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The Theory/Observation connection lecture 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?

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The theory observation connection lecture 4 dark energy linking with observations

The Theory/Observation connectionlecture 4dark energy: linking with observations

Will Percival

The University of Portsmouth

Lecture outline
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
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


  • 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


Albrecht & Weller 2002, astro-ph/0106079

Parameterizations of w
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

can parameterise using

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

Bassett et al. 2004, astro-ph/0407364

Tangled defects
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
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
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 gravity1
modified gravity

  • Example from history: Mercury perihilion

    • Newton + dark planet?

  • No! Modified gravity (GR)

Today, we need a modified Friedmann equation

Modified gravity2
modified gravity

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

DGP modifed gravity (5D braneworld)

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)

Problems with the data
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

All strong evidence is geometrical
All strong evidence is geometrical acceleration …

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

equation of state of dark energyp = w(a)

Snls hubble diagram

First-Year SNLS Hubble Diagram acceleration …

SNLS Hubble diagram

Astier et al (2006)

A&A, 447, 31

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

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

Supernovae observations
Supernovae observations acceleration …

  • Initially assumed all SN1a have same intrinsic peak brightness

  • Now refined so that

Apparent magnitude of supernova

Stretch parameter s: corrects for lightcurve shape via 

Luminosity distance to supernova

Absolute magnitude of supernova (assumed constant for all SN1a)

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

Supernovae systematics
Supernovae systematics acceleration …

  • “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
Hubble diagram by galaxy type acceleration …

  • 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

Star-forming hosts

Passive hosts

Future supernovae prospects
Future supernovae prospects acceleration …


  • 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
Galaxy clustering acceleration …

The power spectrum turn over
The power spectrum turn-over acceleration …

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.

varying the matter density

times the Hubble constant

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

Problem galaxy bias
Problem: galaxy bias acceleration …

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
Baryon Acoustic Oscillations acceleration …

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

varying the

baryon fraction

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

Sound speed cs

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

Comparing cmb bao
Comparing CMB & BAO acceleration …



CREDIT: WMAP & SDSS websites

Comparing bao at different redshifts
Comparing BAO at different redshifts acceleration …

SDSS main galaxies + 2dFGRS


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



CREDIT: WMAP & SDSS websites

Bao as a standard ruler
BAO as a standard ruler acceleration …

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 ruler1
BAO as a standard ruler acceleration …

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

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

Radial direction

(evolution of Universe)

Angular direction

(line of sight)

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

Varying rs/DV

Why bao are a good ruler
Why BAO are a good ruler acceleration …

Linear baryon acoustic oscillations

are ratio of linear matter power

spectrum to a smooth fit

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

Linear bias model also predicts this form

Then observed oscillations are related to linear BAO by

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

No change in position of oscillations,

just a damping term.

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

Eisenstein, Seo & White 2006, astro-ph/0604361

Percival et al. 2007, astro-ph/0705.3323

Going to 2nd order
Going to 2nd order … acceleration …

Perturbative treatment of

(CDM+baryon) fluid system

(e.g., Suto & Sasaki 1991)

New approach

Based on field-theoretical approach,

Standard PT calculation can be improved by re-summing an

infinite class of perturbative corrections at all orders.

“Renormalized Perturbation Theory (RPT)”

Crocce & Scoccimarro (2006ab,2007)

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

Going to 2nd order1
Going to 2nd order … acceleration …

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

Shifts are <1%, and can be calculated

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

Crocce & Scoccimarro 2007; astro-ph/0704.2783

Bao from all the sdss dr5 galaxies
BAO from all the SDSS DR5 galaxies acceleration …

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:

Overall P(k) shape

Observed baryon acoustic oscillations (BAO)

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

Bao from the 2dfgrs sdss
BAO from the 2dFGRS + SDSS acceleration …

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
BAO distance scale constraints acceleration …

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




Constraint fitting rs/DV(z)

Constraint from


Future bao prospects
Future BAO prospects acceleration …


  • 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
Further reading acceleration …

  • 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