dark energy

Dark EnergyDark EnergyDavid SpergelDavid Spergel

Princeton UniversityPrinceton University

Evidence for cosmic acceleration: Evidence for cosmic acceleration: Supernovae type IaSupernovae type Ia

Many Form of EvidenceMany Form of Evidence

Stellar AgesStellar Ages ISW EffectISW Effect Baryon WigglesBaryon Wiggles Cluster EvolutionCluster Evolution CMB & Growth of StructureCMB & Growth of Structure Cluster Properties versus RedshiftCluster Properties versus Redshift

Jimenez

ISW EffectISW Effect

Measures the Measures the evolution of the evolution of the potential on large potential on large scalesscales

Detected through Detected through cross-correlationscross-correlations SDSSSDSS APMAPM 2-MASS2-MASS Radio SourcesRadio Sources X-ray SourcesX-ray Sources

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Nolta et al. 2005

SDSS and Baryon WigglesSDSS and Baryon Wiggles

Purely geometric testPurely geometric test

(SDSS + WMAP)(SDSS + WMAP)



Eisenstein et al. (2005)



Growth of Growth of StructureStructure

SDSS Tegmark et al.

Astro-ph/0310723

Verde et al. (2003)

Consistent ParametersConsistent Parameters

WMAP+CBI+WMAP+CBI+ACBARACBAR

All CMB(Bond)All CMB(Bond) CMB+CMB+

2dFGRS2dFGRS

CMB+SDSS CMB+SDSS (Tegmark)(Tegmark)

bbhh22 .023 .023 + .001 .0230 .0230 + .0011 .023 .023 + .001 .0232 .0232 + .0010

xxhh22 .117 .117 + .011 .117 .117 + .010 .121 .121 + .009 .122 .122 + .009

hh .73 .73 + .05 .72 .72 + .05 .73 .73 + .03 .70 .70 + .03

nnss.97 .97 + .03 .967 .967 + .029 .97 .97 + .03 .977 .977 + .03

.83 .83 + .08 .85 .85 + .06 .84.84 + .06 .92 .92 + .08

What is Dark Energy ?What is Dark Energy ?What is Dark Energy ?What is Dark Energy ?

“ ‘Most embarrassing observation in physics’ – that’s the only quick thing I can say about dark energy that’s also true.”

Edward Witten

What is the Dark Energy?What is the Dark Energy?

Cosmological ConstantCosmological Constant Failure of General RelativityFailure of General Relativity QuintessenceQuintessence Novel Property of MatterNovel Property of Matter

Simon Dedeo Simon Dedeo astro-ph/0411283

Why is the total value measured from Why is the total value measured from cosmology so cosmology so small compared to quantum field theory calculations of small compared to quantum field theory calculations of vacuum energy? vacuum energy? From cosmology: 0.7 critical density ~ 10-From cosmology: 0.7 critical density ~ 10-48 48 GeVGeV44

From QFT estimation at the Electro-Weak (EW) scales: From QFT estimation at the Electro-Weak (EW) scales: (100 GeV)(100 GeV)44

At EW scales ~56 orders difference, at Planck scales At EW scales ~56 orders difference, at Planck scales ~120 orders~120 orders

Is it a fantastic cancellation of a puzzling smallness?Is it a fantastic cancellation of a puzzling smallness?

Why did it become dominant during the “present” epoch of Why did it become dominant during the “present” epoch of cosmic evolution? Any earlier, would have prevented cosmic evolution? Any earlier, would have prevented structures to form in the universe (cosmic coincidencestructures to form in the universe (cosmic coincidence))

COSMOLOGICAL CONSTANT??

Anthropic Solution?Anthropic Solution?

Not useful to discuss creation science in Not useful to discuss creation science in any of its forms….any of its forms….

QuintessenceQuintessence

Introduced mostly to address Introduced mostly to address the “why now?” problemthe “why now?” problem

Potential determines dark Potential determines dark energy properties (w, sound energy properties (w, sound speed)speed) Scaling models (Wetterich; Scaling models (Wetterich;

Peebles & RatraPeebles & Ratra))V(V() = exp) = exp

Most of the tracker models predicted w > -0.7

matter



Zlatev and Steinhardt (1999)

Dark Energy EvolutionDark Energy Evolution

The shape of the The shape of the quintessence quintessence potential determines potential determines the evolution of the the evolution of the dark energydark energy



Dark Energy Equation of StateDark Energy Equation of State w = pressure (tension) / density = p/c2

In this plot, w<-1 has been ignored

Strong consistency

Current ConstraintsCurrent Constraints



Seljak et al. 2004



Looking for QuintessenceLooking for Quintessence

Deviations from w = -1Deviations from w = -1 BUT HOW BIG?BUT HOW BIG?

