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Dark Matter and Energy Rocky I: Dark Matter Rocky II: Dark Energy ISAPP September 2010 Rocky Kolb The University of Chicago Radiation: Chemical Elements: 0.005% (other than H & He) 0.025% Neutrinos: 0.17% Stars: 0.8% LCDM H & He: gas 4% Cold Dark Matter: (CDM) 25% Dark Energy (L): 70% Cosmological Constant (Dark Energy) 1917 Einstein proposed cosmological constant, L. 1929 Hubble discovered expansion of the Universe. 1934 Einstein called it “my biggest blunder.” 1998 Astronomers found evidence for it, and renamed it “Dark Energy.” Cosmological Constant (Dark Energy) Einstein’s Equations: R 1 g R Lg 8 GT 2 Equation of State: T g p p UU Conservation of stress-energy: T ; 0 a31w p w 1. If p (w 1) then T g and L 8 G L Cosmological constant behaves like fluid with w 1 2. Vacuum energy unchanged in expansion a 0 Vacuum energy behaves like fluid with w 1 L 8 G L The Cosmological Constant The CosmoillogicalConstant 10–30 g cm3 So small, and yet not zero! The Unbearable Lightness of Nothing The Cosmoillogical Constant Dark (and Useless) Energy 1 MeV liter1 The Cosmoillogical Constant Illogical magnitude (what’s it related to?): 10 10 4 4 L 10 g cm 30 -3 4 eV 3 cm 10 cm 10 eV 2 2 L 8 G L 29 33 The Cosmoillogical Constant All fields: harmonic oscillators with zero-point energy classical quantum E 0 E 1 2 The Cosmoillogical Constant All fields: harmonic oscillators with zero-point energy Photons: Lamb shift Gravitons: Vacuum energy e- e- g g e+ e+ LC all particles d 3k k 2 m2 all particles dk k 3 LC : L 4 bad prediction LC M Pl : L M Pl 4 10 90 g cm 3 LC M SUSY : L M SUSY 4 10 30 g cm 3 LC 104 eV: L Observed 1030 g cm 3 The Cosmoillogical Constant Vf high- temperature low- temperature DV L f GUT: 1074 g cm3 SUSY: 1030 g cm3 EWK: 1024 g cm3 CHIRAL: 1013 g cm 3 OBSERVED: 1030 g cm3 The Cosmoillogical Constant The Cosmoillogical Constant Illogical magnitude (what’s it related to?): 10 10 4 4 L 10 g cm 30 -3 4 eV 3 cm 10 cm 10 eV 2 2 L 8 G L 29 33 Illogical timing (cosmic coincidence?): M R GUT EWK BBN REC TODAY L The Cosmoillogical Constant Global warming, but universal cooling: The Universe is cold and dark….and getting colder and darker! (Dark Energy is now 700,000 ppm and will only increase!) Cosmoillogical Constant (Dark Energy) Do not directly observe • acceleration of the universe • dark energy We infer acceleration/dark energy by comparing observations with the predictions of a model All evidence for dark energy/acceleration comes from measuring the expansion history of the Universe Edwin Hubble University of Chicago 1909 National Champions Hubble’s Discovery Paper - 1929 s v H 0d H 0 Hubble' s constant Riess et al. Expansion History of the Universe distance: D a (cosmic scale factor) velocity: a H (Hubble’s constant acceleration: a G ( 3p) (acceleration) acceleration a0 3p 0 scale factor a scale factor a deceleration L: p a0 3p 0 time time Hubble Diagram apparent brightness of standard candle distant universe past velocity acceleration 1998–today 1929–1998 nearby universe present velocity H0 redshift of spectral lines Expansion History of the Universe Friedmann-Robertson-Walker metric dr 2 2 ds dt a t 2 2 2 r d r sin df 2 2 2 2 1 kr 2 a(t) = cosmic scale factor k 1, 0 spatial curvature constant: 3R 6k/a2(t) Friedmann equation (G00 8 GT00) 2 a k 3 3 2 8 G a a Expansion History of the Universe Friedmann equation (G00 8 GT00) k 8 G H 2 2 a 3 i t0 i C 3H 02 critical density: C 8 G a0 redshift: 1 z a t Expansion History of the Universe Friedmann equation (G00 8 GT00) Hubble constant curvature matter radiation H 2 z H 02 k 1 z M 1 z R 1 z 2 3 4 • k M R 1 H 2 z H 02 1 M R 1 z M 1 z R 1 z 2 3 4 • radiation contribution (R) small for z 103 H 2 z H 02 1 M 1 z M 1 z 2 3 • “All of observational cosmology is a search for two numbers.” (H0 and M) — Sandage, Physics Today, 1970 Expansion History of the Universe Many observables based on H(z) [ or dz H1(z) ] • Luminosity distance Flux = (Luminosity / 4 dL2) • Angular diameter distance a Physical size / dA • Volume (number counts) N / V 1(z) • Age of the universe • Distances Precision Cosmology "How helpful to us is astronomy's pedantic accuracy, which I used to secretly ridicule!" Einstein’s statement to Arnold Sommerfeld on December 9, 1915 (regarding measurements of the advance of the perihelion of Mercury) 2.0 Astier et al. (2006) Hubble Diagram SNLS 1.5 1. Find standard candle (SNe Ia) 2. Observe magnitude & redshift 3. Assume a cosmological model L 1.0 4. Compare observations & model 0.5 0 0 0.5 1.0 M Einstein–de Sitter model Expansion History of the Universe Friedmann equation (G00 8 GT00) Hubble cosmological constant constant curvature matter radiation H 2 z H 02 L 1 z k 1 z M 1 z R 1 z 0 2 3 4 • [Could add walls ( 1 z )1] • 1 L k M R • radiation contribution (R) small for z 103 • k well determined (close to zero) from CMB • M reasonably well determined Expansion History of the Universe Friedmann equation (G00 8 GT00) dark energy curvature matter radiation 31 w H 2 z H0 w 1 z k 1 z M 1 z R 1 z 2 2 3 4 Equation of state parameter: w p / w 1 for L 31 w z dz if w w(z): 1 z exp 3 1 w z 0 z parameterize: w(z) w0 wa z / (1 z) Cosmology is a search for two numbers (w0 and wa). The Cosmoillogical Constant LCDM related to supernova brightness confusing astronomical notation (maximum theoretical bliss) matter-dominated model spatially flat, k 1, Einstein-de Sitter: Astier et al. (2006) SNLS supernova redshift z The case for L: 1) Hubble diagram (SNe) 5) Galaxy clusters 2) Cosmic Subtraction 6) Age of the universe 3) Baryon acoustic oscillations 7) Structure formation 4) Weak lensing The Cosmoillogical Constant dynamics lensing x-ray gas simulations cmb power spectrum TOTAL 1 M ~ 0.3 CMB many methods 1.0 0.3 0.7 0 How We “Know” Dark Energy Exists • Assume model cosmology: – Friedmann-Lemaître-Robertson-Walker (FLRW) model Friedmann equation: H2 8 G / 3 k/a2 – Energy (and pressure) content: M R L + – Input or integrate over cosmological parameters: H0, B, etc. • Calculate observables dL(z), dA(z), H(z), • Compare to observations • Model cosmology fits with L, but not without L • All evidence for dark energy is indirect : observed H(z) is not described by H(z) calculated from the Einstein-de Sitter model [spatially flat (from CMB) ; matter dominated ( M)] Taking Sides! • Can’t hide from the data – LCDM too good to ignore – SNe – Subtraction: 1.0 0.3 