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## Dark Energy

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**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.