Clustering of dark energyClustering of dark energy Variations in coupling constants (e.g., Variations in coupling constants (e.g., ))

FF/MFF/MPLPL

Current limits constrain Current limits constrain < 10< 10-6-6

If dark energy properties are time dependent, so are other basic physical parameters

A New Kind of Particle

picks a preferred frame.

Take it to be the “CMB” frame, i.e.:

New axial coupling

Standard Dirac Fermion(electron, neutrino, &c.)

(Kostelecky, Jacobson & Mattingly, &c — standard particle physics modification.)

DEDEO 2005

What is ?

Older studies: is fixed; an “aether.”

Instead make dynamical.

⇒ spontaneous symmetry breaking⇒ fluctuations possible:

Final choice: take to be the gradient of a scalar:

dimensional considerations : take to be Planck scale

mass scale of the theory

see, e.g., Arkani-Hamed et al. 2004

Particle Dark Energy

The equation of state of this gas of particles can become negative without invoking a cosmological constant.

(Note: w<-1 allowed as well: another unusual result.)

particle momentum

Dark Energy Sound Speed

Need to consider not only , but also (adiabatic sound speed) and (entropy perturbation.)

Adiabatic sound speed & w(a) related ⇒ two parameters

• Most models (e.g., scalar field quintessence) have unity sound speed.

• New models: k-essence & Chaplytin gases, and now particle dark energy, where sound speed ⇒ zero.


“negative” sound speed: instabilities

grow exponentially

positive sound speed: power

is damped below the horizon as

system oscillates

zero sound speed (CDM)

Bean & Doré, 2004

Hintsof a dark energy sound

speed??Bean & Doré : phenomenological models of clustering dark energy.

Hand-write equation of state and sound speed.

ISW suppression.

Suppression of the ISW as DE can cluster, slowing potential decay (“missing quadrupole” important part of signal.)

Oscillatory features in the power spectrum depending on detailed sound speed history.DeDeo, Caldwell, Steinhardt, 2003

Power Spectrum Oscillations

• Allow for near-zero sound speed at early times:

• Dark Energy can cluster with the CDM

• (Suppression of ISW as discussed.)

• Because sound speed is not precisely zero, can get oscillations: Jeans length is non-zero.

• (A classic problem with “unified” models: even a very small sound speed can produce noticiable differences from CDM at small scales.)

Does Particle Dark Energy Cluster?

• A general answer is not (yet) known.

• However, we can make some general statements.

° DψCDM : CDM particles cluster, then decay

Initial conditions for the ψ particles is perturbed.

° As for scalar field: must go beyond adiabatic sound speed: coupled, self-interacting particle fluid.

Crossing .

• Can be associated with gravitational instabilities.

• Hu (2004; astro-ph/0401680): internal degrees of freedom halt the generic instability.

• As with Chaplytin gases and classical scalar fields, the question of non-adiabatic (entropy) perturbations is crucial (e.g., Reis et al. 2003) in the transition.

Crossing continued

Standard perturbations:

There appears to be a singularity at the crossing-point.

However: physically meaningful term is:(fractional momentum transfer.) Recasting the equations:

a gravitational instability becomes an anti-gravitational instability.

see Caldwell & Doran (2004), Vikman (2004)

Open Questions

Observation: Evolution of perturbations. Complicated! We know enough to say clustering probably occurs when w=0. Intriguing: let’s look for DE’s sound speed.

Theory: Particle physics of the dark sector: now we know the trick, what other kinds of Lorentz violations can lead to Dark Energy behaviour?

Theory: What is the underlying source of Lorentz violation? Scalar field, vector field, extra dimensions, “arrow of time,” &c &c.

General Relativity: ReviewGeneral Relativity: Review

Riemann Tensor: Unique combination of second derivatives of metric

Ricci tensor Curvature Scalar

Einstein Equation

Newtonian limit of Einstein equation

GR from Least Action GR from Least Action PrinciplePrinciple

Least Action:

Once you start adding terms, there may be no stopping:

e.g., Carroll et al., astro-ph/0413001

What is this doing here?

Big Bang CosmologyBig Bang Cosmology

Homogeneous, isotropic universe

(flat universe)

Rulers and Standard CandlesRulers and Standard Candles

Luminosity Distance

Angular Diameter Distance

Flat M.D. UniverseFlat M.D. Universe

D = 1500 Mpc for z > 0.5

VolumeVolume

TechniquesTechniques

Measure H(z)Measure H(z) Luminosity Distance (Supernova)Luminosity Distance (Supernova) Angular diameter distanceAngular diameter distance

Growth rate of structureGrowth rate of structure.

