Physique d’Astroparticule 3eme cours Jürgen Brunner CPPM / Luminy

Plan de cours (24 h) 19/12/06 (mar) 4h 8:00 – 12:00 (JB) 10/01/07 (mer) 2h 8:00 – 10:00 (perdu) 22/01/07 (lun) 4h 8:00 – 12:00 (JB) 25/01/07 (jeu) 4h 14:00 – 18:00 31/01/07 (mer) 4h 8:00 – 12:00 EK 01/02/07 (jeu) 4h 14:00 – 18:00 07/02/07 (mer) 4h 8:00 – 12:00 EK

Big Bang temperature of universe 1010 K 3000 K nuclei atoms 100 s Equilibrium n/p ends Nucleosynthesis begins 1010 K Neutral hydrogen forms universe transparent to light fossil photon radiation frozen temperature of universe 3000 K nuclei atoms 100 s 3 105 y time after big bang

Description de l’univers Équation de la relativité générale Gab : Einstein Tensor - description de la déviation de la géométrie par rapport à la géométrie Euclidienne Tab : Énergie/stress Tensor: description de la matière a,b,, : indices (0,1,2,3)  : constante de proportionnalité, définie par correspondance avec loi de la gravitation classique G : constant de la Gravitation c : vitesse de la lumière

Metriques Definition de g : Règles de sommation : Règles de dérivation :

Metriques-Exemples Coordonnées Cartésiennes (2-dimensionnel) Courbature 0 Coordonnées Polaires (2-dimensionnel) Courbature 0 Coordonnées Polaires (2-dimensionnel) Courbature 0

Metriques- Espace/temps Minkowski (relativité restreinte) Convention des coordonnées

Einstein tensor Tenseur de Riemann Tenseur de Ricci Scalaire de Ricci Tenseur d’Einstein

Tenseur d’énergie/tension (angl.stress) T00 = densité d’énergie T0i = flux d’énergie = Quantité de mouvement Tii = flux de quantité de de mvt (stress ou pression) Tij = shear stress

Courbature d’espace/temps Distribution de la matière (aussi : radiation, énergie etc) déforment l’espace/temps Visualisation pour un monde 2-dimensionnel

La constante cosmologique Problème: Cette équation n’a pas de solutions stables. L’univers stationnaire n’est pas possible. Explication naïve: force gravitationnelle est toujours positive, chaque distribution de masses initiales s’effondra (par attraction) Version modifiée Elle permet des solutions stationnaires mais instables dés lors qu’on s’écarte de l’état d’équilibre  : constante cosmologique peut être vu comme “pression du vacuum, qui contrebalance la force gravitationnelle

Model d’univers Conditions basées sur observations et/ou des arguments philosophiques L’univers est homogène, ça veut dire invariant par translation, “il n’y a pas d’endroit particulier” (Ex.: structure cristalline ) L’univers est isotrope, ca veut dire invariant par rotation “dans tous les directions on voit la même chose” (Ex.: on imagine des sphères concentriques contenues les unes dans les autres ) La structure visible aujourd'hui est la résultat des petits fluctuations primordiales

Friedman-Lemaitre-Robertson-Walker metrique Solution pour l’univers decrit au-dessus a(t) : paramètre d’échelle, décrit l’évolution du taille d’univers k = -1,0,1 : type de la géométrie (hyperbolique, plat, sphérique) H : taux d’expansion Acceleration d’expansion  : densité de la matière

Hubble 1920-1930 Measure of red shift for many distant galaxies Conclusion: the Universe expands ! galaxies receding the faster the further they are

Redshift

Hubble’s law Today: H0 = 71 ± 4 (km/s) / Mpc Slope = H0 (Hubble constant)

Once upon a time... our Universe was smaller Primordial singularity !!! => BIG BANG Dawn of time Origin of space

How far in time ? Extrapolating backwards the present expansion speed towards the big bang T  1/H0 ~ 14 billion years (note that the present best estimate, with a lot of complicated physics inside, is T = 13.7 ± 0.2 Gyr) Consistent with the age of the oldest stars

