with ground-based measurements. Distance measurements from cluster multiple arc systems. Usefulness still to be demonstrated. More discovery and light curves of supernovae at z > 1?

What more should HST contribute? More discovery and light curves of supernovae at z > 1? Won’t compete with ground-based surveys for precision on w. Very unlikely to demonstrate redshift dependence of w.

Conclusions Dark energy is: Here to stay. Surprising. A possibly unique window into fundamental physics. Nearly all proposed observational tests measure some combination of H(z), d(z), linear growth factor.  m & w have degenerate effects. Multiple observables or multiple redshifts can lift degeneracy. Demonstration of time-dependent w unlikely, at least pre-SNAP. Figure of merit should therefore be precision on (constant) w. HST has played important role, but may not compete with ground-based surveys on this figure of merit.