Checks Einstein equations to first order in perturbation theory

Growth Rate of StructureGrowth Rate of Structure Galaxy SurveysGalaxy Surveys

Need to measure biasNeed to measure biasNon-linear dynamicsNon-linear dynamicsGravitational LensingGravitational LensingHalo ModelsHalo ModelsBias is a function of galaxy properties, Bias is a function of galaxy properties,

scale, etc….scale, etc….

Non-linear DynamicsNon-linear Dynamics

Once the growth of Once the growth of structure enters the structure enters the non-linear regime, non-linear regime, dense regions grow dense regions grow faster than low faster than low density regions.density regions. Density distribution is skewedDensity distribution is skewed The amplitude of this effect The amplitude of this effect

depends on the amplitude of depends on the amplitude of the mass fluctuationsthe mass fluctuations

Can measure bias as Can measure bias as a function of scalea function of scale

Verde et al. 2002

Measuring Bias From Weak Measuring Bias From Weak LensingLensing

Cross-correlate Cross-correlate lensing of background lensing of background galaxies with lensing galaxies with lensing of foreground of foreground galaxiesgalaxies

Determine bias as a Determine bias as a function of galaxy function of galaxy propertiesproperties

Normalize power Normalize power spectrumspectrum

Seljak et al. 2004

Halo ModelsHalo Models Simulations and analytical theory Simulations and analytical theory

predict halo mass distribution predict halo mass distribution and clustering propertiesand clustering properties

Need to relate halo mass to Need to relate halo mass to observed galaxy propertiesobserved galaxy properties

Analytical halo modelsAnalytical halo models

Uses clustering data on smaller Uses clustering data on smaller physical scales physical scales

Abazajian et al.

2004

Gravitational LensingGravitational Lensing

Advantage: directly measures Advantage: directly measures massmass

DisadvantagesDisadvantages Technically more difficultTechnically more difficult Only measures projected mass-Only measures projected mass-

distributiondistribution

Tereno et al. 2004

Refregier et al. 2002

Baryon OscillationsBaryon Oscillations

C()

C()

CMB

Galaxy Survey

Baryon oscillation scale

1o

photo-z slices

Selection

function

Limber Equation

(weaker effect)

Baryon Oscillations as a Baryon Oscillations as a Standard RulerStandard Ruler

In a redshift survey, we In a redshift survey, we can measure correlations can measure correlations along and across the line along and across the line of sight.of sight.

Yields Yields HH((zz) and ) and DDAA((zz)!)!

[Alcock-Paczynski Effect][Alcock-Paczynski Effect]

Observer

r = (c/H)zr = DA

Large Galaxy Redshift SurveysLarge Galaxy Redshift Surveys

By performing large spectroscopic surveys, we can measure the By performing large spectroscopic surveys, we can measure the acoustic oscillation standard ruler at a range of redshifts.acoustic oscillation standard ruler at a range of redshifts.

Higher harmonics are at Higher harmonics are at kk~0.2h Mpc~0.2h Mpc-1-1 ( (=30 Mpc).=30 Mpc). Measuring 1% bandpowers in the peaks and troughs requires about 1 Measuring 1% bandpowers in the peaks and troughs requires about 1

GpcGpc33 of survey volume with number density ~10 of survey volume with number density ~10-3-3 galaxy Mpc galaxy Mpc-3-3. ~1 . ~1 million galaxies!million galaxies!

SDSS Luminous Red Galaxy Survey has done this at SDSS Luminous Red Galaxy Survey has done this at zz=0.3!=0.3! A number of studies of using this effectA number of studies of using this effect

Blake & Glazebrook (2003), Hu & Haiman (2003), Linder (2003), Blake & Glazebrook (2003), Hu & Haiman (2003), Linder (2003), Amendola et al. (2004)Amendola et al. (2004)

Seo & Eisenstein (2003), ApJ 598, 720 [source of next few figures]Seo & Eisenstein (2003), ApJ 598, 720 [source of next few figures]

ConclusionsConclusions

We don’t understand the implications of the accelerating We don’t understand the implications of the accelerating universeuniverse

We don’t know really know what to measureWe don’t know really know what to measure OK, theorists have lots of suggestions… but don’t take them too OK, theorists have lots of suggestions… but don’t take them too

seriouslyseriously

Importance of multiple techniquesImportance of multiple techniques Control of systematicsControl of systematics Test basic modelTest basic model

Distance measuresDistance measures H(z)H(z)

Ages versus redshiftAges versus redshift Alcock-Pacyznski EffectAlcock-Pacyznski Effect

Growth of structureGrowth of structure Evolution of fundamental constants Evolution of fundamental constants


Simon DeDeo : astro-ph/0411283Princeton University

Outline1. The physics of particle dark energy.

