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
a 1 x 3 Euclidean space a 1 x 2 a 0 x 3 a 1 x 1 scale factor a ( t ) > a( t ) 0 1 a 0 x 2 a 0 x 1
λ λ obs em a = 0 = 1+ a 1 z
Mount Wilson Edwin P. Hubble
Mount Wilson Edwin P. Hubble Mount Palomar
Z=0.1 Z=0.6
Z=1.1 Z=1.6
Z=2.1 Z=2.6
Z=3.1 Z=3.6
Z=4.1 Z=4.6
Redshifts to galaxies Hubble law H 0 for d = z zc v < < 1
HST Key Project
Hubble (1929) HST (1999) H 0 = 500km/s/Mpc H = 70 ± 7 km/s/mpc Dominated by 0 systematic errors! z 0. 1
The Accelerating Universe
Supernovae la Lightcurves & Stretch-factor SNIa as Standard Candles
Riess et al. (2004)
Riess et al. (1998) Riess et al. (2004) 129+16 SNIa Flat Universe Ω Ω M Λ = 0. 29 ± 0. 05 = 0. 71± 0. 05
Normal Matter ρ < ρ 2 1 p > 0 d (ρv ) + pdv = TdS = 0 ρ = ρ 2 1 p < 0 Vacuum Energy
The Aging Universe
If the universe is expanding, necessarily it must have been denser and hotter in the past Tracing the past history of the universe, we reach the realm of high energy physics and particle accelerators
T ( z) = T ( 1+ z) 0 a( z) a0 = ( 1 + z)
inflation now
inflation Large scale structure
inflation first galaxies
inflation microwave background
primordial nucleosynthesis
baryogenesis
inflation
Quantum Fluctuations CMB Anisotropies Structure Formation
Inflationary Paradigm Why is the Universe spatially flat? Why is the Universe homogeneous on large scales? What is the origin of all matter and radiation? What is the origin of the fluctuations that gave rise to galaxies and other large structures?
Constant Density GR Exponential growth Flatness
Constant Density GR Exponential growth Flatness + Homogeneity + Reheating
Metric perturbations Quantum Fluctuations within the horizon
Scale Invariant Spectrum φ H 2π 2 e folds t H 1 1 e fold
Metric Perturbation λ a Enters horizon Horizon H d H 1 Exits horizon Inflation Radiation Matter z z end eq 0 z
After Inflation λ > d H λ d H λ < d H Outside Horizon Enters the Horizon Inside Horizon
Horizon Crossing λ a d H H 1 z dec Inflation Radiation Matter z z end eq z0
Φ(x) δ ρ (x) ρ Gaussian Random Field
Cosmic Microwave Background
Discovery of CMB Arno Penzias Robert Wilson (1965) Blackbody Spectrum T=3K very isotropic
COBE (1989-1996)
T CMB = 2. 725± 0. 002K
Temperature Anisotropies
COBE 4-year Measurements (1992-1996) First Measurements Temperature Anisotropies (1992) T T 0 10 5
gravity Photon-Baryon Plasma in equilibrium: Thomson Scattering velocity density Metric Perturbation
Superhorizon Gravitational Potential Angular Power Spectrum Compression Rarefaction Subhorizon Acoustic Harmonic Oscillations Compression δt [ l( l + 1) Cl ] 1/ 2 Rarefaction Compression θ o = 180 θ o 0.8 l = 2 l 220 l θ 1
All CMB Exp. (2002)
Best fit to all CMB data (2002)
Wilkinson Microwave Anisotropy Probe
Wilkinson Microwave Anisotropy Probe (2003)
COBE (1992) 7 WMAP (2003) 10
Cosmological Parameters: WMAP et al. Rate of expansion Age of the Universe Spatial Curvature Cosmological Constant Dark Matter Baryon Density Neutrino Density Spectral Amplitude Spectral tilt Tensor-scalar ratio H 0 = ± 71 3 km/s/mpc = 13. 7 ± 0 2 Gyr ΩK < 0. 02 ( 95% c. l.) Ω Λ = 0. 73± 0. 04 Ω M = 0. 23± 0. 04 Ω B = 0. 044± 0. 004 < 0. 0076 ( 95% c. l.) A s = 0. 833± 0. 085 n s = 0. 93± 0. 03 r < 0. 71 ( 95% c. l.) Ω ν t 0.
