An Acoustic Primer. Wayne Hu Astro 448. l (multipole) BOOMERanG MAXIMA Previous COBE. W. Hu Dec. 2000
|
|
- Alexia Sullivan
- 5 years ago
- Views:
Transcription
1 An Acoustic Primer 100 BOOMERanG MAXIMA Previous 80 T (µk) COBE W. Hu Dec l (multipole) Wayne Hu Astro 448
2 CMB Anisotropies COBE Maxima Hanany, et al. (2000) BOOMERanG de Bernardis, et al. (2000)
3 Ringing in the New Cosmology
4 Physical Landscape
5 Acoustic Oscillations
6 z > 1000; T γ > 3000K Hydrogen ionized Free electrons glue photons to baryons γ e p compton scattering coulomb interactions Photon baryon fluid Potential wells that later form structure Thermal History tightly coupled fluid cold hot mean free path << wavelength hot
7 Thermal History z > 1000; T γ > 3000K Hydrogen ionized Free electrons glue photons to baryons γ e p compton scattering coulomb interactions Photon baryon fluid Potential wells that later form structure z ~ 1000; T γ ~ 3000K Recombination Fluid breakdown z < 1000; T γ < 3000K Gravitational redshifts & lensing Reionization; rescattering last scattering λ k -1 surface z=1000 θ l -1 recombination observer
8 Initial Conditions
9 Inflation and the Initial Conditions Inflation: (nearly) scale-invariant curvature (potential) perturbations Superluminal expansion superhorizon scales "initial conditions" Accompanying temperture perturbations due to cosmological redshift cold Time Newtonian Comoving hot Space Potential perturbation Ψ = time-time metric perturbation δt/t = Ψ δt/t = δa/a = 2/3δt/t = 2/3Ψ Sachs & Wolfe (1967); White & Hu (1997)
10 Initial Conditions & the Sachs-Wolfe Effect Initial temperature perturbation Observed temperature perturbation Gravitational redshift: Ψ + Initial temperature: + Θ Time Newtonian Comoving Potential = time-time metric perturbations Ψ = δt/t Space
11 Initial Conditions & the Sachs-Wolfe Effect Initial temperature perturbation Observed temperature perturbation Gravitational redshift: Ψ + Initial temperature: + Θ Time Newtonian cold Comoving Potential = time-time metric perturbations Ψ = δt/t Matter dominated expansion: a t 2/3, δa/a = 2/3 δt/t Temperature falls as: T a 1 Temperature fluctuation: δt/t = δa/a hot Space
12 Initial Conditions & the Sachs-Wolfe Effect Initial temperature perturbation Observed temperature perturbation Gravitational redshift: Ψ + Initial temperature: + Θ Time Newtonian cold Comoving Potential = time-time metric perturbations Ψ = δt/t Matter dominated expansion: a t 2/3, δa/a = 2/3 δt/t Temperature falls as: T a 1 Temperature fluctuation: Result Initial temperature perturbation: δt/t = δa/a Θ δt/t = δa/a = 2/3 δt/t = 2/3 Ψ Observed temperature perturbation: (δt/t ) obs = Θ+Ψ = 1/3 Ψ hot Space Sachs & Wolfe (1967) White & Hu (1997)
13 Acoustic Oscillations
14 Gravitational Ringing Potential wells = inflationary seeds of structure Fluid falls into wells, pressure resists: acoustic oscillations
15 Photon pressure resists compression in potential wells Acoustic oscillations Acoustic Oscillations Photon Pressure Effective Mass Peebles & Yu (1970) Potential Well Ψ Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997)
16 Acoustic Oscillations Photon pressure resists compression in potential wells Acoustic oscillations Gravity displaces zero point Θ δt/t = Ψ Oscillation amplitude = initial displacement from zero pt. Θ (-Ψ) = 1/3Ψ T/T Θ+Ψ η initial displ. zero point Ψ /3 Peebles & Yu (1970) Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997)
17 Acoustic Oscillations Photon pressure resists compression in potential wells Acoustic oscillations Gravity displaces zero point Θ δt/t = Ψ Oscillation amplitude = initial displacement from zero pt. Θ (-Ψ) = 1/3Ψ Gravitational redshift: observed (δt/t) obs = Θ +Ψ oscillates around zero T/T Θ+Ψ First Extrema η Ψ /3 Peebles & Yu (1970) Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997)
18 Acoustic Oscillations Photon pressure resists compression in potential wells Acoustic oscillations Gravity displaces zero point Θ δt/t = Ψ Oscillation amplitude = initial displacement from zero pt. Θ (-Ψ) = 1/3Ψ Gravitational redshift: observed (δt/t) obs = Θ +Ψ oscillates around zero T/T Θ+Ψ Second Extrema η Ψ /3 Peebles & Yu (1970) Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997)
19 Plane Waves Potential wells: part of a fluctuation spectrum Plane wave decomposition
20 Harmonic Modes Frequency proportional to wavenumber: ω=kc s Twice the wavenumber = twice the frequency of oscillation
21 Harmonic Peaks Oscillations frozen at last scattering Wavenumbers at extrema = peaks Sound speed c s T/T Θ+Ψ Last Scattering First Peak Ψ /3 k 1 =π/ sound horizon η Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997)
22 Harmonic Peaks Oscillations frozen at last scattering Wavenumbers at extrema = peaks Sound speed c s T/T Θ+Ψ Last Scattering Frequency ω = kc s ; conformal time η last scattering Phase k ; φ = 0 dη ω = k Harmonic series in sound horizon sound φn = nπ kn = nπ/ First Peak T/T Θ+Ψ horizon Last Scattering sound horizon Ψ /3 k 1 =π/ sound horizon Ψ /3 Hu & Sugyama (1995); Hu, Sugiyama & Silk (1997) η k 2 =2k 1 Temporal Coherence in IC η Second Peak
23 Seeing Sound Oscillations frozen at recombination Compression=hot spots, Rarefaction=cold spots
24 Harmonic Modes Frequency proportional to wavelength: ω=kc s Modes reaching extrema are integral multiples harmonics 1:2:3
25 Peaks in Angular Power Oscillations frozen at recombination Distant hot and cold spots appear as temperature anisotropies