• fermion — condensate coupling.• physical properties of the system.

2. Cosmological models.

• early vs. late decoupling• decaying dark matter

3. Contemporary questions in dark energy studies.

• freestreaming and small scale power• the nature of clustering dark energy

A New Kind of Particle

picks a preferred frame.

Take it to be the “CMB” frame, i.e.:

New axial coupling

Standard Dirac Fermion

(electron, neutrino, &c.)

(Kostelecky, Jacobson & Mattingly, &c — standard particle physics modification.)

“Spontaneous” Lorentz Violation

Standard vector field

High temperatures, early universe

Thermal fluctuations make

the field non-zero

Standard vector field

Low temperatures:

system relaxes to minimum energy

expectation value goes to zero

The Vector HiggsMechanism

High temperatures, early universe.

Thermal fluctuations make

the field non-zero.

The Vector HiggsMechanism

Minimum energy is non-zero vector

magnitude.

At low temperatures,system picks a

particular direction

What is ?

Older studies: is fixed; an “aether.”

Instead make dynamical.

⇒ spontaneous symmetry breaking⇒ fluctuations possible:

Final choice: take to be the gradient of a scalar:

dimensional considerations : take to be Planck scale

mass scale of the theory

see, e.g., Arkani-Hamed et al. 2004

ψ and Gravity

“particle physics” energy

gravitational energy cancelled by dynamics of

the scalar field

“The system conspires to satisfy the

Equivalence Principle”

particle production when— not important since particle wavelength is much smaller than universe

A New Kind of Dirac Equation

Equation of motion from in curved spacetime:

Non-perturbative solution: particle is coupled — not free — but coupling does not have to be small.

The Unusual Properties of ψ

ψ particle with b coupling has unusual dispersion relationship; positive and negative helicity particles behave differently. Energy at minimum for non-zero momentum.

Ordinary dispersion relation, m=1

ψ particle group velocity can become anti-aligned with the momentum of the particle: carries +x momentum k, but in the -x direction when k<b.

CPT spontaneously violated.

Energy per particle

Momentum

-ve helicity +ve helicity

ψ in an expanding universe...

...redshifts

Can be found from requiring conservation of stress-energy or by invoking Noether’s theorem


The equation of state of this gas of particles can become negative without invoking a cosmological constant.

(Note: w<-1 allowed as well: another unusual result.)

Particle leaving box in +x

direction takes away -x

momentum

group velocity

momentum

The Origin of Negative Pressure

(intuitive version)

Early Decoupling

Early Decoupling Scenario: particles drop out of thermal equilibrium at high temperature; distribution redshifts.

QuickTime™ and aAnimation decompressor


Dirac δ-function distribution: large w excursions. Early decoupling

scenario: excursionsare smoothed out.

As the Universe cools, particles collect in the “well” of the dispersion relation, where and

cold particles behave like cold dark matter!

Thermal Equilibrium



Decoupling in (some) Detail

As the Universe expands, number density decreases.

When interaction time ~ Hubble time, the particles decouple from each other:

(number density)x(cross section)x(velocity) ~ (1/age)

(becomes non-

relativistic before the epoch of

nucleosynthesis.)

Late Time Decoupling: ψCDM

A (to first order) viable particle dark energy scenario:

1. 100 MeV Particles remain in thermal equilibrium until just before today, behaving like dark matter with w=0.

2. Particles drop out of equilibrium, redshift into w<-1/3 region of the equation of state, causing cosmic acceleration.

(3. Future behaviour: particles asymptote back to w~0.)




Particles have been driven to this narrow distribution by the requirement of thermal equilibrium.

Decoupling ⇒ redshift into the w<0 region and dark energy-like behavior.


(how this looks as an effective w)

ψCDM with one particular choice of :

• strength of coupling to ϕ• decoupling time• decoupling width

ΛCDM


ψCDMΛCDMTo zeroth order, we havea plausible explaination ofthe dark energy — we will consider perturbations shortly

Particle Physics of the Dark Sector DψCDM: Decaying Dark

Matter“Classical” Decaying Dark Matter :

• Massive CDM decays into relativistic particle on a time scale roughly the current age of the Universe.

• First proposed by Cen (2001) as means of smoothing small scale power in galactic halos: particles stream out of overdensities.

• We can mimic this model, and produce cosmic acceleration if the decay product is a ψ particle.