0.7 – Baryon acoustic oscillations H(z) not given by – Galaxy clusters Einstein–de Sitter – Weak lensing –… G00 (FLRW) 8 G T00(matter) • Modify right-hand side of Einstein equations (DT00) 1. Constant (“just” a cosmoillogical constant) 2. Not constant (dynamics described by a scalar field) • Modify left-hand side of Einstein equations (DG00) 3. Beyond Einstein (non-GR) 4. (Just) Einstein (back reaction of inhomogeneities) Tools to Modify the Right-Hand Side 1964 Austin-Healey Sprite 1974 Fiat 128 Tools to Modify the Right-Hand Side scalar fields (quintessence) Duct Tape anthropic principle (the landscape) Anthropic/Landscape/DUCTtape • Many sources of vacuum energy • String theory has many (10500 ?) vacua • Some of them correspond to cancellations that yield a small L • Although exponentially uncommon, they are preferred because … • More common values of L results in an inhospitable universe Quintessence/WD–40 • Many possible contributions. • Why then is total so small? • Perhaps unknown dynamics sets global vacuum energy equal to zero……but we’re not there yet! V(f) Requires mf 1033 eV L 0 f Tools to Modify the Left-Hand Side • Braneworld modifies Friedmann equation Binetruy, Deffayet, Langlois • Gravitational force law modified at large distance Deffayet, Dvali & Gabadadze Five-dimensional at cosmic distances • Tired gravitons Gregory, Rubakov & Sibiryakov; Gravitons metastable - leak into bulk Dvali, Gabadadze & Porrati • Gravity repulsive at distance R Gpc Csaki, Erlich, Hollowood & Terning • n = 1 KK graviton mode very light, m (Gpc)1 Kogan, Mouslopoulos, Papazoglou, Ross & Santiago • Einstein & Hilbert got it wrong f (R) x g R R Carroll, Duvvuri, Turner, Trodden S 16 G 1 d 4 4 • “Backreaction” of inhomogeneities Räsänen; Kolb, Matarrese, Notari & Riotto; Notari; Kolb, Matarrese & Riotto Backreaction of Inhomogeneities Homogeneous model Inhomogeneous model h i x a Vh 3 h a Vi 3 i H h ah ah H i ai ai h i x H h H i ? We think not! (Buchert & Ellis) Backreaction of Inhomogeneities G (g) G ( g) Inhomogeneities–Example Kolb, Matarrese, Notari & Riotto • Perturbed Friedmann–Lemaître–Robertson–Walker model: G x , t G t G x , t FLRW G00 t G00 x , t 8 GT00 x , t FLRW a 8 G 2 3 G00 a 3 8 G . 2 • (a/a) is not 8 G /3 . • (a/a is not even the expansion rate) • Could G00 be large, or is it 1010? • Could G00 play the role of dark energy? Backreaction of Inhomogeneities • The expansion rate of an inhomogeneous universe of average density need NOT be! the same as the expansion rate of a homogeneous universe of average density ! Ellis, Barausse, Buchert • Difference is a new term that enters an effective Friedmann equation — the new term need not satisfy energy conditions! • We deduce dark energy because we are comparing to the wrong model universe. Célérier; Räsänen; Kolb, Matarrese, Notari & Riotto; Schwarz, … Backreaction of Inhomogeneities • Most conservative approach — nothing new – no new fields (like 1033 eV mass scalars) – no extra long-range forces – no modification of general relativity – no modification of gravity at large distances – no Lorentz violation – no extra dimensions, bulks, branes, etc. – no anthropic/landscape/faith-based reasoning • Magnitude?: calculable from observables related to / • Why now?: acceleration triggered by era of non-linear structure • Possible attractor for effective L Backreaction of Inhomogeneities LCDM is the correct phenomenological model, but … … there is no dark energy, gravity is not modified, and the universe is not accelerating (in the usual sense). Backreaction Causes Allergic Reaction Acceleration From Inhomogeneities • View scale factor as zero-momentum mode of gravitational field • In homogeneous/isotropic model it is the only degree of freedom • Inhomogeneities: non-zero modes of gravitational field • Non-zero modes interact with and modify zero-momentum mode Cosmology scalar field theory analogue cosmology scalar-field theory zero-mode a f (vev of a scalar field) non-zero modes inhomogeneities thermal/finite-density bkgd. physical effect modify a(t) modify f (t) e.g., acceleration e.g., phase transitions Acceleration From Inhomogeneities Standard approach Our approach • Model an inhomogeneous • Expansion rate of Universe as a homogeneous inhomogeneous Universe expansion rate of homogeneous Universe model with Universe with • Inhomogeneities modify • a(t) / V1/3 is the zeromode of a homogeneous model zeromode [effective scale with factor is aD VD1/3 ] • Inhomogeneities only have a • Effective scale factor has a local effect on observables (global) effect on observables • Cannot account for observed • Potentially can account for acceleration acceleration without dark energy or modified GR Subtraction i i/C C 3H02/ 8G dynamics lensing x-ray gas simulations cmb power spectrum TOTAL 1 (CMB) M 0.3 1 0.3 0.7 TOTAL M L Subtraction How can 1.0 = 0.3? For a spatially flat FLRW universe H 2 8 G / 3 This is another way of stating 1. This expression is not valid if FLRW is not valid 8 G 3 e.g., H 2 G00 3 8 G Lemaître–Tolman–Bondi Célérier Iguchi, Nakamura, Nakao Moffat Nambu and Tanimoto Mansouri • Advantages: Chang, Gu, Hwang Alnes, Amarzguioui, Grøn – Solvable inhomogeneous model Mansouri – Can describe wide variety of Apostolopoulos, Brouzakis, Tetradis, Tzavara Garfinkle dynamics Kai, Kozaki, Nakao, Nambu, Yoo Marra, Kolb, Matarrese, Riotto Mustapha, Hellaby, Ellis Iguchi, Nakamura, Nakao • Disadvantages: Vanderveld, Flanagan, Wasserman – Can’t encompass strong (volume) Enqvist and Mattsson Biswas, Mansouri, Notari backreaction (spherical symmetry) Marra, Kolb, Matarrese Marra – Generically have small dynamical Brouzakis, Tetradis, Tzavara range before shell crossing Biswas and Notari Brouzakis and Tetradis Alnes and Amarzguioui Garcia-Bellido and Haugboelle Lemaître–Tolman–Bondi Spherically symmetric metric R2 r , t 2 d dt d dr ds 2 dt 2 dr R 2 r , t d 2 1 r Expansion rates H R R 2 H r2 R2 R2 a r, t Spherically symmetric density 8 G r , t R 2 r , t R r , t R r , t ra t R r , t a t FRW r kr 2 a r H 02 M r 3 Lemaître–Tolman–Bondi • Spherical model • Overall Einstein–de Sitter • Inner underdense Gpc region • Calculate dL(z) Alnes at al. • Compare to SNe data • Fit with L 0! • No local acceleration (counterexample to no-go theorems) Lemaître–Tolman–Bondi • Possible to produce model with EXACT dL(z) and (z) of LCDM Célérier, et al. 2009 • Slight local overdensity. Backgrounds and Backreactions