26 Projection into Angular Peaks Peaks in spatial power spectrum Projection on sphere Spherical harmonic decomposition Maximum power at l = kd Extended tail to l << kd Described by spherical bessel function j l (kd) peak d observer j l (kd)y l 0 Y 0 0 (2l+1)j l (100) l Bond & Efstathiou (1987) Hu & Sugiyama (1995); Hu & White (1997)
27 Projection into Angular Peaks Peaks in spatial power spectrum Projection on sphere Spherical harmonic decomposition Maximum power at l = kd Extended tail to l << kd 2D Transfer Function T 2 (k,l) ~ (2l+1) 2 [ T/T] 2 j l 2 (kd) log(k Mpc) Transfer Function Streaming Oscillations SW Acoustic log(x) log(l) Bessel Functions Projection Oscillations Main Projection Hu & Sugiyama (1995)
28 Doppler Effect Relative velocity of fluid and observer Extrema of oscillations are turning points or velocity zero points Velocity π/2 out of phase with temperature Velocity maxima Velocity minima
29 Doppler Effect Relative velocity of fluid and observer Extrema of oscillations are turning points or velocity zero points Velocity π/2 out of phase with temperature No baryons Zero point not shifted by baryon drag Increased baryon inertia decreases effect m eff V 2 1/2 = const. V m eff = (1+R) 1/2 T/T η Ψ /3 V Velocity maxima Baryons V T/T η Velocity minima Ψ /3
30 Doppler Peaks? Doppler effect has lower amplitude and weak features from projection d observer j l (kd)y l 0 Y 0 0 d observer j l (kd)y l 0 Y 1 0 Temperature peak Doppler (2l+1)j l (100) (2l+1)j l '(100) no peak l l Hu & Sugiyama (1995)
31 Relative Contributions Spatial Power 10 5 total temp dopp Hu & Sugiyama (1995); Hu & White (1997) kd
32 Relative Contributions l Angular Power 10 5 Spatial Power 10 5 total temp dopp Hu & Sugiyama (1995); Hu & White (1997) kd
33 Mechanics of the Calculation Radiation distribution: f(x=position,t=time;n=direction,ν=frequency) Expand in basis functions: (local angular dependence spatial dependence) m e ik x sy l Sources (radiation & metric: monopole, dipole, quadrupole) hierarchy Addition of Angular Momentum integral plane wave ~ gradient plane wave j 0 ly l m 0 sy l' Y 1 m 0 sy l' Y l'' original codes Bond & Efstathiou (1984) Vittorio & Silk (1983) l'±1 l±l' l'+l'' Σ Observables CMBFast Seljak & Zaldarriaga (1996) Hu & White (1997) (clebsch-gordan) j l l' l'' semi-analytic Hu & Sugiyama (1995) Seljak (1994)
34 Semi-Analytic Calculation Treat Sources in the Tight Coupling Approximation Expand the Boltzmann hierarchy equations in 1/(optical depth per λ) Also the trick to numerically integrating the stiff hierarchy equations Closed Euler equation + Continuity equation = Oscillator equation Project Sources at Last Scattering Integral equations Visibility function of recombination + =
35 The First Peak
36 Shape of the First Peak Consistent with potential wells in place on superhorizon scale (inflation) Sharp fall from first peak indicates no continuous generation (defects) BOOMERanG MAXIMA Previous T (µk) l~ l (multipole) 1000
37 Angular Diameter Distance A Classical Test Standard(ized) comoving ruler Measure angular extent Absolute scale drops out Infer curvature Upper limit 1st Peak Scale (Horizon) Upper limit on Curvature Calibrate 2 Physical Scales Sound horizon (peak spacing) Diffusion scale (damping tail) Ω m h 2 Ω b h 2 IC s Flat Kamionkowski, Spergel & Sugiyama (1994) Hu & White (1996) Closed Power Ω m curvature 0.1 flat 1.0 critical 0.1 open Ω m h 2 =0.25; Ω b h 2 = l
38 Curvature in the Power Spectrum Features scale with angular diameter distance Angular location of the first peak
39 A Flat Universe!...? ΩΛ h<0.8 Ω b h 2 <0.025 Perlmutter et al. (1998) Riess et al. (1998) BOOMERanG 0.2 MAXIMA closed open Priors! Ω m
40 First Peak Location BOOM's parabolic peak fit 185<l 1 <209 (2σ) MAX's value l 1 ~ BOOMERanG MAXIMA Previous T (µk) l (multipole) l
41 Are They Consistent? Using ΛCDM models: 184<l 1 <216 (2σ; BOOM) Joint analysis: 194<l 1 <218 (2σ; BOOM+MAX) 20 χ upper limits consistent! lower limits tightened Hu, Fukugita, Zaldarriaga, Tegmark (2000) 2.5σ BOOM BOOM+MAX l 1
42 Is the Scale too Large? Fiducial flat Ω m =0.35, h=0.65 model: l 1 =221 (excluded at ~2.5σ) (a) positive curvature (b) high Hubble constant / matter (c) dark energy h l 1 /l 1 = 1.4 Ω tot /Ω tot 0.48 h/h 0.15 Ω m /Ω m 0.11 w/w Ω b h 2 /Ω b h Hu, Fukugita, Zaldarriaga, Tegmark (2000) Ω m Ω b h 2 > 0.019
43 Age and Dark Energy Flat solutions involve decreasing age of universe through h, Ω m or dark energy equation of state w=p/ρ (< Gyr) h Gyr Gyr 12Gyr Hu, Fukugita, Zaldarriaga, Tegmark (2000) Ω m
44 Age and Dark Energy Region of consistency shrinking headed to crisis? New physics? w, m ν, α f b f b 0.9 σ 8 σ 8 h 0.8 h 0.7 f b BBN t l Hu, Fukugita, Zaldarriaga, Tegmark (2000) Ω m
45 The Second Peak
46 Baryon & Inertia Baryons add inertia to the fluid Equivalent to adding mass on a spring Same initial conditions Same null in fluctuations Unequal amplitudes of extrema
47 Baryons provide inertia Relative momentum density R = (ρ b + p b )V b / (ρ γ + p γ )V γ Ω b h2 Effective mass m eff = (1 + R) Baryon Drag T/T zero pt Low Baryon Content Ψ /3 η Hu & Sugiyama (1995)
48 Baryons provide inertia Relative momentum density R = (ρ b + p b )V b / (ρ γ + p γ )V γ Ω b h2 Effective mass m eff = (1 + R) Baryon Drag Baryons drag photons into potential wells zero point Amplitude Frequency (ω m eff 1/2 ).. Constant R, Ψ: (1+ R) Θ + (k 2 /3)Θ = (1+ R) (k 2 /3)Ψ Θ + Ψ = [Θ(0) + (1+ R) Ψ(0)] cos [ kη/ 3 (1+ R)] RΨ Θ+Ψ T/T η zero pt High Baryon Content Ψ /3 Hu & Sugiyama (1995)