Hubble law in 2003: supernovae Implosion of core of red giant Expansion of matter shock wave  0.5 c Explosion of star Supernova Supernova Remnant SNIa occurs at Chandra mass, 1.4 Msun  ‘Standard Candle’ measure brightness  distance: B = L / 4pd2 measure host galaxy redshift  get recession velocity test Hubble’s Law: v = H d, at large distances

Expansion with Supernovae Ia effective magnitude  brightness  distance Acceleration of universe expansion non-linear v = H(t) d Deviation from Hubble’s law The expansion accelerates WL ~ 0.7 redshift  recession velocity

Time & temperature (=energy) Once upon a time, our Universe was hotter Expansion requires work (and this is the most adiabatic expansion one can imagine, so the work comes from internal energy)

Decoupling g  particles+antiparticles g  proton-antiproton Time g  particles+antiparticles g  proton-antiproton g  electron-positron (…) then matter became stable Two epochs

Energy versus temperature L’univers peut être décrit comme corps incandescent Spectre typique comme mesure dans les lampe Dépendance de la température du longueur d’onde

Formule du Planck – début de la théorie quantique E=h Relation entre énergie et fréquence pour photons k – constante de Boltzman E ~ kT relation entre energie et temperature dans un gas ideal

Back to thermal history t = 10-35 s Density perturbations (inflation?) t ~ 2000 yrs Matter domination t ~ 300000 yrs Recombination: p+e-  H+g Matter: Gravitational collapse Photons: Free propagation observable Galaxies, clusters CMB

End of opaque Universe Multiple scatterings of g on e- produces “thermal” spectrum at T = 3000 K (z ~ 1100 = a0 / arec) Cannot see further back “Uniform” background at T0 = 2.7 K

Discovery Discovered in 1965 as “excess noise” (Noble Prize in 1978) 25 years later Bell Labs COBE 1992 Bell Labs Wilson Penzias (+ Robert Dicke)

COBE project 1990-1994 George F. Smoot John C. Mather Nobel prize 2006 "for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiation".

COBE-IRAS spectrum Excellent accord avec formule de Planck L’univers est un corps incandescent beaucoup plus précise que une lampe ordinaire

COBE-IRAS spectrum Déviation du theorie au niveau 10-3 seulement

COBE sky maps T = 2.7 K DT = 3.4 mK DT = 18 mK (after subtraction of constant emission) DT = 18 mK (after subtraction of dipole)

COBE sky maps scale 0-4 K: very isotrope  cosmological origin Yet, regions > 1° apart never in causal contact Inflation ? z t LSS 103 x 3.105 qLSS ~ rad ~1° 14.109 t now

COBE sky maps Doppler effect due to motion of Earth w.r.t. CMB (v = 370 km/s towards Virgo) Anisotropies : potential wells Early seeds for structure formation? (+ foregrounds)

Anisotropies l(l-1)Cl (power) l ~ 200/q (deg) Before recombination, Universe = plasma of free e- and protons Oscillations due to opposite effects of - gravity - pressure Presented as a power spectrum l(l-1)Cl (power) cosmology l ~ 200/q (deg)

Max. scale of anisotropies Limited by causality (remember?)  maximum scale  Max scale relates to total content of Universe Wtot (= WM+W)

2nd generation satellite COBE (7 degree resolution) WMAP (0.25 degree resolution) (l  20) (l  700)

WMAP WMAP on its way to L2 Very low temperature signal shield Back to back primary mirrors Very low temperature signal  Need shielding from Sun, Earth, Moon, (Jupiter) Lagrange point L2: position of co-rotation with Earth  Stability of conditions Measure of T differences 5 frequency channels Foreground removal (90 GHz) Launch: Jun. 2001 First results: 2003

Cosmological parameters b h2 = m h2 = h = … ns = 8 = 0.0223 +/-0.001 0.13 +/-0.01 0.73 +/- 0.03 … 0.95 +/- 0.02 0.74 +/- 0.06 Typically ± 5-10% + H0 from HST m =  = 0.24 +/- 0.04 0.72 +/- 0.04

Beyond WMAP - More frequency channels background removal - Improved resolution background removal 90 GHz 70 GHz 30 GHz 20 GHz 40 GHz Weighted sum

