Understanding Cosmic Acceleration V(!) ! E Hivon Hiranya Peiris Hubble Fellow/ Enrico Fermi Fellow University of Chicago #OMPOSITIONOFAND+ECosmic HistoryY%VENTS$ UR/ INGTHE%CosmicVOLUTIONOFTHE5 MysteryNIVERSE presentpresent energy energy Y density "7totTOT = 1(k=0)K density DAR RADIATION KENER dark energy YDENSIT DARK G (73%) DARKMATTER Y G ENERGY dark matter DARK MA(23.6%)TTER TIONOFENER WHITEWELLUNDERSTOOD DARKNESSPROPORTIONALTOPOORUNDERSTANDING BARYONS BARbaryonsYONS AC (4.4%) FR !42 !33 !22 !16 !12 Fractional Energy Density 10 s 10 s 10 s 10 s 10 s 1 sec 380 kyr 14 Gyr ~1015 GeV SCALEFACTimeTOR ~1 MeV ~0.2 MeV 4IME TS TS TS TS TS TSEC TKYR T'YR Y Y Planck GUT Y T=100 TeV nucleosynthesis Y IES TION TS EOUT DIAL ORS TIONS G TION TION Z T Energy THESIS symmetry (ILC XA 100) MA EN EE WNOF ESTHESIS V IMOR GENERATEOBSERVABLE IT OR ELER ALTHEOR TIONS EF SIGNATURESINTHE#-" EAKSYMMETR EIONIZA INOFR Y% OMBINA R E6 EAKDO #X ONASYMMETR SIC W '54SYMMETR IMELINEOF EFFWR Y Y EC TUR O NUCLEOSYN ), * +E R 4 PLANCKENER Generation BR TR TURBA UC PH Cosmic Microwave NEUTR OUSTICOSCILLA BAR TIONOFPR ER A AC STR of primordial ELEC non-linear growth of P 44 LIMITOFACC Background Emitted perturbations perturbations: GENER ES carries signature of signature on CMB TUR GENERATIONOFGRAVITYWAVES INITIALDENSITYPERTURBATIONS acoustic#-"%MITT oscillationsED NON LINEARSTR andUCTUR EIMPARTS #!0-!0OBSERVES#-" ANDINITIALDENSITYPERTURBATIONS GROWIMPARTINGFLUCTUATIONS CARIESSIGNATUREOFACOUSTIC SIGNATUREON#-"THROUGH *throughEFFWRITESUPANDGR weakADUATES WHICHSEEDSTRUCTUREFORMATION TO#-" OSCILLATIONSANDPpotentiallyOTENTIALLYPR IMORprimordialDIAL GRAVITATIONALLENSING IGNA 3 GRAVITYWAVES INTHE#-" gravitational waves gravitational lensing Diagram adapted from Jeff McMahon’s Thesis Roadmap • Background: cosmic acceleration – Inflation – Dark energy • Constraining Inflation with Cosmological Data – “Worked example”: Cosmic Microwave Background – WMAP data and “standard” inflationary constraints – Slow Roll Reconstruction: connecting theory and data – Future Prospects • Constraining Dark Energy with Cosmological Data – Extending reconstruction toolbox to dark energy – Dynamics of generic quintessence potentials – Future Prospects The Cosmic Microwave Background (CMB) 60 K Credit: NASA/WMAP Science Team The Horizon Problem In Standard Big Bang Model, horizon scale at CMB release subtends ~ 1 deg 60 K Regions separated by more than 1 deg could not have interacted previously 1 deg 1 deg So why is the temperature of these patches the same to 1/100000? Credit: NASA/WMAP Science Team Inflation: vacuum-driven super-expansion Inflationary epoch 1040 1020 Standard Big Bang expansion 100 10-20 Radius of Observable Radius of universe 10-40 Universe 10-60 10-45 10-35 10-25 10-15 10-5 105 1015 Time after t=0 (secs) If inflation lasts long enough, CMB patches on opposite sides of the sky would have been close enough to communicate in the primordial times. Inflation Implemented as a slowly-rolling scalar field evolving in a potential: 2 2 a˙ expansion H = POTENTIAL V(!) !a" rate 8πG 1 2 = φ˙ + V (φ) 3 #2 $ Inflation density Standard φ¨ + 3Hφ˙ + V ! = 0 H ~ const expansion friction FIELD ! Energy converted to heat of BIG BANG Guth (1981), Linde (1982), Albrecht & Steinhardt (1982), Sato (1981), Mukhanov & Chibisov (1981), Hawking (1982), Guth & Pi (1982), Starobinsky (1982), J. Bardeen, P.J. Steinhardt, M. Turner (1983), Mukhanov et al. 1992), Parker (1969), Birrell and Davies (1982) Perturbations from inflation Cosmological perturbations arise from quantum fluctuations, evolve classically. 