49 Baryons provide inertia Relative momentum density R = (ρ b + p b )V b / (ρ γ + p γ )V γ Ω b h2 Effective mass m eff = (1 + R) Baryon Drag Baryons drag photons into potential wells zero point Amplitude Frequency (ω m eff 1/2 ).. Constant R, Ψ: (1+ R) Θ + (k 2 /3)Θ = (1+ R) (k 2 /3)Ψ Θ + Ψ = [Θ(0) + (1+ R) Ψ(0)] cos [ kη/ 3 (1+ R)] RΨ T/T Θ+Ψ zero pt Alternating Peak Heights Ψ /3 η Hu & Sugiyama (1995)
50 Baryons in the CMB Power Baryon Drag Power/Damping Power High odd peaks 500 l 1000 Ω b h Additional Effects Time varying potential Dissipation/Fluid imperfections 0.1 Power W. Hu 2/ l 0.1
51 Baryons in the Power Spectrum
52 Height of the Second Peak BOOM and MAX both show a low power at l 2 = 2.4 l 1 H 2 = power at 1st/2nd = ( T l 2 / T l1 ) BOOMERanG MAXIMA Previous T (µk) H l (multipole) 1000
53 Height of the Second Peak BOOM : BOOM+MAX: H 2 =0.37 ±0.044 (1σ) H 2 =0.38 ±0.04 (1σ) χ < l < < l < 600 (Ω Λ, Ω b h 2, n) 5 BOOM BOOM+MAX H 2 2.5σ H 2 /H 2 = 0.65 Ω b h 2 /Ω b h n/n Ω m h 2 /Ω m h 2
54 Height of the Second Peak Excludes fiducial LCDM (n=1, Ω b h 2 =0.02, H 2 =0.51) at ~3.3σ Requires Ω b h 2 > 0.022n (if Ω m h 2 >0.16, from l 1, flat, h<0.8) Ω m h 2 = Ω b h n
55 Height of the Second Peak Excludes fiducial LCDM (n=1, Ω b h 2 =0.02, H 2 =0.51) at ~3.3σ Requires Ω b h 2 > 0.022n (if Ω m h 2 >0.16, from l 1, flat, h<0.8) Ω m h 2 = Ω b h ISM D Conservative BBN upper limit QSOa D Tytler et al. ~5% n
56 Score Card
57 Higher Peaks
58 Radiation and Dark Matter Radiation domination: potential wells created by CMB itself Pressure support potential decay driving Heights measures when dark matter dominates
59 Driving Effects and Matter/Radiation Potential perturbation: Radiation Potential: k 2 Ψ = 4πGa 2 δρ generated by radiation inside sound horizon δρ/ρ pressure supported δρ hence Ψ decays with expansion Ψ T/T η Θ+Ψ Hu & Sugiyama (1995)
60 Driving Effects and Matter/Radiation Potential perturbation: Radiation Potential: Potential Radiation: Feedback stops at matter domination k 2 Ψ = 4πGa 2 δρ generated by radiation inside sound horizon δρ/ρ pressure supported δρ hence Ψ decays with expansion Ψ decay timed to drive oscillation 2Ψ + (1/3)Ψ = (5/3)Ψ 5x boost Ψ T/T Θ+Ψ η Hu & Sugiyama (1995)
61 Driving Effects and Matter/Radiation Potential perturbation: Radiation Potential: Potential Radiation: Feedback stops at matter domination k 2 Ψ = 4πGa 2 δρ generated by radiation inside sound horizon δρ/ρ pressure supported δρ hence Ψ decays with expansion Ψ decay timed to drive oscillation 2Ψ + (1/3)Ψ = (5/3)Ψ 5x boost Ψ T/T Θ+Ψ η Hu & Sugiyama (1995)
62 Potential Envelope Similar to matter transfer function, acoustic oscillations, as a function of k, enveloped by a function that depends only on k/ω m h 2 Unlike matter transfer function, the potential envelope increases with k Combination distiguishes between dynamical effects and initial conditions: complementarity 4 2 k 3/2 (Θ 0 +Ψ) 0 2 Hu & White (1997) 4 0 Ω m h 2 =0.25 Ω m h 2 = k/ω m h 2 (Mpc 1 )
63 Matter Density in the CMB Power Ω m h 2 Power/Damping Amplitude ramp across matter radiation equality Radiation density fixed by CMB temperature & thermal history 5 Power Ω m h Measure Ω m h 2 from peak heights 1 Power W. Hu 2/ l
64 Dark Matter in the Power Spectrum
65 Damping Tail
66 Diffusion Damping Diffusion inhibited by baryons Random walk length scale depends on time to diffuse: horizon scale at recombination
67 Diffusion Damping Random walk during recombination Dissipation as hot meets cold Physical scale for standard ruler or calibration
68 Dissipation / Diffusion Damping Imperfections in the coupled fluid mean free path λ C in the baryons Random walk over diffusion scale: geometric mean of mfp & horizon λ D ~ λ C N ~ λ C η >> λ C Overtake wavelength: λ D ~ λ ; second order in λ C /λ Viscous damping for R<1; heat conduction damping for R>1 N=η / λ C 1.0 λ D ~ λ C N λ Power 0.1 perfect fluid instant decoupling Silk (1968); Hu & Sugiyama (1995); Hu & White (1996) l
69 Dissipation / Diffusion Damping Rapid increase at recombination as mfp Independent of (robust to changes in) perturbation spectrum Robust physical scale for angular diameter distance test (Ω K, Ω Λ ) Recombination 1.0 Power 0.1 perfect fluid instant decoupling recombination Silk (1968); Hu & Sugiyama (1995); Hu & White (1996) l
70 Time Evolution Time evolution of an acoustic mode (k=1/mpc, scdm) Acoustic Envelope Θ 0 +Ψ RΨ Hu & Sugiyama (1996)
71 Time Evolution Diffusion length compared with horizon at recombination baryons CMB Ω b h 2 = Ω m h 2 =0.25 Hu & Sugiyama (1996)
72 Acoustic Visibility Effective visibility for CMB and baryons accouting for damping Ω b h 2 = Ω m h 2 =0.25 CMB baryons Hu & Sugiyama (1996)
73 Damping Length as Ruler Damping scale presents another physical scale for curvature test Independent of phase of oscillation (Lasenby's demon: curvature vs. novel isocurvature perturbations)
74 Damping Tail in the Power Spectrum Calibrate the standard rulers in curvature test Depends on baryon-photon ratio and horizon scale at recombination (matter-radiation ratio)
75 The Peaks
76 Physical Decomposition & Information 4 combined Power 3 2 temperature doppler l
77 Physical Decomposition & Information Fluid + Gravity alternating peaks photon-baryon ratio Ω b h 2 4 baryon drag Power l
78 Physical Decomposition & Information Fluid + Gravity alternating peaks photon-baryon ratio Ω b h 2 driven oscillations matter radiation ratio Ω m h 2 Power matter radiation equality l
79 Physical Decomposition & Information Fluid + Gravity alternating peaks photon-baryon ratio Ω b h 2 driven oscillations matter radiation ratio Ω m h 2 Fluid Rulers sound horizon damping scale Power πk A k D diffusion damping perfect fluid 500 l
