Using Baryon Acoustic Oscillationsto test Dark Energy

Will Percival

The University of Portsmouth

(including work as part of 2dFGRS and SDSS collaborations)

Baryon Acoustic Oscillations

“Wavelength” of baryonic acoustic oscillations is determined by the comoving sound horizon at recombination

At early times can ignore dark energy, so comoving sound horizon is given by

Sound speed cs

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varying thebaryon fraction

Gives the comoving sound horizon ~110h-1Mpc, and BAO wavelength 0.06hMpc-1

Image credit: Martin White

BAO as a standard ruler

If we are considering radial and angular directions using randomly placed galaxy pairs, we constrain (to 1st order)

BAO position (in a redshift slice) therefore constrains some multiple of

Varying rs/DV

Changes in cosmological model alter measured BAO scale (∆dcomov) by:

Radial direction

(evolution of Universe)

Angular direction

(line of sight)

Extracting BAO from P(k)

fit data with a 2-component model comprising a smooth spline (node separation 0.05hMpc-1), and the sinusoidal (in the transfer function) multiplicative BAO component usually applied to a CDM model. The ability of this model to fit linear CDM power spectra is good.

Percival et al., 2007, astro-ph/0608635 & astro-ph/0705.3323

The SDSS DR5 sample

Main sample galaxies

Type-I LRGs

Type-II LRGs

After various selection cuts, the DR5 sample gives 51251 LRGs and 462791 main galaxies (factor ~2 larger than previously analysed)

BAO from all the SDSS DR5 galaxies

Compared with WMAP 3-year best fit linear CDM cosmological model. N.B. not a fit to the data, but a prediction from WMAP.

Interesting features:

1. Overall P(k) shape

2. Observed baryon acoustic oscillations (BAO)

Percival et al., 2007, ApJ, 657, 645

Matter density from SDSS BAO

When combined with, and marginalised over the WMAP 3-year peak position, For flat CDM cosmologies

Percival et al., 2007, ApJ, 657, 51

Comparing CMB & BAO

SDSS GALAXIES

CMB

CREDIT: WMAP & SDSS websites

Comparing BAO at different redshifts

CREDIT: WMAP & SDSS websites

SDSS LRGs

SDSS main galaxies + 2dFGRS

Tell us more about the acceleration, rather than just that we need it!

z=0.35z=0.2

Combining the SDSS and 2dFGRS

Work for astro-ph/0705.3323 in collaboration with: Shaun Cole, Dan Eisenstein, Bob Nichol, John Peacock, Adrian Pope, Alex Szalay

BAO from the 2dFGRS + SDSS

BAO detected at low redshift 0<z<0.3 (effective redshift 0.2)

BAO detected at high redshift 0.15<z<0.5 (effective redshift 0.35)

BAO from combined sample (detected over the whole redshift range 0<z<0.5)

Percival et al., 2007, MNRAS, astro-ph/0705.3323

Galaxy distances needed for analysis

Galaxy redshifts need to be converted to distances before BAO can be measured

Not a problem for small numbers of parameters, but time consuming for more

Solve problem by parameterizing distance-redshift relation by smooth fit with small number of modes: can then be used to constrain multiple sets of models

For SDSS+2dFGRS analysis, choose two modes at z=0.2 and z=0.35, for fit to DV

This forms an intermediate link between the cosmological models to be tested and data

BAO distance scale constraints

Constraint fromDV(0.35)/DV(0.2)

Constraint fitting rs/DV(z)

Constraint including observed peak distance constrain from CMB rs/dA(cmb)=0.0104

SCDMSCDM

OCDMOCDMCDMCDM

Cosmological constraints

Constraint fromDV(0.35)/DV(0.2)

Constraint fitting rs/DV

Constraint including distance to CMB

Consider two simple models:1. CDM2. Flat, constant w

Cosmological constraints with SNLS

Consider two simple models:–Lambda-CDM–Flat, constant w

Discrepancy with CDM?

LRG BAO on too small scales: further away than expected, so more acceleration between z=0.2 and 0.35

Discrepancy is 2.4

Can increase BAO damping and reduce significance of result, but then match with data becomes worse

conclusions

BAO offer an attractive method for DE studies– Good reasons to believe that systematics are of low amplitude

– Physics is well known and can be modeled today

SDSS+2dFGRS measures BAO and rs/DV at z=0.2, z=0.35

– Constraint DV(0.35)/DV(0.2) = 1.812 is higher than predicted by LambdaCDM+WMAP+SNLS

DV(0.35)/DV(0.2) = 1.67 (2.4 discrepancy). Needs more acceleration at low redshift

– But, can reduce significance slightly by adjusting BAO fit

Many future BAO experiments are planned– BOSS, DES, PanSTARRS, WFMOS, ADEPT, SPACE, HetDEX, SKA, …