# Presentation: 116029

## Dark Energy: The Observational Challenge

- David Weinberg
- Ohio State University

- Based in part on
- Kujat, Linn, Scherrer, & Weinberg 2002, ApJ, 572, 1

- Riess et al. 2004, astro-ph/0402512

- The current SN Ia evidence

## 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

- Riess et al. 2004

## A Grand Unified Model of Dark Energy

## 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****.**

## 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 ?

## 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

## 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)

## Expansion history observables

-  Hubble parameter
-  Distance                                                              (k=0)
-  Age
-  Linear growth factor:

## 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 – .

## Slide 13

## Slide 14

## Slide 15

## Slide 16

## Slide 17

## Slide 18

## Slide 19

## 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.

## 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 .

- SNAP collaboration 2004

## An optimistic toy model with time-variable w

## Distance relative to best-fit constant-w model

## Distance relative to best-fit constant-w model

## Distance relative to best-fit constant-w model

## Models with 

- Kujat et al. 2002

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

## 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

## 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.

## Wide Field Imaging From Space

- The Beyond Einstein Probes ?  Essential for a healthy space science program.

- Join the dark side, Luke. It is your ..............

## Joint 

- Dark
- Energy
- Mission

## Magnificently 

- Useful

- Supernova

- Telescope

- For

- Learning about the

- Yooniverse

## 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

## Cluster Masses as a Dark Energy Measure

-  Change in growth factor shifts mass scale of cluster mass function n(M).

## 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.

## w = -1 vs. w = -0.8

- J. Yoo

## 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?

## Some Issues For MUSTFLY

- DESTINY version:
-  Without weak lensing, what could confirm an “interesting” 2-3  result?
- SNAP version:
-  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?

## 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.