Can write ds2 (12) dt 2 a 2 (t) (12) dx 2 , but not with a(t) from the underlying EdS model, but a(t) from a LCDM model. How? Give some thought to what is meant by a background solution. Kolb, Marra, Matarrese Backgrounds and Backreactions Some thoughts on cosmological background solutions Global Background Solution: FLRW solution generated using H, 3R 3RH (sub-H Hubble volume average), and the local equation of state (e.o.s.). Average Background Solution: FLRW solution that describes volume expansion of our past light cone. Energy content, curvature, and e.o.s. that generates the ABS need not be H, 3RH, nor local e.o.s. (Buchert formalism) Phenomenological Background Solution: FLRW model that best describes the observations on our light cone. Energy content, curvature, and e.o.s. that generates the PBS need not be H, 3RH, and local e.o.s. (Swiss-cheese example) Kolb, Marra, Matarrese Backgrounds and Backreactions Backreaction: the three backgrounds do not coincide Strong Backreaction: Global Background Solution does not describe expansion history (hence does not describe observations) (Buchert formalism) Weak Backreaction: Global Background Solution describes global expansion, but Phenomenological Background Solution differs (Swiss Cheese) Kolb, Marra, Matarrese “Backreaction” Causes Allergic Reaction • We have been driven to consider some remarkable possibilities – 10500 ground states in the landscape – Modification of GR in the infrared – Lorentz violation – 1033 eV scalar fields – Extra dimensions • There should be some effort in rethinking some basic old things – Is there a global background solution? – Is LCDM just a phenomenological background solution? – Could it revolutionize something in the early universe? • Backreactions can potentially do three remarkable things – Explain “why now” – Express dark energy parameters in terms of observables – Potentially predict L Taking Sides The expansion history of the universe is not described by the Einstein-de Sitter model: 1. Well established: Supernova Ia 2. Circumstantial: subtraction, age, structure formation, … 3. Emergent techniques: baryon acoustic oscillations, clusters, weak lensing Explanations: 1. Right-Hand Side: Dark energy • Constant vacuum energy, i.e., a cosmoillogical constant • Time varying vacuum energy, i.e., quintessence 2. Left-Hand Side • Modification of GR • Standard cosmological model (FLRW) not applicable Phenomenology: 1. Measure evolution of expansion rate: is w 1? 2. Order of magnitude improvement feasible Backgrounds and Backreactions FLRW Assumption: global background solution follows from the cosmological principle Specify 3RH, H, & local e.o.s. Global Background Solution describes a(t), H(t), and all other observables GBS PBS if large peculiar velocities Kolb, Marra, Matarrese Backgrounds and Backreactions Global Peculiar Velocities: velocities obtained after subtracting the Hubble flow of the Global Background Solution Averaged Peculiar Velocities: velocities obtained after subtracting the Hubble flow of the Averaged Background Solution Phenomenological Peculiar Velocities: obtained after subtracting the Hubble flow of the Phenomenological Background Solution Background peculiar velocity not measured as a local effect Kolb, Marra, Matarrese Backgrounds and Backreactions Bare Cosmological Principle: universe is homo/iso on sufficiently large scales can describe observable universe by a mean-field description Average Background Solution exists. Bare Copernican Principle: no special place in the universe every observer can describe the universe by a mean-field description a Phenomenological Background Solution exists for every observer (but not necessarily unique). Kolb, Marra, Matarrese Backgrounds and Backreactions • Global Background Solution follows from the FLRW assumption. • Average Background Solution follows from the Bare Cosmological Principle. • Phenomenological Background Solution follows from the Bare Copernican Principle (the success of LCDM). Kolb, Marra, Matarrese Dark Energy "Nothing more can be done by the theorists. In this matter it is only you, the astronomers, who can perform a simply invaluable service to theoretical physics." Einstein in August 1913 to Berlin astronomer Erwin Freundlich encouraging him to mount an expedition to measure the deflection of light by the sun. Observational Program H(z) dL(z) dA(z) V(z) baryon strong weak strong supernova clusters clusters osc. lensing lensing lensing Growth of k 2 H k 4 G k 0 structure weak clusters lensing P(k,z) source? Test gravity solar millimeter accelerators P(k,z) system scale DETF* Experimental Strategy: • Determine as well as possible whether the accelerating expansion is consistent with being due to a cosmological constant. (Is w 1 ?) • If the acceleration is not due to a cosmological constant, probe the underlying dynamics by measuring as well as possible the time evolution of the dark energy. (Determine w(z).) • Search for a possible failure of general relativity through comparison of the effect of dark energy on cosmic expansion with the effect of dark energy on the growth of cosmological structures like galaxies or galaxy clusters. (Hard to quantify.) * Dark Energy Task Force DETF Cosmological Model Parameterize dark-energy equation of state parameter w as: w(a) w0 wa (1 a) • Today (a 1) w(1) w0 • In the far past (a → 0) w(0) w0 wa Standard eight-dimensional cosmological model: w0 : the present value of the dark-energy eos parameter wa : the rate of change of the dark-energy eos parameter DE : the present dark-energy density M : the present matter density B : the present baryon density H0 : the Hubble constant z : amplitude of rms primordial curvature fluctuations nS : the spectral index of primordial perturbations. w(a) w0 + wa(1a) wa w0 present value wa early value DETF figure of merit: (area)1 of the error ellipse 0 w0 1 Supernova Type Ia • Measure redshift and intensity as function of time (light curve) • Systematics (dust, evolution, intrinsic luminosity dispersion, etc.) • A lot of information per supernova • Well developed and practiced • Present procedure: – Discover SNe by wide-area survey (the “easy” part) – Follow up with spectroscopy (the “hard” part) (requires a lot of time on 8m-class telescopes) – Photometric redshifts? Photometric Redshifts Traditional redshift from spectroscopy 4000 5000 6000 7000 8000 Photometric redshift from multicolor