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)

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1. In future, dark energy EOS is not limited to two numbers.

Sullivan, Holz, Cooray 2007; Sarkar, Amblard, Holz, Cooray 2008Sarkar 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 toabout 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

Equation-of-State: to bin or not to binAn 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 w0-wa

(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) + mh (0.184 +/- 0.021) + M (free)

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Covariance matrix :

C = wwT − w wT

Diagonalize the inverse matrix

C-1 =OTΛO

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)

Equation-of-State: to bin or not to binWhy bin and not fit to the 2-parameter Chevallier-Polarski form?

(SNAP/ADAPT/Euclid)

Future data can measuremore than 2 parameters ofw(z) at better than 10% accuracy (at 1).

This is independent of most assumptions madewrt flatness (Planck K prior),reasonable systematics,priors on H0 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)

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.

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 SFor d/dt[M*(t)]

Extended-type delayed, traces cumulative stellar mass, M*(t)

Prompt: broader lightcurves and expected to be brighterExtended: dominate low-z SNe counts

Scannepieco & Bildsten 2006; Mannucci et al. 2006

II. Two populations of Type Ia Supernovae?

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 promptand extended

then,

where,

and fE(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 fittingfunction with fP(z) . absorbs a constant term independent of redshift).

(two separate fits to data)

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αP = −0.050 ± 0.097 α E = 0.049 ± 0.097

No detection of a systematic.

But a large degeneracy with w (1 errors)

SNe + BAO + WMAP5 + M free

CDM

wCDM with αE w=-0.969 ± 0.177 αE=0 w=-0.956 ± 0.065 (consistent with

WMAP5+ALL results in Komatsu et al. 08)

Davies et al. dataset

A mock JDEM-likedataset.

Errors increase bya factor of 2.FOM (for SNe) is decreased by a factor of 2.

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 of0.06 mag.

Should we test/allow for a systematic like this in future data, with a reduction in DE EOS accuracy?

III. Modifying Gravity at Large ScalesInside the Solar-system, GR is tested with a post-Newtonian parametersusing the Eddington-Robertson-Schiff metric (with α=1):

In GR, ==1. Lunar-ranging and time-delay with spacecraft give

In similar spirit, GR can be tested at cosmological length scales forcosmological perturbations (Bertschinger 2006; Caldwell, Cooray & Melchiorri 2007)

At late-times today in GR, =0

is time-dependent; CCM choice:

Weak lensing modificationsare a combination of andgrowth function.

Daniel, Caldwell, Cooray & Melchiorri 2008

CMB modifications are essentially changes to the ISW

Fu et al. CHFTLS

III. Modifying Gravity at Large Scales

Daniel, Caldwell, Cooray & Melchiorri 2008approach: fix standard cosmology toWMAP-3 ML parameter values and vary

A hint of a detection with WMAP-3+Fu et al.weak lensing data (primarily an issue of8 inconsistency between WMAP3 & WL)

This mostly disappears with new WMAP-5

Daniel, Caldwell, Cooray & Melchiorri 2008

III. Modifying Gravity at Large Scales

(New) Daniel et al 2008approach: vary all cosmological andpost-GR parameters with MCMC and fit toexisting cosmological data

is now fully consistent with zero whenall existing data are combined.

Current data: ±GR is now tested at cosmological lengthscales to 10% to 20% accuracy.

III. Modifying Gravity at Large Scales

Summary

In future, we can probably measure more than 2 numbers of the EOS.Planning, forecasting, and limiting experiments to measure the twonumbers of the fitting function with w0-w1/wa is premature.

If Typa Ia’s are two types (Type-Iap and Type-Iae), then we will knowequally 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 measurementsby 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).