The Theory/Observation connectionlecture 4

dark energy: linking with observations

Will Percival

The University of Portsmouth

Lecture outline

Dark Energy review– cosmological constant?

– quintessence?

– tangled defects?

– phantom dark energy?

– modified gravity?

– problems with the data?

Geometrical tests– SN1a

– BAO

Cosmological constant

Originally introduced by Einstein to make the Universe static Constant vacuum energy density, which is homogeneous and has constant density in time Equation of state

Particle physics provides a natural candidate: zero-point vacuum fluctuations for bosonic or fermionic fields

– typical scale of cosmological constant is (Mcutoff)4, where Mcutoff is UV cutoff of theory describing field

– Planck mass gives planck ~ (1019GeV)4

– Observations show

quintessence

adaption of scalar field theory developed for inflationary theories for late-time dark energy very weak potential required, with very small effective mass

– field can be frozen at early times

– or it can slowly roll down the potential, with energy density tracking dominant fluid until recently (“tracker” models)

equation-of-state generally evolves, although can be constant (with special choice of potential) In fact, any w(z)>-1 history can be obtained with right choice of potential

quintessence

Albrecht & Weller 2002, astro-ph/0106079

Parameterizations of w

If you don’t know the physics, you don’t have a well-defined set of models to test, it’s a free-for-all

Bassett et al. 2004, astro-ph/0407364

can parameterise using

w(a) = w0 + w1(1-a)

Tangled defects

Network of defects formed in phase transition grows with expansion of Universe

– For strings, lengths grow as a, and energy as a-2, so w=-1/3, and no acceleration (just)

– For walls, area grows as a2, and energy drops as a-1, so w=-2/3, which can produce acceleration

but observations show w ~ -1

Phantom dark energy

motivated by early supernovae data which favored strong acceleration w<-1 density increases as Universe expands can lead to divergence in finite time - big rip theoretically difficult to justify

– violate weak energy condition

– lead to ghosts - negative norm energy states

– can be classically and quantum mechanically unstable

If observations continue to show strong acceleration at low redshifts, may need a phase shift in theory

modified gravity

Can separate cosmological constant from stress-energy tensor

Can then imagine moving it to the other side of the equation

Should we consider alternatives if we’re going to be modifying gravity, rather than postulating a new component of energy?

modified gravity

Example from history: Mercury perihilion Newton + dark planet?

No! Modified gravity (GR)

Today, we need a modified Friedmann equation

modified gravity

Problem: we can always explain Adark by either stress-energy component or change to gravity.

Only way of telling apart is by structure formation (see next lecture)

Modified gravity: replace R with f(R) in action for gravity. Gives

DGP modifed gravity (5D braneworld)

Problems with the data …

data depends on astrophysics, so subject to systematics but, more than one test, so need a conspiracy that all the astrophysics points you to acceleration …

Still, worth reviewing all data

With this in mind, lets have a look at the evidence for acceleration …

All strong evidence is geometrical

All of the evidence depends on the expansion geometry, specifically through the Friedmann equation

equation of state of dark energy p = w(a)

SNLS Hubble diagram

First-Year SNLS Hubble Diagram

ΩM = 0.263 ± 0.042 (stat) ± 0.032 (sys)

<w>=-1.02 ± 0.09 (stat) ± 0.054 (sys) (with BAO + Flat Universe)

Astier et al (2006)A&A, 447, 31

Supernovae observations

Initially assumed all SN1a have same intrinsic peak brightness Now refined so that

Luminosity distance to supernova

Apparent magnitude of supernova

Absolute magnitude of supernova (assumed constant for all SN1a)

Stretch parameter s: corrects for lightcurve shape via

c=B-V colour: corrects for extinction/intrinsic effects via

Supernovae systematics

“Experimental Systematics”–Calibration, photometry, Malmquist-type effects

Contamination by other SNe or peculiar SNe Ia–Minimized by spectroscopic confirmation

Non-SNe systematics–Peculiar velocities; Hubble Bubble; Weak lensing

K-corrections and SN spectra–UV uncertain; “golden” redshifts; spectral evolution?

Extinction/Colour–Effective RV; Intrinsic colour versus dust

Redshift evolution in the mix of SNe–“Population drift” – environment?