photometry Baryon Acoustic Oscillations Pre-recombination Post-recombination • universe ionized • universe neutral • photons provide enormous • photons travel freely pressure and restoring force (decoupled from baryons) • perturbations oscillate • perturbations grow (acoustic waves) (structure formation) recombination Big Bang Today ionized z » 1100 neutral t » 380,000 yr T ~ 3000 K Time Eisenstein Eisenstein Baryon Acoustic Oscillations • Each overdense region is an overpressure that launches a spherical sound wave • Wave travels outward at c / 3 • Photons decouple, travel to us WMAP and observable as CMB acoustic peaks • Sound speed plummets, wave stalls • Total distance traveled 150 Mpc SDSS imprinted on power spectrum Baryon Acoustic Oscillations • Acoustic oscillation scale depends on M h2 and B h2 (set by CMB acoustic oscillations) • It is a small effect (B h2 >> M h2) • Dark energy enters through dA and H Baryon Acoustic Oscillations • Virtues – Pure geometry. – Systematic effects should be small. • Problems: – Amplitude small, require large scales, huge volumes – Photometric redshifts? – Nonlinear effects at small z, cleaner at large z ~ 23, but … dark energy is not expected to be important at large z Weak Lensing b observe 4GM DLS dark energy deflection affects geometric angle b DOS distance factors dark energy affects growth rate of M Weak Lensing The signal from any single galaxy is very small, but there are a lot of galaxies! Require photo-z’s? Space vs. Ground: • DES (2012) • Space: no atmosphere PSF – 1000’s of sq. degs. deep multicolor data • Space: Near IR for photo-z’s • LSST (2015) • Ground: larger aperture – full hemisphere, very deep 6 colors • Ground: less expensive • JDEM/Euclid (???) Galaxy Clusters Cluster redshift surveys measure • cluster mass, redshift, and spatial clustering Sensitivity to dark energy • volume-redshift relation • angular-diameter distance–redshift relation • growth rate of structure • amplitude of clustering Problems: • cluster selection must be well understood • proxy for mass? • need photo-z’s Systematics Are The Key The Power of Two (or 3, or 4) Combined Technique A Figure of merit 100 Figure of merit 20 Technique Z Figure of merit 20 Ongoing Next step Ultimate FOM ~ 3× ongoing FOM ~ 10 × ongoing My guess of future progress 95% C.L. What’s Ahead 2008 2010 2015 2020 Lensing CFHTLS SUBARU DES, VISTA DUNE LSST SKA DLS SDSS ATLAS KIDS Hyper suprime JDEM Pan-STARRS BAO FMOS LAMOST DES, VISTA,VIRUS WFMOS LSST SKA SDSS ATLAS Hyper suprime JDEM Pan-STARRS SNe CSP ESSENCE DES LSST SDSS CFHTLS Pan-STARRS JDEM Clusters AMI APEX SPT DES XCS SZA AMIBA ACT CMB WMAP 2/3 WMAP 5 yr Planck Planck 4yr Roger Davies “To me every hour of the light and dark is a miracle. Every cubic inch of space is a miracle.” – Walt Whitman Every cubic inch of space is a miracle! • cosmic radiation • virtual particles • Higgs potential • extra dimensions • dark matter • dark energy Radiation: Chemical Elements: 0.005% (other than H & He) 0.025% Neutrinos: 0.17% Stars: 0.8% LCDM H & He: gas 4% Cold Dark Matter: (CDM) 25% Dark Energy (L): 70% I must reject fluids and ethers of all kinds, magnetical, electrical, and universal, to whatever quintessential thinness they may be treble-distilled and (as it were) super-substantiated. Samuel Taylor Coleridge Theory of Life (1816) Dark Matter and Energy Rocky I: Dark Matter Rocky II: Dark Energy ISAPP September 2010 Rocky Kolb The University of Chicago Dark Energy Task Force Charge “The DETF is asked to advise the agencies on the optimum† near and intermediate-term programs to investigate dark energy and, in cooperation with agency efforts, to advance the justification, specification and optimization of LST# and JDEM‡.” 1. Summarize existing program of funded projects 2. Summarize proposed and emergent approaches 3. Identify important steps, precursors, R&D, … 4. Identify areas of dark energy parameter space existing or proposed projects fail to address 5. Prioritize approaches (not projects) † Optimum minimum (agencies); Optimum maximal (community) # LST Large Survey Telescope ‡ JDEM Joint Dark Energy Mission Dark Energy Task Force Report Context The issue: acceleration of the Universe Possibilities: dark energy (L or not), non-GR Motivation for future investigations Goals and Methodology Goal of dark energy investigations Methodology to analyze techniques/implementations Findings Techniques & implementations (largely from White Papers) Systematic uncertainties What we learned from analysis Recommendations A Dark Energy Primer DETF Fiducial Model and Figure of Merit Staging Stage IV from the Ground and/or Space DETF Technique Performance Projections Dark Energy Projects (Present and Future) Context 1. Conclusive evidence for acceleration of the Universe. Standard cosmological framework dark energy (70% of mass 2. Possibility: Dark Energy constant in space & time (Einstein’s L). 3. Possibility: Dark Energy varies with time (or redshift z or a (1z 4. Impact of dark energy can be expressed in terms of “equation of w(a) p(a) / (a) with w(a) 1 for L. 5. Possibility: GR or standard cosmological model incorrect. 6. Not presently possible to determine the nature of dark energy. Context 7. Dark energy appears to be the dominant component of the physical Universe, yet there is no persuasive theoretical explanation. The acceleration of the Universe is, along with dark matter, the observed phenomenon which most directly demonstrates that our fundamental theories of particles and gravity are either incorrect or incomplete. Most experts believe that nothing short of a revolution in our understanding of fundamental physics will be required to achieve a full understanding of the cosmic acceleration. For these reasons, the nature of dark energy ranks among the very most compelling of all outstanding problems in physical science. These circumstances demand an ambitious observational program to determine the dark energy properties as well as Goals and Methodology 1. The goal of dark-energy science is to determine the very nature of the dark energy . Toward this goal, our observational program must: a. Determine whether the accelerated expansion is due to a cosmological constant. b. If it is not due to a constant, probe the underlying dynamics by measuring as well as possible the time evolution of dark energy, for example by measuring w(a). c. Search for a possible failure of GR through comparison