80 Physical Decomposition & Information Fluid + Gravity alternating peaks photon-baryon ratio Ω b h 2 driven oscillations matter radiation ratio Ω m h 2 Fluid Rulers sound horizon damping scale Geometry angular diameter distance f(ω Λ,Ω K ) + flatness or no Ω Λ, Ω Λ or Ω K Power l A =d A πk A ISW 500 l D =d A k D l
CMB Anisotropies: The Acoustic Peaks. Boom98 CBI Maxima-1 DASI. l (multipole) Astro 280, Spring 2002 Wayne Hu
CMB Anisotropies: The Acoustic Peaks 80 T (µk) 60 40 20 Boom98 CBI Maxima-1 DASI 500 1000 1500 l (multipole) Astro 280, Spring 2002 Wayne Hu Physical Landscape 100 IAB Sask 80 Viper BAM TOCO Sound Waves
More informationRinging in the New Cosmology
Ringing in the New Cosmology 80 T (µk) 60 40 20 Boom98 CBI Maxima-1 DASI 500 1000 1500 l (multipole) Acoustic Peaks in the CMB Wayne Hu Temperature Maps CMB Isotropy Actual Temperature Data COBE 1992 Dipole
More informationCMB Episode II: Theory or Reality? Wayne Hu
s p ac 10 1 CMB Episode II: θ (degrees) n n er p ac u ter 10 1 θ (degrees) 100 80 e 100 80 T (µk) 60 T (µk) 60 40 40 20 20 10 100 l (multipole) 10 100 l (multipole) Theory or Reality? Wayne Hu CMB Anisotropies
More informationLecture II. Wayne Hu Tenerife, November Sound Waves. Baryon CAT. Loading. Initial. Conditions. Dissipation. Maxima Radiation BOOM WD COBE
Lecture II 100 IAB Sask T (µk) 80 60 40 20 Initial FIRS Conditions COBE Ten Viper BAM QMAP SP BOOM ARGO IAC TOCO Sound Waves MAX MSAM Pyth RING Baryon CAT Loading BOOM WD Maxima Radiation OVRO Driving
More informationThe Outtakes. Back to Talk. Foregrounds Doppler Peaks? SNIa Complementarity Polarization Primer Gamma Approximation ISW Effect
The Outtakes CMB Transfer Function Testing Inflation Weighing Neutrinos Decaying Neutrinos Testing Λ Testing Quintessence Polarization Sensitivity SDSS Complementarity Secondary Anisotropies Doppler Effect
More informationProbing the Dark Side. of Structure Formation Wayne Hu
Probing the Dark Side 1 SDSS 100 MAP Planck P(k) 10 3 T 80 60 0.1 LSS Pψ 10 4 10 5 40 20 CMB 10 100 l (multipole) 0.01 k (h Mpc -1 ) 10 6 10 7 10 100 Lensing l (multipole) of Structure Formation Wayne
More informationLecture 3+1: Cosmic Microwave Background
Lecture 3+1: Cosmic Microwave Background Structure Formation and the Dark Sector Wayne Hu Trieste, June 2002 Large Angle Anisotropies Actual Temperature Data Really Isotropic! Large Angle Anisotropies
More informationLecture 3+1: Cosmic Microwave Background
Lecture 3+1: Cosmic Microwave Background Structure Formation and the Dark Sector Wayne Hu Trieste, June 2002 Tie-ins to Morning Talk Predicting the CMB: Nucleosynthesis Light element abundance depends
More informationThe Silk Damping Tail of the CMB l. Wayne Hu Oxford, December 2002
The Silk Damping Tail of the CMB 100 T (µk) 10 10 100 1000 l Wayne Hu Oxford, December 2002 Outline Damping tail of temperature power spectrum and its use as a standard ruler Generation of polarization
More informationAstro 448 Lecture Notes Set 1 Wayne Hu
Astro 448 Lecture Notes Set 1 Wayne Hu Recombination Equilibrium number density distribution of a non-relativistic species n i = g i ( mi T 2π ) 3/2 e m i/t Apply to the e + p H system: Saha Equation n
More informationCMB Anisotropies Episode II :
CMB Anisotropies Episode II : Attack of the C l ones Approximation Methods & Cosmological Parameter Dependencies By Andy Friedman Astronomy 200, Harvard University, Spring 2003 Outline Elucidating the
More informationDark Energy in Light of the CMB. (or why H 0 is the Dark Energy) Wayne Hu. February 2006, NRAO, VA
Dark Energy in Light of the CMB (or why H 0 is the Dark Energy) Wayne Hu February 2006, NRAO, VA If its not dark, it doesn't matter! Cosmic matter-energy budget: Dark Energy Dark Matter Dark Baryons Visible
More informationThe Once and Future CMB
The Once and Future CMB DOE, Jan. 2002 Wayne Hu The On(c)e Ring Original Power Spectra of Maps 64º Band Filtered Ringing in the New Cosmology Gravitational Ringing Potential wells = inflationary seeds
More informationLecture I. Thermal History and Acoustic Kinematics. Wayne Hu Tenerife, November 2007 WMAP
Lecture I WMAP Thermal History and Acoustic Kinematics Wayne Hu Tenerife, November 2007 WMAP 3yr Data WMAP 3yr: Spergel et al. 2006 5000 l(l+1)/2π C l (µk 2 ) 4000 3000 2000 1000 0 200 400 600 800 1000
More informationThe AfterMap Wayne Hu EFI, February 2003
The AfterMap Wayne Hu EFI, February 2003 Connections to the Past Outline What does MAP alone add to the cosmology? What role do other anisotropy experiments still have to play? How do you use the MAP analysis
More informationProbing the Dark Side. of Structure Formation Wayne Hu
Probing the Dark Side 1 SDSS 100 MAP Planck P(k) 10 3 T 80 60 0.1 LSS Pψ 10 4 10 5 40 20 CMB 10 100 l (multipole) 0.01 k (h Mpc -1 ) 10 6 10 7 10 100 Lensing l (multipole) of Structure Formation Wayne
More informationAstro 448 Lecture Notes Set 1 Wayne Hu
Astro 448 Lecture Notes Set 1 Wayne Hu Recombination Equilibrium number density distribution of a non-relativistic species n i = g i ( mi T 2π ) 3/2 e m i/t Apply to the e + p H system: Saha Equation n
More informationA5682: Introduction to Cosmology Course Notes. 11. CMB Anisotropy
Reading: Chapter 8, sections 8.4 and 8.5 11. CMB Anisotropy Gravitational instability and structure formation Today s universe shows structure on scales from individual galaxies to galaxy groups and clusters
More informationPriming the BICEP. Wayne Hu Chicago, March BB
Priming the BICEP 0.05 0.04 0.03 0.02 0.01 0 0.01 BB 0 50 100 150 200 250 300 Wayne Hu Chicago, March 2014 A BICEP Primer How do gravitational waves affect the CMB temperature and polarization spectrum?