Evolution in SN properties–Light-curves/Colors/Luminosities

From talk by Mark Sullivan

Hubble diagram by galaxy type

SNe in passive galaxies show a smaller scatter “Intrinsic dispersion” consistent with zero

(Does intrinsic dispersion in SNe arise from dust?)

Cleaner sample: But SNe in passive galaxies are at high-z (~20%: two component model) + very few locally

Passive hosts Star-forming hosts

Cosmological distribution of galaxy types

Future supernovae prospects

Short-term: Current constraints on <w>: <w>=-1 to ~6-7% (stat)

(inc. flat Universe, BAO+WMAP-3)

At SNLS survey end, statistical uncertainty will be 4-5%:– 500 SNLS + 200 SDSS + larger local samples– Improved external constraints (BAO, WL)

Longer term:

No evolutionary bias in cosmology detected (tests continue!)

SNe in passive galaxies: seem more powerful probes, but substantially rarer (esp. at high-z)

Colour corrections are the dominant uncertainty

– Urgent need for z<0.1 samples with wide wavelength coverage

– Not clear what the “next step” at high-z should be

Galaxy clustering

The power spectrum turn-over

varying the matter densitytimes the Hubble constant

In radiation dominated Universe, pressure support means that small perturbations cannot collapse. Jeans scale changes with time, leading to smooth turn-over of matter power spectrum.

However, it is hard to disentangle this shape change from galaxy bias and non-linear effects

Problem: galaxy bias

Galaxies do not form a Poisson sampling of the matter field

Peaks model: large scale offset in 2-pt clustering strength (next lecture)

Also non-linear effects in the matter

Also effects from the transition from mass to galaxies

Angulo et al., 2007, MNRAS, astro-ph/0702543

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

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

varying thebaryon fraction

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

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

BAO as a standard ruler

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

Radial direction

(evolution of Universe)

Angular direction

(line of sight)

Gives rise to the “rings of power”

Hu & Haiman 2003, astro-ph/0306053

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)

Why BAO are a good ruler

No change in position of oscillations, just a damping term.

Suppose that we measure an observed power that is related to the linear power by (halo model)

Linear baryon acoustic oscillations are ratio of linear matter power spectrum to a smooth fit

Then observed oscillations are related to linear BAO by

To change the observed positions of BAO, we need sharp features in the observed power

Eisenstein, Seo & White 2006, astro-ph/0604361Percival et al. 2007, astro-ph/0705.3323

Linear bias model also predicts this form

For linear bias model, peculiar velocities of galaxies gives Gaussian damping with width ~10Mpc

Going to 2nd order …

Perturbative treatment of (CDM+baryon) fluid system

L+++= )3()2()1( δδδδ

（ e.g., Suto & Sasaki 1991)

Based on field-theoretical approach,

Crocce & Scoccimarro (2006ab,2007)

““Renormalized Perturbation TheoryRenormalized Perturbation Theory ( (RPTRPT)”)”

New approachNew approach

infinite class of perturbative corrections at all orders.Standard PT calculation can be improved by re-summing an

Related works: McDonald, Matarrese & Pietroni, Valageas, Matsubara (‘07)

Going to 2nd order …

At second order we get mode mixing, which causes shifts in the power spectrum BAO peaks

Shifts are <1%, and can be calculated

Crocce & Scoccimarro 2007; astro-ph/0704.2783

Not important for current data, but need to be included for future analyses

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

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

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

Future BAO prospects

Short-term: SDSS-II improves low redshift measurements by factor ~2

– 1000000 galaxy redshifts to z~0.5 Wiggle-Z survey detects BAO at higher redshift

– 400 000 galaxy redshifts to z~1– weak constraints

Longer term:

Photometric surveys (e.g PanSTARRS, DES) find ~2--3% distance constraints out to z~1

Future spectroscopic surveys (e.g. HetDex, BOSS, WFMOS, Space) push to 1% distance constraints over a wide range of redshift (0.5<z<3)

With 1% constraints need to include 2nd order effects in analysis of BAO positions

Further reading

Supernovae– Astier et al. (2005), astro-ph/0510447

BAO– Blake & Glazebrook (2003), astro-ph/0301632– Seo & Eisenstein (2003), ApJ, 598, 720– Hu & Haiman (2003), astro-ph/0306053