INTRODUCTION TO COSMOLOGY AND ASTROPHYSICS

1. INTRODUCTION TOCOSMOLOGY ANDASTROPHYSICS Pierre Darriulat VSOP XII Ha Noi December 2005

2. COSMOLOGICAL(PRINCIPLE)APPROXIMATION A HOMOGENEOUS EXPANDING UNIVERSE • R(t)=R(0) a(t)/a(0) • a(t) defines the scale (a(0) is arbitrary) • X(t)/a(t), Y(t)/a(t), Z(t)/a(t) = comoving coordinates • dR(t)/dt =R(0) da(t)/dt/a(0)= R(t)da(t)/a(t)/dt=R(t)H(t) • H(t)=da/adt=Hubble constant=71km/s/Mpc • Constant in space, not in time! • 1pc(parsec)=π ly (light year) • Age of the universe (horizon) =14Gy

3. Velocities and distances • Doppler effect 1+z=√(1+β)/(1-β)~1+ β • z=redshift→magnification factor • z=1,r=2.5Gpc, z=10,r=4.2Gpc, z=1000,CMB • Parallax 1μm/10m=10-7=.02arcsec→d<50pc • Luminosity (apparent/absolute) α 1/d2 • Cepheids period=f(luminosity) • SNIa White dwarf→Neutron star

4. Non relativistic approximation • A same m (inertial and gravitational) • Energy conservation mv2/2-GmM/r=cte • V(t)2-V(0)2=2GM(1/r-1/ro) • r=∞V(t)=√V(0)2-2GM/ro Vescape=√2GM/ro • M=4/3 π ro3 ρo=4/3 π r3 ρ • At r’=λr V’= λV M’=M λ3 • Let r→∞ V2=8/3 π G ρr2 –K • H2= V2/r2=8/3 π G ρ –K/r2 → ρcritical • Ω= ρ/ ρcritical K/r2= H2(Ω -1)

5. Relativistic case • It is energy that weighs, not mass • E’=chαE+shαP=(1+β)chαE β=gt=gh ΔE~Egh • →replace everywhere ρ by energy density • d(ρU)=-pdU d(ρa3)/da=-3pa2 =ad(ρa2)/da+ρa2 • Cold matter (β<<1) ρa3=cte p=0 • Hot matter (photons, β~1) ρa4=cte p= ρ/3 • V2=8/3 π G ρa2 –K →dV/dt=(4/3)πGd(ρa2)/(Vdt) • d2a/adt2=(4/3)πG(d(ρa2)/dt)/(ada/dt) • d(ρa2)/dt=–(ρ+3p)(ada/dt). • d2a/adt2=–(4/3)πG(ρ+3p)

6. Friedmann Equation(s) Describe the evolution of an expandinghomogeneousuniverse using only three parameters: energy density ρ, pressure p, and curvature k/a2 • H2=(da/adt)2=8/3πGρ–k/a2 k={–1,0,+1} • k/a2=H2(Ω –1) Ω=ρ/ρcritρcrit = 3H2/(8πG) • d2a/adt2= – 4/3 πG(ρ +3p) w=p/ρ (equation of state) • q = –d2a/adt2/H2 = Ω/2+3p/(2ρcrit) = deceleration parameter For a flat universe (k=0) w q n {a(t)=a(0)tn} Matter dominated 0 1/2 2/3 Radiation dominated 1/3 1 1/2 Inflation; dark energy −1 −1 ∞ (exponential)

7. A homogeneous universe? • CMB: the universe was homogeneous to within some 10 ppm when it was only 400kyr old • Today inhomogeneities disappear only above 100 Mpc or so ( some 2% of the horizon) Observations (right) and simulations (left) are in fair agreement

8. The Hubble constant • From Cepheids to SN Ia: H=71±3km/s/Mpc • But large redshift galaxies are too faint: q=-d2a/adt2/H2=-.66±.10 → w=p/ρ=-1.0±0.2

9. Dark matter • Main evidences from stellar rotation curves (v=cte instead of v=1/√r) and from binding energy of clusters of galaxies. Also from gravitational lensing and stability of spirals. • Must be cold (cosmology) • Most popular candidate: LSP (lightest SUSY partner) • ΩCDM=23±4%

10. Cosmic Microwave Background • At an age of ~400 kyr (z~1000) the universe had a temperature in the eV region: electrons and nuclei combined into atoms. It then became transparent to the left over photons that can still be observed today, redshifted by a factor of ~1000. • This tells us about the state of the universe at that time and about its evolution thereafter.