More informationCosmic Microwave Background Introduction
Cosmic Microwave Background Introduction Matt Chasse chasse@hawaii.edu Department of Physics University of Hawaii at Manoa Honolulu, HI 96816 Matt Chasse, CMB Intro, May 3, 2005 p. 1/2 Outline CMB, what
More informationisocurvature modes Since there are two degrees of freedom in
isocurvature modes Since there are two degrees of freedom in the matter-radiation perturbation, there must be a second independent perturbation mode to complement the adiabatic solution. This clearly must
More informationThe Physics of CMB Polarization
The Physics of CMB Polarization Wayne Hu Chicago, March 2004 Chicago s Polarization Orientation Thomson Radiative Transfer (Chandrashekhar 1960 ;-) Reionization (WMAP 2003; Planck?) Gravitational Waves
More informationThe cosmic background radiation II: The WMAP results. Alexander Schmah
The cosmic background radiation II: The WMAP results Alexander Schmah 27.01.05 General Aspects - WMAP measures temperatue fluctuations of the CMB around 2.726 K - Reason for the temperature fluctuations
More informationInvestigation of CMB Power Spectra Phase Shifts
Investigation of CMB Power Spectra Phase Shifts Brigid Mulroe Fordham University, Bronx, NY, 1458 Lloyd Knox, Zhen Pan University of California, Davis, CA, 95616 ABSTRACT Analytical descriptions of anisotropies
More informationReally, really, what universe do we live in?
Really, really, what universe do we live in? Fluctuations in cosmic microwave background Origin Amplitude Spectrum Cosmic variance CMB observations and cosmological parameters COBE, balloons WMAP Parameters
More informationPolarization from Rayleigh scattering
Polarization from Rayleigh scattering Blue sky thinking for future CMB observations Previous work: Takahara et al. 91, Yu, et al. astro-ph/0103149 http://en.wikipedia.org/wiki/rayleigh_scattering Antony
More informationA5682: Introduction to Cosmology Course Notes. 11. CMB Anisotropy
Reading: Chapter 9, sections 9.4 and 9.5 11. CMB Anisotropy Gravitational instability and structure formation Today s universe shows structure on scales from individual galaxies to galaxy groups and clusters
More information20 Lecture 20: Cosmic Microwave Background Radiation continued
PHYS 652: Astrophysics 103 20 Lecture 20: Cosmic Microwave Background Radiation continued Innocent light-minded men, who think that astronomy can be learnt by looking at the stars without knowledge of
More informationLecture 3. - Cosmological parameter dependence of the temperature power spectrum. - Polarisation of the CMB
Lecture 3 - Cosmological parameter dependence of the temperature power spectrum - Polarisation of the CMB Planck Collaboration (2016) Let s understand the peak heights Silk+Landau Damping Sachs-Wolfe Sound
More informationWe finally come to the determination of the CMB anisotropy power spectrum. This set of lectures will be divided into five parts:
Primary CMB anisotropies We finally come to the determination of the CMB anisotropy power spectrum. This set of lectures will be divided into five parts: CMB power spectrum formalism. Radiative transfer:
More informationLecture 4. - Cosmological parameter dependence of the temperature power spectrum (continued) - Polarisation
Lecture 4 - Cosmological parameter dependence of the temperature power spectrum (continued) - Polarisation Planck Collaboration (2016) Let s understand the peak heights Silk+Landau Damping Sachs-Wolfe
More informationLecture 2. - Power spectrum of gravitational anisotropy - Temperature anisotropy from sound waves
Lecture 2 - Power spectrum of gravitational anisotropy - Temperature anisotropy from sound waves Bennett et al. (1996) COBE 4-year Power Spectrum The SW formula allows us to determine the 3d power spectrum
More informationPhysics 463, Spring 07. Formation and Evolution of Structure: Growth of Inhomogenieties & the Linear Power Spectrum
Physics 463, Spring 07 Lecture 3 Formation and Evolution of Structure: Growth of Inhomogenieties & the Linear Power Spectrum last time: how fluctuations are generated and how the smooth Universe grows
More informationCMB Polarization and Cosmology
CMB Polarization and Cosmology Wayne Hu KIPAC, May 2004 Outline Reionization and its Applications Dark Energy The Quadrupole Gravitational Waves Acoustic Polarization and Initial Power Gravitational Lensing
More informationBAO AS COSMOLOGICAL PROBE- I
BAO AS COSMOLOGICAL PROBE- I Introduction Enrique Gaztañaga, ICE (IEEC/CSIC) Barcelona PhD Studenships (on simulations & galaxy surveys) Postdoctoral oportunities: www.ice.cat (or AAS Job: #26205/26206)
More informationPhysical Cosmology 6/6/2016
Physical Cosmology 6/6/2016 Alessandro Melchiorri alessandro.melchiorri@roma1.infn.it slides can be found here: oberon.roma1.infn.it/alessandro/cosmo2016 CMB anisotropies The temperature fluctuation in
More informationGalaxies 626. Lecture 3: From the CMBR to the first star
Galaxies 626 Lecture 3: From the CMBR to the first star Galaxies 626 Firstly, some very brief cosmology for background and notation: Summary: Foundations of Cosmology 1. Universe is homogenous and isotropic
More informationStructure in the CMB
Cosmic Microwave Background Anisotropies = structure in the CMB Structure in the CMB Boomerang balloon flight. Mapped Cosmic Background Radiation with far higher angular resolution than previously available.