Structure Formation
Φ(x) δ ρ (x) ρ Gaussian Random Field
Density Contrast Thresholds QSO First Stars Galaxies Clusters Superclusters Voids
z 1100 CMB Anisotropies z 100 Dark ages z 20 First stars z 10 Galaxies & Quasars z 1 Clusters & Superclusters
Large Scale Structure
Numerical Simulations (beyond pert. Theory)
Large Scale Structure Simulations (1996)
Dark Matter
Rotation curves of galaxies Ωdark 10 Ω stars
HST
t 0 H0 =. Ω M 0. 99 ± 0 05 = 0. 28± 0. 05
log ρ Evolution Universe inflation radiation matter now? loga
Cosmic coincidence?
From Concordance to Standard Model
Cosmic Data (1999)
THE CONCORDANCE MODEL (2001)
EdS Age Universe STANDARD COSMOLOGICAL MODEL (2003) ΩM = 0. 27 ± 0. 04 ΩΛ = 0. 73± 0. 04 Ω0 = 1. 02 ± 0. 02 Ω = 0. 044 ± 0. 004 H B 0 = 71± 3km/s/Mpc t = 13. 6 ± 0. 2 Gyr 0 Precision Cosmology! Errors < few%
THE FUTURE MODEL (2010)
The Global structure of the universe
Conclusions
Cosmology is becoming Cosmonomy, the science of measuring the Cosmos The stuff we are made of amounts to just a few percent of all the matter/energy Dark matter is here to stay. It could open the door to a new type of particle species (e.g. susy) Some kind of dark energy or smooth tension is responsible for the acceleration of the Universe. We have no idea of what it is We may measure our Local Universe but we ignore its Global Structure
The inflationary paradigm provides a general framework in which one can describe all cosmological observations The microwave background anisotropies contain a huge amount of information on the cosmological parameters, with very small systematic errors The Standard Cosmological Model, with errors of 1%, has two unsolved fundamental problems: the nature of dark matter and the dark energy
Addendum
Friedmann equations 2 2 3 3 8 a K G a a Λ + = ρ π + 00 ij 3 3 3 4 Λ + + = ) ( p G a a ρ π 00 Equation of state of matter ) ( ) ( t w t p ρ =
Spatial curvature Closed K = +1 Flat K = 0 Open K = 1
Friedmann equation ( Λ = 0) 1 2 GM K a = 2 a 2 a K = 0 M K > 0 M E = T + = 4π 3 escape ρ V a recollapse 3 velocity K < 0 expand forever
Friedmann equation ( Λ 0) a GM Λ = + a F = m x a 2 3 Matter attraction Cosmic repulsion Who wins? and when?
Friedmann equation ( Λ 0) 1 2 GM 2 K a Λ a = E = T + V 2a62 V (a) a repulsion @ late times attraction @ early times
Cosmological Parameters Rate of Expansion (Hubble) a H10 =)( t= hkm/s/mpc 0 a 0 1 = h 1 H. 9 773 0 Gyr time 1 = h ch 3000 0 1 Mpc distance 1 pc = 3. 262 ly = 3. 086 10 16 m
Critical density (K=0) ρ c ( t ) = 0 3H 2 0 8π G = 1. 88 h 2 10 29 g/cm 3 1 10 11 1 = 2. 77 h M /( h Mpc) Θ 3 2 = 11. 26 h protons/m 3
Density parameter Ω 0 = 8π G 3H 2 ρ ρ( t ) = ( t 0 0 ρ c ) Ω = Ω + Ω + Ω 0 R M Λ Friedmann Eq. Ω R = ρ ρ R c ( t ) 0 Ω M = ρ ρ M c ( t ) 0 Λ Ω K Ω = Λ 3H 2 K a 2 H 2 0 0 0 =
H 0 t 0 = H 0 t 0 = 1. 0 H 0 t 0 = 0. 8 H 0 t 0 =. 0 7 H 0 t 0 =. 0 6 H 0 t 0 =. 0 5 Accelerating Decelerating Expansion Recollapse Closed Open Bounce
Cosmological Parameters H0 t0 q0 ΩK Rate of expansion Age of the Universe Acceleration Parameter Spatial Curvature ΩM ΩΛ ΩB Ων Dark Matter Cosmological Constant Baryon Density Neutrino Density