11. WMAP and the HST

12. A perfect black body spectrum • Evidence for thermal equilibrium • T=2.725(1)K tells us about redshift between now and then

13. The CMB: inhomogeneities Angular aperture of inhomogeneities can’t be larger than ratio of horizons between then and now (400ky/14Gy) multiplied by redshift (1000)Δθ<~1o From COBE to WMAP

14. Spherical harmonic analysis Below some threshold in l the amplitudes of the Ylmtermsshould therefore cancel. The position of the first peak (l~220) tells us about k (namely Ω): Ω=1.02±0.02 the universe isflat

15. Primordial nucleosynthesis • Some 3mn after the big bang the temperature of the universe was in the MeV range where protons and neutrons could combine into nuclei • But there was little time before the expansion would cool it down too much, not enough to jump over the 8Be gap: hence only 4He, 2H and traces of 3He and 6Li could be synthesized. • Their relative abundances today tell us about the state of the universe at this early time

17. Global outcome Putting all these data together we get a consistent picture of a flat universe, 13.7±0.2Gyr old, and having the following energy content: 4% of nuclei (~1% in stars and ~3% in hot gas), 23% of dark matter and the remaining 73%, called dark energy, are a complete mystery

18.  +  < 1% Baryons 4% CDM 23% Dark Energy 73% The energy content of the universe Concordance for an accelerating expansion and an equation of state of dark energy having w=1, hence corresponding to a cosmological constant

19. The main milestones: a summary A billion years or so ago the universe became dark energy dominated Between 400 kyr and then, it was matter dominated; matter started to condense into galaxies; CMB photons traveled freely Before then, the universe was a radiation dominated plasma At an age of ~3mn nucleosynthesis took place At an age of ~1μs quarks and gluons got confined into hadrons Before then a nearly equal number of fermions and antifermions annihilated into photons (1billion per m3 today) leaving a minute excess of matter (1 proton per m3 today) because of CP violation.

20. Inflation There are serious hints in favor of a “grand unification” of the electroweak and strong forces at a mass MGUT ~a few 1016 GeV, close to the Planck mass (1019 GeV) What happened at that time brings up a number of problems: flatness, causality, monopoles, ρa4 . All of these are elegantly solved by assuming an exponential expansion (constant H) during these very early times (t<10-33 s) due to a metastable state having energy density ~MGUT4 However we know of no realistic detailed model of such an inflation mechanism

21. Evolution of the universe: a summary

22. SUSY, SUGRA and Superstrings Before inflation the Planck mass limits our knowledge: Heisenberg uncertainty relations prevent a wave packet of size D to contain a gravitation energy GM2/Dlarger than ħ/(D/c), hence to have a mass in excess of MPlanck=√(ħc/G)=1019 GeV. Hence the need for a new theory. Supersymmetry seems to be an essential ingredient (the commutator of its generators is momentum and gauging it leads to gravity). Current superstrings theories combining SUSY with extra compactified dimensions are the most popular candidates

23. Conclusion • No one any longer doubts the general validity of the big bang model: a universe expanding at a rate of ~70 km/s/Mpc, ~14 Gyr old, where atoms were formed after ~400 kyr, primordial nuclei after ~3 mn and nucleons after ~1μs. • Strong evidence exists in favor of cold dark matter (Ω~23%), the preferred candidate being the LSP that might be soon discovered at LHC, and in favor of a flat universe. • There are strong indications that the universe experienced a rapid inflation in the first 10-33s of its life

24. The most challenging puzzle, by far, is the evidence for 73% of unexplained energy density in the universe. Do we miss some point? Or does it really provide evidence for a new force? The coming years* will, hopefully, shed light on this mystery with many improved measurements and observations to come. • Cosmology/astrophysics is the most exciting and dynamic field of physics today. For Vietnamese students to enjoy learning it, VN universities must teach it. * … and Gerard Blanchard at VSOP XII !

25. For now 40 years astrophysics has made fascinating and spectacular progressThe whole of physics is invited to the banquet: particle, nuclear, atomic, molecular, plasma, solid stateThe whole of physics and also the whole worldOnly a few privileged countries can afford to launch space missions or to build giant telescopes But any country can, in principle, access the dataThis is an opportunity that developing countries should not miss The sky belongs to all of us We are all made of the same star dust