of cosmic expansion with growth of structure. Because the field is so new, it has suffered from a lack of standardization which has made it very difficult to compare directly different approaches. To address this problem we have done our own modeling of the different techniques so that they could be compared in a consistent manner. These quantitative calculations form the basis of our extensive factual findings, on which our recommendations are based Goals and Methodology 4. Goals of dark-energy observational program through measurement of expansion history of Universe [dL(z) , dA(z) , V(z)], and through measurement of growth rate of structure. All described by w(a). If failure of GR, possible difference in w(a) inferred from different types of data. 5. To quantify progress in measuring properties of dark energy we define dark energy figure-of-merit from combination of uncertainties in w0 and wa. The DETF figure-of-merit is the reciprocal of the area of the error ellipse enclosing the 95% confidence limit in the Goals and Methodology 7. We made extensive use of statistical (Fisher-matrix) techniques incorporating CMB and H0 information to predict future performance (75 models). 8. Our considerations follow developments in Stages: I. What is known now (1/1/06). II. Anticipated state upon completion of ongoing projects. III. Near-term, medium-cost, currently proposed projects. IV. Large-Survey Telescope (LST) and/or Square Kilometer Array (SKA), and/or Joint Dark Energy (Space) Mission (JDEM). Eighteen Findings 1. Four observational techniques dominate White Papers: a. Baryon Acoustic Oscillations (BAO) large-scale surveys measure features in distribution of galaxies. BAO: dA(z) and H(z). b. Cluster (CL) surveys measure spatial distribution of galaxy clusters. CL: dA(z), H(z), growth of structure. c. Supernovae (SN) surveys measure flux and redshift of Type Ia SNe. SN: dL(z). d. Weak Lensing (WL) surveys measure distortion of background images due to gravitational lensing. WL: dA(z), growth of structure. 2. Different techniques have different strengths and weaknesses and sensitive in different ways to dark energy and other cosmo. parameters. Eighteen Findings 4. Four techniques at different levels of maturity: a. BAO only recently established. Less affected by astrophysical uncertainties than other techniques. b. CL least developed. Eventual accuracy very difficult to predict. Application to the study of dark energy would have to be built upon a strong case that systematics due to non-linear astrophysical processes are under control. c. SN presently most powerful and best proven technique. If photo-z’s are used, the power of the supernova technique depends critically on accuracy achieved for photo-z’s. If spectroscopically measured redshifts are used, the power as reflected in the figure-of-merit is much better known, with the outcome depending on the ultimate systematic uncertainties. d. WL also emerging technique. Eventual accuracy will be Systematics: none, optimistic, pessimistic Eighteen Findings 5. A program that includes multiple techniques at Stage IV can provide more than an order-of-magnitude increase in our figure-of-merit. This would be a major advance in our understanding of dark energy. 6. No single technique is sufficiently powerful and well established that it is guaranteed to address the order-of- magnitude increase in our figure-of-merit alone. Combinations of the principal techniques have substantially more statistical power, much more ability to discriminate among dark energy models, and more robustness to systematic errors than any single technique. Also, the case for multiple techniques is supported by the critical need for confirmation of results from any single method. Co m Technique #2 bi na tio n Technique #1 Eighteen Findings 7. Results on structure growth, obtainable from weak lensing or cluster observations, are essential program components in order to check for a possible failure of general relativity. 8. In our modeling we assume constraints on H0 from current data and constraints on other cosmological parameters expected to come from measurement of CMB temperature and polarization anisotropies. a. These data, though insensitive to w(a) on their own, contribute to our knowledge of w(a) when combined with any of the dark energy techniques we have considered. b. Increased precision in a particular cosmological parameter may improve cosmological parameters tend not to 9. Improvements in dark energy constraints from a single technique, valuable for energy from a multi-technique improve knowledge of darkcomparing independent methods. 10. program Setting spatial curvature to zero greatly helps SN, but modest impact on other techniques. Little difference when in Eighteen Findings s (H 0): 8 km s 1 Mpc1 4 km s1 Mpc1 k 0 prior Eighteen Findings 12. Our inability to forecast reliably systematic error levels is the biggest impediment to judging the future capabilities of the techniques. We need a. BAO– Theoretical investigations of how far into the non-linear regime the data can be modeled with sufficient reliability and further understanding of galaxy bias on the galaxy power spectrum. b. CL– Combined lensing and Sunyaev-Zeldovich and/or X-ray observations of large numbers of galaxy clusters to constrain the relationship between galaxy cluster mass and observables. c. SN– Detailed spectroscopic and photometric observations of about 500 nearby supernovae to study the variety of peak explosion magnitudes and any associated observational signatures of effects of evolution, metallicity, or reddening, as well as improvements in the system of photometric calibrations. d. WL– Spectroscopic observations and multi-band imaging of tens to hundreds of thousands of galaxies out to high redshifts and faint magnitudes in order to calibrate the photometric redshift technique and understand its limitations. It is also necessary to establish how well corrections can be made for the intrinsic shapes and alignments of galaxies, removal of the effects of optics (and from the ground) the atmosphere and to characterize the anisotropies in Eighteen Findings 13. Six types of Stage III projects have been considered: a. a BAO survey on an 8-m class telescope using spectroscopy b. a BAO survey on an 4-m class telescope using photo-z’s c. a CL survey on an 4-m class telescope using photo-z’s for clusters detected in ground-based SZ surveys d. a SN survey on a 4-m class telescope using spectroscopy from a 8-m class telescope e. a SN survey on a 4-m class telescope using photo-z’s f. A WL survey on a 4-m class telescope using photo-z’s a. These projects are typically projected by proponents to cost in the range of 10s of $M. Eighteen Findings 14. Our findings regarding Stage-III projects are 1. Only an incremental increase in knowledge of dark-energy parameters is likely to result from a Stage-III BAO project using photo-z’s. The primary benefit would be in exploring photo-z uncertainties. 