DψCDM : Decaying Dark Matter



Have CDM decay into ψ particles; if masses are roughly equal, then decay into negative helicity states is energetically forbidden.

ψ particles are produced in the “well,” and quickly redshift into the region of w<0.


ΛCDM

DψCDM with different choices of :

• CDM lifetime• strength of coupling to condensate

Again: to zeroth order, we can explain the cosmic acceleration by a particle dark energy model

DψCDMΛCDM


Detecting Dark Energy 1• Geometric tests:

Supernovae, X-ray Clusters, CMB first peak, &c.

• Growth of Structure tests:

Often folded in to single growth function D(z)

Different expansion histories give different growth:

ΛCDM

Evolving w

Detecting Dark Energy 2

Different w prime

Growth rate can tell us the expansion history —

— but does this exhaust the dark energy parameters?


Need to consider not only , but also (adiabatic sound speed) and (entropy perturbation.)

Adiabatic sound speed & w(a) related ⇒ two parameters

Dispelling Myths about the Sound Speed: 1

• In this context, sound speed has nothing to do with the propagation of waves in the material.

• e.g., k-essence has a sound speed >> unity without violating causality.

• only in the case of pure CDM or pure radiation:

BUT

in general.

Dispelling Myths about the Sound Speed: 2

• The sound speed is not just the adiabatic sound speed:

• This assumes that the fluid has no internal degrees of freedom: constant density and constant pressure slices line up.

• Not true, even in the simplest cases, e.g., scalar field quintessence! Fold entropy perturbation into new rest frame sound speed as second DE parameter.

• Most models (e.g., scalar field quintessence) have unity sound speed.

• Only recently received attention: k-essence & Chaplytin gases (and some others...) where sound speed ⇒ zero.


“negative” sound speed: instabilities

grow exponentially

positive sound speed: power

is damped below the horizon as

system oscillates

CDM

ISW suppression

Decay of potential in acceleration phase leads to increased power from additional blueshift.

Clustering dark energy suppresses the potential decay, leading to reduced power at large angular scales.

Wayne Hu: background.uchicago.edu

Bean & Doré, 2004

A 1-σ detectionof a dark energy sound speed?

Bean & Doré : phenomenological models of clustering dark energy.

Hand-write equation of state and sound speed.

ISW suppression.

Suppression of the ISW as DE can cluster, slowing potential decay (“missing quadrupole” important part of signal.)

Oscillatory features in the power spectrum depending on detailed sound speed history.DeDeo, Caldwell, Steinhardt, 2003

Power Spectrum Oscillations

• Allow for near-zero sound speed at early times:

• Dark Energy can cluster with the CDM

• (Suppression of ISW as discussed.)

• Because sound speed is not precisely zero, can get oscillations: Jeans length is non-zero.

• (A classic problem with “unified” models: even a very small sound speed can produce noticiable differences from CDM at small scales.)

Does Particle Dark Energy Cluster?

• A general answer is not (yet) known.

• However, we can make some general statements.

° DψCDM : CDM particles cluster, then decay

Initial conditions for the ψ particles is perturbed.

° As for scalar field: must go beyond adiabatic sound speed: coupled, self-interacting particle fluid.

Crossing .

• Can be associated with gravitational instabilities.

• Hu (2004; astro-ph/0401680): internal degrees of freedom halt the generic instability.

• As with Chaplytin gases and classical scalar fields, the question of non-adiabatic (entropy) perturbations is crucial (e.g., Reis et al. 2003) in the transition.

Crossing continued

Standard perturbations:

There appears to be a singularity at the crossing-point.

However: physically meaningful term is:(fractional momentum transfer.) Recasting the equations:

a gravitational instability becomes an anti-gravitational instability.

see Caldwell & Doran (2004), Vikman (2004)

Conclusions

• We have demonstrated a novel connection between spontaneous Lorentz violation and dark energy.

• Our model directly applies to current debates on:

° The sound speed of dark energy° Small scale power & late-time

freestreaming° Theoretical investigations into w < -1

• Open questions . . .

Open Questions

Observation: Evolution of perturbations. Complicated! We know enough to say clustering probably occurs when w=0. Intriguing: let’s look for DE’s sound speed.

Theory: Particle physics of the dark sector: now we know the trick, what other kinds of Lorentz violations can lead to Dark Energy behaviour?

Theory: What is the underlying source of Lorentz violation? Scalar field, vector field, extra dimensions, “arrow of time,” &c &c.

dark energy

Documents

dark energy thats

dark energy properties

dark energy evolutionthe

wdark energy sound speedneed

unity sound speed

adiabatic sound speed

new models

tracker models