More informationOverview. Chapter Cosmological Background
1 Chapter 1 Overview Is the azure of the sky its true color? Or is it that the distance into which we are looking is infinite? The P eng never stops flying higher till everything below looks the same as
More informationConcordance Cosmology and Particle Physics. Richard Easther (Yale University)
Concordance Cosmology and Particle Physics Richard Easther (Yale University) Concordance Cosmology The standard model for cosmology Simplest model that fits the data Smallest number of free parameters
More informationModern Cosmology / Scott Dodelson Contents
Modern Cosmology / Scott Dodelson Contents The Standard Model and Beyond p. 1 The Expanding Universe p. 1 The Hubble Diagram p. 7 Big Bang Nucleosynthesis p. 9 The Cosmic Microwave Background p. 13 Beyond
More informationThe cosmic microwave background radiation
The cosmic microwave background radiation László Dobos Dept. of Physics of Complex Systems dobos@complex.elte.hu É 5.60 May 18, 2018. Origin of the cosmic microwave radiation Photons in the plasma are
More informationLecture 09. The Cosmic Microwave Background. Part II Features of the Angular Power Spectrum
The Cosmic Microwave Background Part II Features of the Angular Power Spectrum Angular Power Spectrum Recall the angular power spectrum Peak at l=200 corresponds to 1o structure Exactly the horizon distance
More informationSecond Order CMB Perturbations
Second Order CMB Perturbations Looking At Times Before Recombination September 2012 Evolution of the Universe Second Order CMB Perturbations 1/ 23 Observations before recombination Use weakly coupled particles
More informationRayleigh Scattering and Microwave Background Fluctuations
Rayleigh Scattering and Microwave Background Fluctuations Qingjuan Yu, David N. Spergel 1 & Jeremiah P. Ostriker Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 ABSTRACT
More informationLicia Verde. Introduction to cosmology. Lecture 4. Inflation
Licia Verde Introduction to cosmology Lecture 4 Inflation Dividing line We see them like temperature On scales larger than a degree, fluctuations were outside the Hubble horizon at decoupling Potential
More informationStructures in the early Universe. Particle Astrophysics chapter 8 Lecture 4
Structures in the early Universe Particle Astrophysics chapter 8 Lecture 4 overview Part 1: problems in Standard Model of Cosmology: horizon and flatness problems presence of structures Part : Need for
More informationTHE PHYSICS OF. MICROWAVE BACKGROUND ANISOTROPIES y. Department of Astronomy and Physics. and Center for Particle Astrophysics
CfPA-TH-95-09, UTAP-204 THE PHYSICS OF MICROWAVE BACKGROUND ANISOTROPIES y Wayne Hu, 1 Naoshi Sugiyama 1;2, & Joseph Silk 1 1 Department of Astronomy and Physics and Center for Particle Astrophysics 2
More informationTheory of Cosmological Perturbations
Theory of Cosmological Perturbations Part III CMB anisotropy 1. Photon propagation equation Definitions Lorentz-invariant distribution function: fp µ, x µ ) Lorentz-invariant volume element on momentum
More informationKIPMU Set 4: Power Spectra. Wayne Hu
KIPMU Set 4: Power Spectra Wayne Hu Planck Power Spectrum B-modes: Auto & Cross Scalar Primary Power Spectrum 10 3 10 2 temperature Power (µk 2 ) 10 1 10 0 reion. τ=0.1 cross 10-1 E-pol. 10-2 10 1 10 2
More informationNeoClassical Probes. of the Dark Energy. Wayne Hu COSMO04 Toronto, September 2004
NeoClassical Probes in of the Dark Energy Wayne Hu COSMO04 Toronto, September 2004 Structural Fidelity Dark matter simulations approaching the accuracy of CMB calculations WMAP Kravtsov et al (2003) Equation
More informationH 0 is Undervalued BAO CMB. Wayne Hu STSCI, April 2014 BICEP2? Maser Lensing Cepheids. SNIa TRGB SBF. dark energy. curvature. neutrinos. inflation?
H 0 is Undervalued BICEP2? 74 Maser Lensing Cepheids Eclipsing Binaries TRGB SBF SNIa dark energy curvature CMB BAO neutrinos inflation? Wayne Hu STSCI, April 2014 67 The 1% H 0 =New Physics H 0 : an end
More information3 Observational Cosmology Evolution from the Big Bang Lecture 2
3 Observational Cosmology Evolution from the Big Bang Lecture 2 http://www.sr.bham.ac.uk/~smcgee/obscosmo/ Sean McGee smcgee@star.sr.bham.ac.uk http://www.star.sr.bham.ac.uk/~smcgee/obscosmo Nucleosynthesis
More informationThermal History of the Universe and the Cosmic Microwave Background. II. Structures in the Microwave Background
Thermal History of the Universe and the Cosmic Microwave Background. II. Structures in the Microwave Background Matthias Bartelmann Max Planck Institut für Astrophysik IMPRS Lecture, March 2003 Part 2:
More informationRayleigh scattering:
Rayleigh scattering: blue sky thinking for future CMB observations arxiv:1307.8148; previous work: Takahara et al. 91, Yu, et al. astro-ph/0103149 http://en.wikipedia.org/wiki/rayleigh_scattering Antony
More informationCosmological Structure Formation Dr. Asa Bluck
Cosmological Structure Formation Dr. Asa Bluck Week 6 Structure Formation in the Linear Regime II CMB as Rosetta Stone for Structure Formation Week 7 Observed Scale of the Universe in Space & Time Week
More informationn=0 l (cos θ) (3) C l a lm 2 (4)
Cosmic Concordance What does the power spectrum of the CMB tell us about the universe? For that matter, what is a power spectrum? In this lecture we will examine the current data and show that we now have
More informationThe physics of the cosmic microwave background
The physics of the cosmic microwave background V(φ) φ Hiranya Peiris STFC Advanced Fellow University of Cambridge Before we start... Acknowledgment: Anthony Challinor (University of Cambridge) for invaluable
More informationarxiv: v1 [astro-ph] 25 Feb 2008
Lecture Notes on CMB Theory: From Nucleosynthesis to Recombination by Wayne Hu arxiv:0802.3688v1 [astro-ph] 25 Feb 2008 Contents CMB Theory from Nucleosynthesis to Recombination page 1 1 Introduction 1
More informationLecture 03. The Cosmic Microwave Background
The Cosmic Microwave Background 1 Photons and Charge Remember the lectures on particle physics Photons are the bosons that transmit EM force Charged particles interact by exchanging photons But since they
More informationCosmology & CMB. Set6: Polarisation & Secondary Anisotropies. Davide Maino
Cosmology & CMB Set6: Polarisation & Secondary Anisotropies Davide Maino Polarisation How? Polarisation is generated via Compton/Thomson scattering (angular dependence of the scattering term M) Who? Only
More informationTomography with CMB polarization A line-of-sight approach in real space
Tomography with CMB polarization A line-of-sight approach in real space University of Pennsylvania - feb/2009 L. Raul Abramo Instituto de Física University of Sao Paulo L. Raul Abramo & H. Xavier, Phys.
