1. Uncorrelated bins, two-population Supernovae, and Modified Gravity Asantha Cooray STScI - Dark Energy, May 08 Dark energy: Devdeep Sarkar (UCI) Alex Amblard (UCI) Daniel Holz (LANL) Mod. Gravity: Scott Daniel (Dartmouth) Robert Caldwell (Dartmouth) Alessandro Melchiorri (Rome) Paolo Serra (UCI)

2. 1. In future, dark energy EOS is not limited to two numbers. Sullivan, Holz, Cooray 2007; Sarkar, Amblard, Holz, Cooray 2008 Sarkar et al. PRL submitted 2008 (Huterer & Cooray 2005) 2. If SNe Ia are two types, dark energy EOS errors increase by a factor of 2 to 3. Sarkar et al. ApJL in prep (Howell et al; Scannapieco & Bildsten) 3. GR can now be tested at cosmological length scales to about 10% accuracy (in the Solar system, GR is now tested to 10 -4 to 10 -5 ) Caldwell, Cooray, Melchiorri 2007; Daniel, Caldwell, Cooray, Melchiorri 2008 Daniel et al. PRD in prep Overview

3. Equation-of-State: to bin or not to bin An approach not recommended: parameterize w(z) to functions with a finite number of parameters. There is some effort to push a 2-parameter form with w 0 -w a (also used by the DETF). Our approach: bin w(z) in redshift and de-correlate these bins by diagonalizing the covariance matrix. Huterer & Cooray 2005. SNe data + WMAP5 R (1.71 +/- 0.019) + BAOs + h (0.721 +/- 0.075) +  m h (0.184 +/- 0.021) + M (free) wzbinned: Free MCMC code (available on the web) to fit w(z) bins to SNe Hubble diagram, BAOs, CMB R - update with WL shear correlation functions soon. freedom: # of bins, width, location (given data, choices can be optimized)

4. Equation-of-State: to bin or not to bin Why bin and not fit to the 2-parameter Chevallier-Polarski form? (SNAP/ADAPT/Euclid) Future data can measure more than 2 parameters of w(z) at better than 10% accuracy (at 1  ). This is independent of most assumptions made wrt flatness (Planck  K prior), reasonable systematics, priors on H 0 etc. Thus, the DETF FoM has limited use as it is based on 2 numbers. Future is not limited to 2 numbers of the EOS. Usefulness: Test departures from w=-1 to 5%-8% level using independent estimates at several redshift bins. (Sarkar et al. 2008, PRL submitted)

5. II. Two populations of Type Ia Supernovae? Howell et al. 2007 Strovink 2007 12% diff in Luminosity of two types. Expected to be corrected by light-curve fitters. 0.06 mag diff in two types based on the (rise-fall) time differences.

6. Could there be two types? Should we be worried? yes, since one type dominates low-z SNe counts while the other dominates counts at high-z’s Prompt-type traces instantaneous SF or d/dt[M * (t)] Extended-type delayed, traces cumulative stellar mass, M * (t) Prompt: broader lightcurves and expected to be brighter Extended: dominate low-z SNe counts Scannepieco & Bildsten 2006; Mannucci et al. 2006 II. Two populations of Type Ia Supernovae?

7. What happens if light-curve fitters do not perfectly correct the difference in luminosity between the two types? If there is a residual difference in luminosity between prompt and extended then, where, and f E (z) is the fraction of extended types in the Hubble diagram as a function of redshift. Full details in Sarkar, Amblard, Holz, Cooray in prep. (one can also do the averaging relative to prompt leading to a similar fitting function with f P (z). absorbs a constant term independent of redshift).

8. (two separate fits to data) No detection of a systematic. But a large degeneracy with w (1  errors) SNe + BAO + WMAP5 + M free  CDM wCDM with α E w=-0.969 ± 0.177 α E =0 w=-0.956 ± 0.065 (consistent with WMAP5+ALL results in Komatsu et al. 08)

9. Davies et al. dataset A mock JDEM-like dataset. Errors increase by a factor of 2. FOM (for SNe) is decreased by a factor of 2.

10. What can JDEM do? Detect a residual difference in absolute magnitude of two-types at 0.025 mag at more than 2 sigma. Can easily test e.g., Strovink systematic magnitude difference of 0.06 mag. Should we test/allow for a systematic like this in future data, with a reduction in DE EOS accuracy?

11. III. Modifying Gravity at Large Scales Inside the Solar-system, GR is tested with a post-Newtonian parameters using the Eddington-Robertson-Schiff metric (with  =1): In GR,  =  =1. Lunar-ranging and time-delay with spacecraft give In similar spirit, GR can be tested at cosmological length scales for cosmological perturbations (Bertschinger 2006; Caldwell, Cooray & Melchiorri 2007) At late-times today in GR,  =0  is time-dependent; CCM choice:

12. Weak lensing modifications are a combination of  and growth function. Daniel, Caldwell, Cooray & Melchiorri 2008 CMB modifications are essentially changes to the ISW Fu et al. CHFTLS III. Modifying Gravity at Large Scales

13. Daniel, Caldwell, Cooray & Melchiorri 2008 approach: fix standard cosmology to WMAP-3 ML parameter values and vary  A hint of a detection with WMAP-3+Fu et al. weak lensing data (primarily an issue of  8 inconsistency between WMAP3 & WL) This mostly disappears with new WMAP-5 Daniel, Caldwell, Cooray & Melchiorri 2008 III. Modifying Gravity at Large Scales

14. (New) Daniel et al 2008 approach: vary all cosmological and post-GR parameters with MCMC and fit to existing cosmological data  is now fully consistent with zero when all existing data are combined. Current data:    ±  GR is now tested at cosmological length scales to 10% to 20% accuracy. III. Modifying Gravity at Large Scales

15. Summary In future, we can probably measure more than 2 numbers of the EOS. Planning, forecasting, and limiting experiments to measure the two numbers of the fitting function with w 0 -w 1 /w a is premature. If Typa Ia’s are two types (Type-Iap and Type-Iae), then we will know equally more about the physics of supernovae Ia’s as physics of dark energy with an experiment like JDEM. This is at the expense of reducing the accuracy of EOS measurements by a factor of 2 with JDEM, unless we are confident our light-curve fitters can remove the systematic exactly. General relativity is now tested for cosmological perturbations at 10% accuracy (we have a long way to go to reach accuracies within the Solar system).