2. A modest increase in knowledge of dark-energy parameters is likely to result from Stage-III SN project using photo-z’s. Such a survey would be valuable if it were to establish the viability of photometric determination of supernova redshifts, types, and evolutionary effects. 3. A modest increase in knowledge of dark-energy parameters is likely to result from any single Stage-III CL, WL, spectroscopic BAO, or spectroscopic SN survey. 4. The SN, CL, or WL techniques could, individually, produce factor-of-two improvements in the DETF figure-of-merit, if DETF Projections Combination of all techniques from a Stage-III photometric survey Stage II Stage III-p Stage III-o Eighteen Findings 15. Four types of next-generation (Stage IV) projects have been considered: a. an optical Large Survey Telescope (LST), using one or more of the four techniques b. an optical/NIR JDEM satellite, using one or more of four techniques c. an x-ray JDEM satellite, which would study dark energy by the cluster technique d. a Square Kilometer Array, which could probe dark energy by weak lensing and/or the BAO technique through a hemisphere-scale survey of 21-cm emission Each of these projects is in the $0.3-1B range, but dark energy is not the only (in some cases not even the primary) science that would be done by these projects. According to the White Papers received by the Task Force, the technical Eighteen Findings 17. The Stage IV experiments have different risk profiles: a. SKA would likely have very low systematic errors, but needs technical advances to reduce its cost. The performance of SKA would depend on the number of galaxies it could detect, which is uncertain. b. Optical/NIR JDEM can mitigate systematics because it will likely obtain a wider spectrum of diagnostic data for SN, CL, and WL than possible from ground, incurring the usual risks of a space mission. c. LST would have higher systematic-error risk, but can in many respects match the statistical power of JDEM if systematic errors, especially those due to photo-z measurements, are small. An LST Stage IV program can be effective only if photo-z uncertainties on very large samples of galaxies can be made smaller than what has Eighteen Findings 18. A mix of techniques is essential for a fully effective Stage IV program. The technique mix may be comprised of elements of a ground-based program, or elements of a space-based program, or a combination of elements from ground- and space-based programs. No unique mix of techniques is optimal (aside from doing them all), but the absence of weak lensing would be the most damaging provided this technique proves as effective as projections suggest. DETF Projections Combination of all techniques from Stage-IV ground-based survey Stage II Stage IV-p Stage IV-o DETF Projections Combination of all techniques from Stage-IV space-based survey Stage II Stage IV-p Stage IV-o DETF Projections Six Recommendations I. We strongly recommend that there be an aggressive program to explore dark energy as fully as possible, since it challenges our understanding of fundamental physical laws and the nature of the cosmos. II. We recommend that the dark energy program have multiple techniques at every stage, at least one of which is a probe sensitive to the growth of cosmological structure in the form of galaxies and clusters of galaxies. III. We recommend that the dark energy program include a combination of techniques from one or more Stage III projects designed to achieve, in combination, at least a factor of three gain over Stage II in the DETF figure-of- merit, based on critical appraisals of likely statistical and Six Recommendations IV. We recommend that the dark energy program include a combination of techniques from one or more Stage IV projects designed to achieve, in combination, at least a factor of ten gain over Stage II in the DETF figure-of- merit, based on critical appraisals of likely statistical and systematic uncertainties. Because JDEM, LST, and SKA all offer promising avenues to greatly improved understanding of dark energy, we recommend continued research and development investments to optimize the programs and to address remaining technical questions and systematic-error risks. V. We recommend that high priority for near-term funding should be given as well to projects that will improve our understanding of the dominant systematic effects in dark Six Recommendations VI. We recommend that the community and the funding agencies develop a coherent program of experiments designed to meet the goals and criteria set out in these recommendations. DETF Legacy I. Standardization 1. Parameterize dark energy as w0 – wa 2. Eight-parameter cosmological model 3. Priors 4. Figure of merit II. Importance of combinations We have a website with library of Fisher matrices & combiner programs (All power to the people!) III. DETF Technique Performance Projections 1. Thirty-two (count ‘em, 32!) data models 2. Optimistic & pessimistic projections 3. Four techniques, two stages, five platforms IV. Use DETF Technique Performance Projections as a FoMSWG JOINT DARK ENERGY MISSION SCIENCE WORKING GROUP STATEMENT OF TASK June 2008 The purpose of this SWG is to continue the work of the Dark Energy Task Force in developing a quantitative measure of the power of any given experiment to advance our knowledge about the nature of dark energy. The measure may be in the form of a “Figure of Merit” (FoM) or an alternative formulation. DETF FoM DE DE (today) exp {3[1 w (a) ] d ln a} LCDM: w (a) 1 w(a) = w0 wa(1 a) w w0 today & w w0 wa in the far past w0 Marginalize over all other parameters and find uncertainties in LCDM value DETF FoM (area of ellipse)1 1 errors in w0 and wa are correlated 0 wa FoMSWG From DETF: The figure of merit is a quantitative guide; since the nature of dark energy is poorly understood, no single figure of merit is appropriate for every eventuality. FoMSWG emphasis! FoMSWG FoMSWG (like DETF) adopted a Fisher (Information) Matrix approach toward assessing advances in dark energy science. 