Dark Energy David Spergel Princeton University
Many Form of Evidence Jimenez • Stellar Ages • ISW Effect • Baryon Wiggles • Cluster Evolution • CMB & Growth of Structure • Cluster Properties versus Redshift
ISW Effect • Measures the evolution of the potential on large scales • Detected through cross-correlations • SDSS • APM • 2-MASS • Radio Sources • X-ray Sources Nolta et al. 2005
SDSS and Baryon Wiggles • Purely geometric test (SDSS + WMAP) Eisenstein et al. (2005)
Growth of Structure SDSS Tegmark et al. Astro-ph/0310723 Verde et al. (2003)
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? • Cosmological Constant • Failure of General Relativity • Quintessence • Novel Property of Matter • Simon Dedeo astro-ph/0411283
COSMOLOGICAL CONSTANT?? • Why is the total value measured from cosmology so small compared to quantum field theory calculations of vacuum energy? • From cosmology: 0.7 critical density ~ 10-48 GeV4 • From QFT estimation at the Electro-Weak (EW) scales: (100 GeV)4 • At EW scales ~56 orders difference, at Planck scales ~120 orders • Is it a fantastic cancellation of a puzzling smallness? • Why did it become dominant during the “present” epoch of cosmic evolution? Any earlier, would have prevented structures to form in the universe (cosmic coincidence)
Anthropic Solution? • Not useful to discuss creation science in any of its forms….
Quintessence • Introduced mostly to address the “why now?” problem • Potential determines dark energy properties (w, sound speed) • Scaling models (Wetterich; Peebles & Ratra) V(f) = exp(-f) matter r Zlatev and Steinhardt (1999) Most of the tracker models predicted w > -0.7
Dark Energy Evolution • The shape of the quintessence potential determines the evolution of the dark energy
w = pressure (tension) / density = p/rc2 Dark Energy Equation of State Strong consistency In this plot, w<-1 has been ignored
Current Constraints Seljak et al. 2004
Looking for Quintessence • Deviations from w = -1 • BUT HOW BIG? • Clustering of dark energy • Variations in coupling constants (e.g., a) lfFF/MPL • Current limits constrain l < 10-6 If dark energy properties are time dependent, so are other basic physical parameters
New axial coupling picks a preferred frame. Take it to be the “CMB” frame, i.e.: A New Kind of Particle Standard Dirac Fermion (electron, neutrino, &c.) DEDEO 2005 (Kostelecky, Jacobson & Mattingly, &c — standard particle physics modification.)
mass scale of the theory dimensional considerations : take to be Planck scale 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: see, e.g., Arkani-Hamed et al. 2004
Particle Dark Energy particle momentum 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.)
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
Dark Energy Sound Speed • 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 zero sound speed (CDM) positive sound speed: power is damped below the horizon as system oscillates
Hints of a dark energy sound speed?? Bean & Doré : phenomenological models of clustering dark energy. Hand-write equation of state and sound speed. ISW suppression. Bean & Doré, 2004
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: 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 Principle Least Action: What is this doing here? Once you start adding terms, there may be no stopping: e.g., Carroll et al., astro-ph/0413001
Big Bang Cosmology Homogeneous, isotropic universe (flat universe)
Rulers and Standard Candles Luminosity Distance Angular Diameter Distance
Flat M.D. Universe D = 1500 Mpc for z > 0.5
Techniques • Measure H(z) • Luminosity Distance (Supernova) • Angular diameter distance • Growth rate of structure . Checks Einstein equations to first order in perturbation theory
Growth Rate of Structure • Galaxy Surveys • Need to measure bias • Non-linear dynamics • Gravitational Lensing • Halo Models • Bias is a function of galaxy properties, scale, etc….
Non-linear Dynamics • Once the growth of structure enters the non-linear regime, dense regions grow faster than low density regions. • Density distribution is skewed • The amplitude of this effect depends on the amplitude of the mass fluctuations • Can measure bias as a function of scale Verde et al. 2002
Measuring Bias From Weak Lensing • Cross-correlate lensing of background galaxies with lensing of foreground galaxies • Determine bias as a function of galaxy properties • Normalize power spectrum Seljak et al. 2004
Halo Models Abazajian et al. 2004 • Simulations and analytical theory predict halo mass distribution and clustering properties • Need to relate halo mass to observed galaxy properties • Analytical halo models • Uses clustering data on smaller physical scales
Gravitational Lensing Refregier et al. 2002 • Advantage: directly measures mass • Disadvantages • Technically more difficult • Only measures projected mass-distribution Tereno et al. 2004
Baryon Oscillations CMB C(q) Baryon oscillation scale q 1o Galaxy Survey Limber Equation C(q) (weaker effect) Selection function q photo-z slices
dr = (c/H)dz dr = DAdq Observer Baryon Oscillations as a Standard Ruler • In a redshift survey, we can measure correlations along and across the line of sight. • Yields H(z) and DA(z)! [Alcock-Paczynski Effect]
Large Galaxy Redshift Surveys • By performing large spectroscopic surveys, we can measure the acoustic oscillation standard ruler at a range of redshifts. • Higher harmonics are at k~0.2h Mpc-1 (l=30 Mpc). • Measuring 1% bandpowers in the peaks and troughs requires about 1 Gpc3 of survey volume with number density ~10-3 galaxy Mpc-3. ~1 million galaxies! • SDSS Luminous Red Galaxy Survey has done this at z=0.3! • A number of studies of using this effect • Blake & Glazebrook (2003), Hu & Haiman (2003), Linder (2003), Amendola et al. (2004) • Seo & Eisenstein (2003), ApJ 598, 720 [source of next few figures]
Conclusions • We don’t understand the implications of the accelerating universe • We don’t know really know what to measure • OK, theorists have lots of suggestions… but don’t take them too seriously • Importance of multiple techniques • Control of systematics • Test basic model • Distance measures • H(z) • Ages versus redshift • Alcock-Pacyznski Effect • Growth of structure • Evolution of fundamental constants
Particle Dark Energy Simon DeDeo : astro-ph/0411283 Princeton University
Outline 1. 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
New axial coupling picks a preferred frame. Take it to be the “CMB” frame, i.e.: A New Kind of Particle 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 Higgs Mechanism High temperatures, early universe. Thermal fluctuations make the field non-zero.