Dark Energy
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Transcript of 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
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Nolta et al. 2005
SDSS and Baryon WigglesSDSS and Baryon Wiggles
Purely geometric testPurely geometric test
(SDSS + WMAP)(SDSS + WMAP)
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Eisenstein et al. (2005)
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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
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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
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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
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Seljak et al. 2004
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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.
Dark Energy Sound Speed
“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
Particle Dark Energy
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
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 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.
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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
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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.)
Late Time Decoupling: ψCDM
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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.
Late Time Decoupling: ψCDM
(how this looks as an effective w)
ψCDM with one particular choice of :
• strength of coupling to ϕ• decoupling time• decoupling width
ΛCDM
Late Time Decoupling: ψCDM
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
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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.
DψCDM : Decaying Dark Matter
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
DψCDM : Decaying Dark Matter
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?
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
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.
Dark Energy Sound Speed
“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.