1 f f observe b quantities ij 2 bi bj observable b function of parameter pi : f (pi) b s b p p FoMSWG 1. Pick a fiducial cosmological model. Not much controversy: LCDM [assumes Einstein gravity (GR)]. 1. ns scalar spectral index 2. M present matter density M h2 3. B present baryon density 4. k present curvature density 5. DE present dark energy density 6. D g departure of growth from GR prediction caused by dar 7. DM SNe absolute magnitude 8. G0 departure of growth during linear era (unity if GR) 9. ln D2S(k*) primordial curvature perturbation amplitude FoMSWG 2. Specify cosmological parameters of fiducial cosmological model (including parameterization of dark energy). Not much controversy in non-dark energy parameters (we use WMAP5). Parameterize dark energy as a function of redshift or scale factor FoMSWG 2. Specify cosmological parameters of fiducial cosmological model (including parameterization of dark energy). Issue #1: parameterization of w(a) (want to know a function—but can only measure parameters) • DETF: w(a) w0 wa(1 a) w w0 today & w w0 wa in the far past – advantage: (only) two parameters – disadvantages: can’t capture more complicated behaviors of w – FoM based on excluding w 1 (either w0 1 or wa 0) • FoMSWG: w(a) described by 36 piecewise constant values wi defined in bins between a 1 and a 0.1 –advantage: can capture more complicated behaviors –disadvantage: 36 parameters (issue for presentation, not FoMSWG 2. Specify cosmological parameters of fiducial cosmological model (including parameterization of dark energy). Issue #2: parameterization of growth of structure (testing gravity) • DETF discussed importance of growth of structure, but offered no measure • Many (bad) ideas on how to go beyond Einstein gravity—no community consensus on clean universal parameter to test for modification of gravity • FoMSWG made a choice, intended to be representative of Growth of Structure Growth of Structure (GR) + Dg ln M(z) the trends Dg : one-parameter measure of departure from Einstein gravity FoMSWG 3. For pre-JDEM and for a JDEM, produce “data models” including systematic errors, priors, nuisance parameters, etc. • Most time-consuming, uncertain, controversial, and critical aspect • Have to predict* “pre-JDEM” (circa 2016) knowledge of cosmological parameters, dark energy parameters, prior information, and nuisance parameters • Have to predict how a JDEM mission will perform • Depends on systematics that are not yet understood or We made “best guess” for pre-JDEM completely quantified Strongly recommend don’t reopen this can of worms * Predictions are difficult, particularly about the future FoMSWG 4. Predict how well JDEM will do in constraining dark energy. This is what a Fisher matrix was designed to do: • can easily combine techniques • tool (blunt instrument?) for optimization and comparison Technical issues, but fairly straightforward FoMSWG 5. Quantify this information into a “figure of merit” Discuss DETF figure of merit Discuss where FoMSWG differs DETF FoM w (w0, wa ) (wp, wa) excluded wp DETF FoM (area of ellipse)1 sw0 swp) w [s(wp)s(wa)]1 1 excluded 0 zp z 1 errors in wp and wa are uncorrelated 0 wa FoMSWG “… no single figure of merit is appropriate …” … but a couple of graphs and a few numbers can convey a l I. Determine the effect of dark energy on the expansion history of the universe by determining w(a), parametrized as described above (higher priority) II. Determine the departure of the growth of structure from the result of the fiducial model to probe dark energy and test gravity proposal should be free to argue for their own figure of merit FoMSWG I. Determine the effect of dark energy on the expansion history of the universe by determining w(a), parametrized as described above (higher priority) 1. Assume growth of structure described by GR 2. Marginalize over all non-w “nuisance” parameters 3. Perform “Principal Component Analysis” of w(a) 4. Then assume simple parameterization w(a) = w0 wa (1 a) and calculate s(wp), s(wa), and zp FoMSWG w0 • Generally, errors in different wi 1 are correlated (like errors in w0 and wa) 0 wa wp • Expand w(a) in a complete set of 1 orthogonal eigenvectors ei(a) 35 1 w(a ) a with eigenvalues iaeii a(like wp i 0 and wa) 0 wa • Have 36 principal components – Errors s (a i) are uncorrelated – Rank how well principal components are measured • Can do this for each technique individually & in combination FoMSWG • Graph of principal components as function of z informs on redshift sensitivity of technique [analogous to z p] (may want first fe • Desirable to have reasonable redshift coverage FoMSWG • Graph of s for various principal components informs on sensitivity to w 1 [analogous to s(wa) and s(wp)] • If normalize to pre-JDEM, informs on JDEM improvement over pre FoMSWG 1. Assume growth of structure described by GR 2. Marginalize over all non-w parameters 3. Perform “Principal Component Analysis” of w(a) DETF 4. Then assume simple parameterization w(a) = w0 wa (1 a) analysis 5. Calculate s(wp), s(wa), and zp FoMSWG II. Determine the departure of the growth of structure from the result of the fiducial model to probe dark energy and test gravity Calculate fully marginalized s(Dg) FoMSWG proposal should be free to argue for their own figure of merit Different proposals will emphasize different methods, redshift ranges, and aspects of complementarity with external data. There is no unique weighting of these differences. Proposers should have the opportunity to frame their approach quantitatively in a manner that they think is most compelling for the study of dark energy. Ultimately, the selection committee or project office will have to judge these science differences, along with all of the other factors (cost, risk, etc). The FoMSWG method will supply one consistent point of comparison for the proposals. FoMSWG Judgment on ability of mission to determine departure of Dark Energ 1. Graph of first few principal components for individual techniques and combination • Redshift coverage • Complementarity of techniques 2. Graph of how well can measure modes • Can easily compare to pre-JDEM (as good as data models) • Relative importance of techniques (trade offs) 3. Three numbers: s(wp), s(wa), and zp • Consistency check FoMSWG Conclusions: 1. Figure(s) of Merit should not be the sole (or even most important) criterion 1. Systematics 2. Redshift coverage 3. Departure from w 1 must be convincing! 