2 ¯h H4 PR ! scalar 2 4 2 ˙2 H π ! φ "k=aH Pφ(k) ! ¯h !2π " 2h¯ H 2 P ! h 2 tensor π !mPl "k=aH The dark side of the universe Independent lines of evidence for dark energy: •Type Ia supernovae (standard candles): the universe is accelerating in its expansion •CMB (standard ruler): the universe is at the critical density (i.e. its geometry is flat) density pressure a¨ 4πG •Galaxy surveys: 27% of the density = − (ρ + 3P ) of the universe behaves as (atomic a 3 +dark) matter P 1 w = < − for acceleration ρ 3 Riess et al. (1998), Perlmutter et al. (1999), Spergel et al. (2003), Peacock et al. (2001), Tegmark et al. (2003) What is the nature of dark energy? Possibilities: •Λ: vacuum energy, a.k.a. cosmological constant •Q : scalar field (slowly varying dynamical component) •A modification to General Relativity 1 G ≡ R − g R µν µν 2 µν = 8πGTµν + Λgµν Peebles and Ratra (1987), Frieman and Olinto (1990), Caldwell, Dave & Steinhardt (1998) Roadmap • Background: cosmic acceleration – Inflation – Dark energy • Constraining Inflation with Cosmological Data – “Worked example”: Cosmic Microwave Background – WMAP data and “standard” inflationary constraints – Slow Roll Reconstruction: connecting theory and data – Future Prospects • Constraining Dark Energy with Cosmological Data – Extending reconstruction toolbox to dark energy – Dynamics of generic quintessence potentials – Future Prospects History of CMB temperature measurements 60 K 2.725 K WMAP Science Team GODDARD PRINCETON U. U. CHICAGO Robert Hill Chris Barnes Stephan Meyer Gary Hinshaw Norman Jarosik Hiranya Peiris Al Kogut Lyman Page Michele Limon David Spergel UCLA Edward Wright Nils Odegard Cornell U. Janet Weiland Rachel Bean U. BRIT COLUMBIA Edward Wollack Mark Halpern JOHNS HOPKINS U BROWN U. Charles Bennett, P.I. Greg Tucker U. Texas, Austin Eiichiro Komatsu U. Penn. Licia Verde U. Toronto Michael Nolta Olivier Dore Compress the CMB map to study cosmology Express sky as: δT (θ, φ) = ! almYlm(θ, φ) l,m If the anisotropy is a Gaussian random field (real and imaginary parts of each alm independent normal deviates, not correlated) all the statistical information is contained in the angular power spectrum. Komatsu et al. (2003) 0.06% of map 5 deg 1 2 Cl = |alm| X 1 deg 2! + 1 ! m ANGULAR POWER SPECTRUM Raw 94 GHz +/- 32 uK Raw 61 GHz near NEP near NEP Power Spectrum Measurements Before WMAP Angular Scale (deg.) ) 2 K µ anisotropy power ( multipole moment l WMAP 3 year temperature power spectrum Hinshaw et al. (2003) Types of CMB polarization CMB polarization can be decomposed into two orthogonal modes. E- mode is the curl-free mode (“Electric”). B-mode is the divergence- free mode (“Magnetic”). E-mode B-mode B mode discriminates between scalar and tensor perturbations Generation of CMB polarization • Temperature quadrupole at the surface of last scatter generates polarization. electron isotropic no net polarization Thomson Scattering anisotropic net polarization Quadrupole generated by velocity gradients at Last Scattering Surface Polarization by metric tensor perturbations Image from J. Ruhl Image from J. Ruhl Generation of CMB Polarization 1. z=1089 decoupling: scattering of CMB from electrons with non-random velocities polarization correlates with temperature map 1st detected by DASI, now have power spectrum 2. z~10 reionization: scattering of CMB from free electrons uniformly suppress l>40 anisotropy by 30% (!) First detected by WMAPI in temp-pol cross correlation Now have polarization auto-power spectrum. 3. Gravitational waves: Inflation-generated gravity waves polarize CMB not observed yet! WMAP 3 year polarization data • Three Years (TE,EE,BB) – Foreground Removal • Done in pixel space – Null Tests • Year Difference & TB, EB, BB K) – Data Combination µ • Only Q and V are used – Data Weighting • Optimal weighting (C-1) – Likelihood Form • Gaussian for the pixel data • Cl not used at l<23 r=0.3 sqrt anisotropy power ( temperature temp X E-pol E-pol multipole moment l B-pol (68% upper limit) Page et al. (2006) Roadmap • Background: cosmic acceleration – Inflation – Dark energy • Constraining Inflation with Cosmological Data – “Worked example”: Cosmic Microwave Background – WMAP data and “standard” inflationary constraints – Slow Roll Reconstruction: connecting theory and data – Future Prospects • Constraining Dark Energy with Cosmological Data – Extending reconstruction toolbox to dark energy – Dynamics of generic quintessence potentials – Future Prospects Constraining the Primordial Power Spectrum P (k) CMB physics nS < 1 k power P (k) CMB physics n > 1 S k large small scales scales What does inflation have to do with the first stars? WMAP I WMAP I Ext S n WMAP 3 scalar spectral index optical depth to reionization # Reducing the noise by sqrt(time) degeneracies broken Spergel et al (WMAP Collaboration) (astro-ph/0603449) Generic predictions of simplest inflation models • Nearly scale invariant primordial fluctuations [COBE]: ns−1 – WMAP3: ns = 0.960 ± 0.016 P (k) ∝ k • Flatness of the universe [TOCO, BOOMERanG, Maxima, Archeops, ..., WMAPI] κ – WMAP3 + HST prior: Ω = − k a2H2 – "k = -0.014 ± 0.017 • Gaussianity of primordial perturbations [WMAPI] G – WMAP3: -54 < ƒNL < 114 (95%) Φ(!x) = Φ (!x) 2 + fNL !ΦG(!x)" • Adiabatic initial conditions and superhorizon fluctuations [large scale TE anticorrelation, WMAPI] Spergel, Verde, Peiris et al. (2003), Komatsu et al. (2003), Peiris et al. (2003), Spergel et al (WMAP Collaboration) (astro-ph/0603449) Detailed Predictions of Inflation Models •The primordial power spectrum is not a perfect power law. k ns(k) = ns(k0) + α ln !k0 " •There could be observable “running”: dns/d ln k gravitational waves. ij hij h (k0) r " tensor - to - scalar ratio = R R (k0 ) (The shape of the tensor power spectrum is determined by nt = -r/8 using predictions of single field inflationary models.) We use k = 0.002 Mpc-1 (l ~ 30) ! 0 Constraints on tensor modes r 1.01.0 -1 WMAP WMAP + SDSS 0.80.8 N= 50 60 N= 50 60