Planck - Freq coverage from 30 to 850 GHz (9 channels) - Polarization sensitive - Launch foreseen spring 2008

Big Bang temperature of universe 1010 K 3000 K nuclei atoms 100 s Equilibrium n/p ends Nucleosynthesis begins 1010 K Neutral hydrogen forms universe transparent to light fossil photon radiation frozen temperature of universe 3000 K nuclei atoms 100 s 3 105 y time after big bang

Which elements ? BBN Elements METALS H He Li Be

Proton - neutron conversion Age < 1s, T > 1 MeV Collisions maintain thermal equilibrium Proton - neutron conversion Maxwell-Boltzmann distribution : N  m3/2 exp - mc2 kBT n p N (neutron) N (proton) = ~ e mc2/kT ~ 1 n p  0 as T  0 BUT freeze-out (m = 1.3 MeV)

n-p freeze-out     - Weak reaction n  p rate: Gweak = ns|v|  GF2 T5 (n  T3 and s  GF2 T2) - Expansion rate: H = a/a  r1/2 with r  g* T4 (Stefan’s law) so H  g* 1/2 T2 .     3 Gweak T Freeze-out when Gweak ~ H with ~ H 0.8 MeV  drop-out of equilibrium at T ~ 0.8 MeV n p = e m/kT = e -(1.3 MeV / 0.8 MeV) ~ 0.2

Deuterium bottleneck - nB small  2-body reactions only - Formation of D - Binding Energy (D) = 2.2 MeV E g energy distribution nB / ng ~ 10-10  D photo-disintegrated Tail of high energy photons prevents formation of Deuterium until T ~ 0.1 MeV

t=1-3 mn, T=0.3-0.1 MeV - neutron decay:  n/p ~ (n/p)0 e-(t/) - Deuterium (all n): - Helium (all D ie. all n + equal number of p): 2n H abundance ~ 0.75 Helium abundance ~ ~ 0.25 n+p h = nB/ng   D bottleneck lasts less  n/p   He 

2H 3He 4He 6Li 7Be 7Li 8Be 1H pp-I pp-II pp-III

BBN essentially STOPS at He4 Heavier elements - BBN No A=5, A=8 stable nuclei + 2-body reactions only Li5  He4+p He5  He4+n Be8  He4+He4 BBN essentially STOPS at He4 He4+H3  Li7+g He4+He3  Be7+g Be7 +g  Li7+p Trace amounts of 3Li7, 4Be7 :

Heavier elements - Stars Produced in stars (high densities  triple alpha reactions allowed) Spread in ISM by SN explosions Crab nebula (SN II)

Origin of elements formed in: Big Bang Nucleosynthesis Hot stars Cosmic-ray interactions on inter-stellar medium Supernova explosions

Observational constraints - Stars are net producers of He4 and metals  use metal poor stars upper limit on primordial abundance of He4 (and on h) D weakly bound measure in ISM lower limit on primordial abundance of D (upper limit on h) D burnt to He3 and He3 produced by stars D+He3 increases with time upper limit on D+He3 ie lower limit on h Li7 very fragile, burnt in stars  use old metal poor stars, require Li6 (more fragile)

Abundances Observational concordance Agreement of abundances over 10 orders of magnitude  Major success of Big-Bang CMB: ng = 411 cm-3 h = nB/ng = (41).10-10 WB = = rB rc nBmB 3H2/8pG WB h702 ~ 0.04 h

BBN and neutrinos H  g* 1/2 T2 (remember?) where g* includes relativistic ’s so Nn   H   sooner freeze-out  n/p   He4  He mass fraction upper limit on He4 Nn = 3

LEP and light neutrinos Nn = 2.994  0.012

Matter/Energy in the Universe Wtotal = WM + WL  1 matter dark energy Matter: WM = Wb + W + WCDM  0.27 baryons neutrinos cold dark matter Baryonic matter : Wb ~ 0.04 stars, gas, brown dwarfs, white dwarfs CDM Neutrinos: W ~ 0.003 if M(n) ~ 0.1 eV Dark Energy Cold Dark Matter : WCDM  0.23 WIMPS/neutralinos, axions, …