4. Ability to differentiate “true” dark energy from modified gravity is important 5. Multiple techniques important 6. Robustness 2. Crucial to have common fiducial model and priors 3. Fisher matrix is the tool of choice 1. FoMSWG (and DETF) put enormous time & effort into data models 2. Data models can not be constructed with high degree of “Backreaction” Causes Allergic Reaction • No compelling argument that backreactions are the answer – We don’t know necessary or sufficient conditions – Just because some unrealistic model seems to give SNe dL(z) doesn’t mean that backreactions are the answer • No proof that backreactions are not the answer – Physics is littered with discarded no-go theorems – Just because some unrealistic model doesn’t give SNe dL(z) doesn’t mean that backreactions are not the answer Strong Allergic Reaction • No-go theorem: local deceleration parameter positive. irrelevant • Why take spatial average at fixed time ? light-cone average • Don’t see it in Newtonian limit. not Newtonian • Don’t see it in perturbation theory. not perturbative • Even with large non-linear perturbations, can write metric in perturbed Newtonian form ds 2 (12) dt 2 + a2(t) (12) dx 2 with 1. red herring • If this is a large effect one would expect to see large velocities. with respect to which background? Inhomogeneities–Cosmology • For a general fluid, four velocity u (1,0) (local observer comoving with energy flow) • For irrotational dust, work in synchronous and comoving gauge ds dt hij ( x, t )dx dx 2 2 i j • Velocity gradient tensor Qi j ui; j 1 hik hkj Q i j s i j 2 (s i j is traceless) • Q is the volume-expansion factor and s ij is the shear tensor (shear will have to be small) • For flat FLRW, hij(t) a2(t)ij Q 3H and s ij = 0 What Accelerates? • No-go theorem: Local deceleration parameter positive: 3Q Q 6 s 2 Hirata & Seljak; 2 G 0 Flanagan; q 2 Giovannini; Q 2 Ishibashi & Wald • However must coarse-grain over some finite domain: Q D h Q d 3x D h d 3x D • Evolution and smoothing do not commute: Q D Q D Q Q Q Q Q 2 2 Buchert & Ellis; D D D D D Kolb, Matarrese & Riotto • Q D Q Can have q 0 but qD 0 (“no-go” goes) D Inhomogeneities and Smoothing • Define a coarse-grained scale factor: Kolb, Matarrese & Riotto astro-ph/0506534; aD VD VD 0 VD d 3 x h 1/3 Buchert & Ellis D • Coarse-grained Hubble rate: aD 1 HD 3 Q D aD • Effective evolution equations: aD 4 G R 3 eff 3 peff eff D QD D not aD 3 16 G 16 G described 2 aD 8 G 3 3QD R by a simple eff 3 peff D pw aD 3 16 G 16 G • Kinematical back reaction: QD 2 3 Q2 D Q 2 D 2 s 2 D Inhomogeneities and Smoothing • Kinematical back reaction: QD 2 3 Q2 D Q 2 D 2 s 2 D QD • For acceleration: eff 3 peff 0 D 4 G a Q a • Integrability condition (GR): 6 D D a 4 D 2 D 3 R 0 D • Acceleration is a pure GR effect: – curvature vanishes in Newtonian limit – QD will be exactly a pure boundary term, and small • Particular solution: 3QD h3RiD const. – i.e., Leff QD (so QD acts as a cosmological constant) Any Indication in Perturbation Theory? Kolb, Notari, Matarrese & Riotto (KNMR) • 2nd-order perturbation theory in fx) (Newtonian potential): QH 20 2 2 23 4 2 f f 2f mean of 2f 0 H 9 54 130 2 ,i 4 4 27 f f,i 27 2f 2f f ,ij f,ij Post-Newtonian Newtonian – Each derivative accompanied by conformal time = 2/aH – Each factor of accompanied by factor of c. – Highest derivative is highest power of / c : “Newtonian” – Lower derivative terms / cn : “Post-Newtonian” – f and its derivatives can be expressed in terms of / Any Indication in Perturbation Theory? kH 1 a • f f dk k T k 2 2 2 5 A 2 2 10 a H 0 a0 2 a kH 1 • 4 f f 2 2 2 A 4 4 dk k 3 T 2 k 0 10 a H 0 a0 – Individual Newtonian terms large, i.e., hr2fr2fi 1 Räsänen – But total Newtonian term vanishes hr2fr2fi hf,,ijf,ij i KNMR – Post-Newtonian: hrf ¢ rf i 105) huge! (large k2/a2H2) Any Indication in Perturbation Theory? DH / a3(2f)n1 (f)2 ~ a3(k/aH)2nf n1 • f A 2 £ 105 • (aH)2n a02nH02n (a0 /a)n • H01 3000h1 Mpc • (k/aH)2nf n1 » (3£103)2n (k/h Mpc1)2n (2£105)n1 – n 1: 4£103 (k/h Mpc1)2 (a0/a)2 : curvature – n 2: 6£101 (k/h Mpc1)4 (a0/a)1 :? – n 3: 9£101 (k/h Mpc1)6 (a0/a)0 :L • Of course have to include transfer function, integrate over k, etc. Any Indication in Perturbation Theory? • First term in gradient expansion (2 spatial derivatives): 3 R aD2 QD 0 no acceleration D • In general, gradient expansion gives Notari; Kolb, Matarrese, & Riotto 2n m 3 R rn a n 3 rn 2n derivatives f D n 1 mn 2n QD qn a n 3 qn 2n derivatives f m n2 mn • Newtonian terms, (2f)n » (k/aH)2nf n, individually are large, but only appear as surface terms, hence small in total • Post-Newtonian terms, (f)2n ~ (k/aH)2nf 2n, individually are small, but do not appear as surface terms • Dominant term is combination: (2f)n1 (f)2 ~ (k/aH)2nf n+1 Any Indication in Perturbation Theory? • Lowest-order term to make big contribution is n 3 (6 derivatives) • Notice n 3 contributes to QD and h3RiD terms / a0, i.e., expansion as if driven by a cosmological constant !!! • But why stop at n = 3 ????? • We have developed a RG-improved calculation (still inadequate) Many issues: • non-perturbative nature • how are averaged quantities related to observables? • comparison to observed LSS • gauge/frame choices • physical meaning of coarse graining? Program: • can inhomogeneities change effective zero mode? • how does it affect observables? • can one design an inhomogeneous universe that “accelerates”? • could it lead to an apparent dark energy? • can it be reached via evolution from usual initial conditions? • does it at all resemble our universe? • large perturbative terms resum to something harmless? • is perturbation theory relevant? Thinking Forward about Backreactions • Can the effect be large for many smaller ( H01) voids? • Can one large void be compatible with observations? • Is the spherical symmetry of LTB a bug or a feature? • Voids caustics, walls, coherent structures not in P(k)! • Must be able to express backreactions in terms of w(a). – eventually we must make a prediction! • If backreactions are important, i.m.o., it must be an effect that is – non-Newtonian – non-perturbative • Someone please solve the “cosmological constant problem.”

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