More informationThe Cosmic Microwave Background and Dark Matter. Wednesday, 27 June 2012
The Cosmic Microwave Background and Dark Matter Constantinos Skordis (Nottingham) Itzykson meeting, Saclay, 19 June 2012 (Cold) Dark Matter as a model Dark Matter: Particle (microphysics) Dust fluid (macrophysics)
More informationWeek 10: Theoretical predictions for the CMB temperature power spectrum
Week 10: Theoretical predictions for the CMB temperature power spectrum April 5, 2012 1 Introduction Last week we defined various observable quantities to describe the statistics of CMB temperature fluctuations,
More informationSecondary Polarization
Secondary Polarization z i =25 0.4 Transfer function 0.2 0 z=1 z i =8 10 100 l Reionization and Gravitational Lensing Wayne Hu Minnesota, March 2003 Outline Reionization Bump Model independent treatment
More informationToward Higher Accuracy: A CDM Example
197 Appendix A Toward Higher Accuracy: A CDM Example The scale invariant cold dark matter (CDM) model with Ω 0 = 1.0 andω b h 2 near the nucleosynthesis value Ω b h 2 0.01 0.02 is elegantly simple and
More informationBAO & RSD. Nikhil Padmanabhan Essential Cosmology for the Next Generation VII December 2017
BAO & RSD Nikhil Padmanabhan Essential Cosmology for the Next Generation VII December 2017 Overview Introduction Standard rulers, a spherical collapse picture of BAO, the Kaiser formula, measuring distance
More informationWhat can we Learn from the Cosmic Microwave Background
What can we Learn from the Cosmic Microwave Background Problem Set #3 will be due in part on April 8 and in full on April 11 Solutions to Problem Set #2 are online... graded versions soon Again I m asking
More informationarxiv:astro-ph/ v1 16 Jun 1997
A CMB Polarization Primer Wayne Hu 1 Institute for Advanced Study, Princeton, NJ 08540 arxiv:astro-ph/9706147v1 16 Jun 1997 Martin White Enrico Fermi Institute, University of Chicago, Chicago, IL 60637
More informationPerturbation Evolution
107 Chapter 5 Perturbation Evolution Although heaven and earth are great, their evolution is uniform. Although the myriad things are numerous, their governance is unitary. Chuang-tzu, 12 Superhorizon and
More informationAnalyzing the CMB Brightness Fluctuations. Position of first peak measures curvature universe is flat
Analyzing the CMB Brightness Fluctuations (predicted) 1 st rarefaction Power = Average ( / ) 2 of clouds of given size scale 1 st compression 2 nd compression (deg) Fourier analyze WMAP image: Measures
More informationIntroduction. How did the universe evolve to what it is today?
Cosmology 8 1 Introduction 8 2 Cosmology: science of the universe as a whole How did the universe evolve to what it is today? Based on four basic facts: The universe expands, is isotropic, and is homogeneous.
More informationCosmic sound: near and far
Cosmic sound: near and far Martin White UCB/LBNL for the Planck & BOSS teams Planck BOSS 1 Outline! The standard cosmological model and the CMB. Acoustic oscillations in the infant Universe.! Planck: mission.!
More informationCOSMIC MICROWAVE BACKGROUND Lecture I
COSMIC MICROWAVE BACKGROUND Lecture I Isabella Masina Univ. & INFN Ferrara, Italy CP3-Origins SDU, Denmark 18/10/2010 CP3-Origins SUGGESTED BIBLIOGRAPHY 1. W. Hu Lectures and animations http://background.uchicago.edu/~whu/physics/physics.html
More informationDetails create the big picture the physics behind the famous image of the cosmic microwave background. Marieke Postma
Details create the big picture the physics behind the famous image of the cosmic microwave background Marieke Postma last week Inflation period of accelerated expansion a(t) eht - creates homogeneous and
More informationInflationary Cosmology and Alternatives
Inflationary Cosmology and Alternatives V.A. Rubakov Institute for Nuclear Research of the Russian Academy of Sciences, Moscow and Department of paricle Physics abd Cosmology Physics Faculty Moscow State
More informationCosmology in a nutshell + an argument against
Cosmology in a nutshell + an argument against Ω Λ = based on the inconsistency of the CMB and supernovae results Charles H Lineweaver arxiv:astro-ph/983v Mar 998 University of New South Wales, Sydney,
More informationPrimordial nongaussianities I: cosmic microwave background. Uros Seljak, UC Berkeley Rio de Janeiro, August 2014
Primordial nongaussianities I: cosmic microwave bacground Uros Selja, UC Bereley Rio de Janeiro, August 2014 Outline Primordial nongaussianity Introduction and basic physics CMB temperature power spectrum
More informationarxiv:astro-ph/ v3 23 Aug 2001
Rayleigh Scattering and Microwave Background Fluctuations Qingjuan Yu, David N. Spergel 1 & Jeremiah P. Ostriker Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544 arxiv:astro-ph/0103149v3
More informationThe Cosmic Microwave Background and Dark Matter
The Cosmic Microwave Background and Dark Matter (FP7/20072013) / ERC Consolidator Grant Agreement n. 617656 Constantinos Skordis (Institute of Physics, Prague & University of Cyprus) Paris, 30 May 2017
More informationAST5220 lecture 2 An introduction to the CMB power spectrum. Hans Kristian Eriksen
AST5220 lecture 2 An introduction to the CMB power spectrum Hans Kristian Eriksen Cosmology in ~five slides The basic ideas of Big Bang: 1) The Big Bang model The universe expands today Therefore it must
More informationUseful Quantities and Relations
189 APPENDIX B. USEFUL QUANTITIES AND RELATIONS 190 Appendix B Useful Quantities and Relations B.1 FRW Parameters The expansion rate is given by the Hubble parameter ( ) 1 H 2 da 2 (ȧ ) a 2 0 = a dt a
More informationCMB beyond a single power spectrum: Non-Gaussianity and frequency dependence. Antony Lewis
CMB beyond a single power spectrum: Non-Gaussianity and frequency dependence Antony Lewis http://cosmologist.info/ Evolution of the universe Opaque Transparent Hu & White, Sci. Am., 290 44 (2004) CMB temperature
More informationPhysical Cosmology 18/5/2017
Physical Cosmology 18/5/2017 Alessandro Melchiorri alessandro.melchiorri@roma1.infn.it slides can be found here: oberon.roma1.infn.it/alessandro/cosmo2017 Summary If we consider perturbations in a pressureless
More informationThe Outtakes. Back to Talk
The Outtakes CMB Transfer Function Testing Inflation Weighing Neutrinos Decaying Neutrinos Testing Λ Testing Quintessence Polarization Sensitivity SDSS Complementarity Secondary Anisotropies Doppler Effect
More informationMODERN COSMOLOGY LECTURE FYTN08
1/43 MODERN COSMOLOGY LECTURE Lund University bijnens@thep.lu.se http://www.thep.lu.se/ bijnens Lecture Updated 2015 2/43 3/43 1 2 Some problems with a simple expanding universe 3 4 5 6 7 8 9 Credit many
More informationCosmology. Jörn Wilms Department of Physics University of Warwick.
Cosmology Jörn Wilms Department of Physics University of Warwick http://astro.uni-tuebingen.de/~wilms/teach/cosmo Contents 2 Old Cosmology Space and Time Friedmann Equations World Models Modern Cosmology
More informationPhysics 218: Waves and Thermodynamics Fall 2003, James P. Sethna Homework 11, due Monday Nov. 24 Latest revision: November 16, 2003, 9:56
Physics 218: Waves and Thermodynamics Fall 2003, James P. Sethna Homework 11, due Monday Nov. 24 Latest revision: November 16, 2003, 9:56 Reading Feynman, I.39 The Kinetic Theory of Gases, I.40 Principles
More informationCMB Anisotropies and Fundamental Physics. Lecture II. Alessandro Melchiorri University of Rome «La Sapienza»
CMB Anisotropies and Fundamental Physics Lecture II Alessandro Melchiorri University of Rome «La Sapienza» Lecture II CMB & PARAMETERS (Mostly Dark Energy) Things we learned from lecture I Theory of CMB
More informationEl Universo en Expansion. Juan García-Bellido Inst. Física Teórica UAM Benasque, 12 Julio 2004
El Universo en Expansion Juan García-Bellido Inst. Física Teórica UAM Benasque, 12 Julio 2004 5 billion years (you are here) Space is Homogeneous and Isotropic General Relativity An Expanding Universe
More informationCosmological Signatures of a Mirror Twin Higgs
Cosmological Signatures of a Mirror Twin Higgs Zackaria Chacko University of Maryland, College Park Curtin, Geller & Tsai Introduction The Twin Higgs framework is a promising approach to the naturalness
More informationPower spectrum exercise
Power spectrum exercise In this exercise, we will consider different power spectra and how they relate to observations. The intention is to give you some intuition so that when you look at a microwave
More informationAST5220 lecture 2 An introduction to the CMB power spectrum. Hans Kristian Eriksen
AST5220 lecture 2 An introduction to the CMB power spectrum Hans Kristian Eriksen Cosmology in ~five slides The basic ideas of Big Bang: 1) The Big Bang model The universe expands today Therefore it must
More informationThe Power. of the Galaxy Power Spectrum. Eric Linder 13 February 2012 WFIRST Meeting, Pasadena
The Power of the Galaxy Power Spectrum Eric Linder 13 February 2012 WFIRST Meeting, Pasadena UC Berkeley & Berkeley Lab Institute for the Early Universe, Korea 11 Baryon Acoustic Oscillations In the beginning...
More informationCOSMIC MICROWAVE BACKGROUND ANISOTROPIES
COSMIC MICROWAVE BACKGROUND ANISOTROPIES Anthony Challinor Institute of Astronomy & Department of Applied Mathematics and Theoretical Physics University of Cambridge, U.K. a.d.challinor@ast.cam.ac.uk 26
More informationI Cosmic Microwave Background 2. 1 Overall properties of CMB 2. 2 Epoch of recombination 3
Contents I Cosmic Microwave Background 2 1 Overall properties of CMB 2 2 Epoch of recombination 3 3 emperature fluctuations in the CMB 4 3.1 Many effects contribute.................................. 4
More informationAstronomy 182: Origin and Evolution of the Universe
Astronomy 182: Origin and Evolution of the Universe Prof. Josh Frieman Lecture 11 Nov. 13, 2015 Today Cosmic Microwave Background Big Bang Nucleosynthesis Assignments This week: read Hawley and Holcomb,
More informationCosmology: An Introduction. Eung Jin Chun
Cosmology: An Introduction Eung Jin Chun Cosmology Hot Big Bang + Inflation. Theory of the evolution of the Universe described by General relativity (spacetime) Thermodynamics, Particle/nuclear physics
More informationDetection of Polarization in the Cosmic Microwave Background using DASI
Detection of Polarization in the Cosmic Microwave Background using DASI Thesis by John M. Kovac A Dissertation Submitted to the Faculty of the Division of the Physical Sciences in Candidacy for the Degree
More informationStructures in the early Universe. Particle Astrophysics chapter 8 Lecture 4
Structures in the early Universe Particle Astrophysics chapter 8 Lecture 4 overview problems in Standard Model of Cosmology: horizon and flatness problems presence of structures Need for an exponential
More information