Standard ΛCDM Model Parameters 2015: Planck (+BAO+SN) Hubble constant H0=67.8  0.9 km s-1 Mpc-1 Total density Ωm+λ = 1.000  0.005 Dark energy density ΩΛ=0.692  0.012 Mass density Ωm=0.308  0.012 Baryon density Ωb=0.0478  0.0004 Fluctuation spectral index ns=0.968  0.006 Fluctuation amplitude σ8=0.830  0.015 Optical depth =0.066  0.016 Age of universe t0=13.80  0.02 Gyr

Beyond the Standard ΛCDM Model 2015: Planck (+BAO+SN) Total density Ωtot = 1-Ωk = 1.001  0.004 Equation of state w = -1.006  0.045 Tensor/scaler fluctuations r < 0.11 (95% CL) Running of spectral index dn/dlnk = -0.03  0.02 Neutrino mass ∑ mν < 0.23 eV (95% CL) # of light neutrino families Neff=3.15  0.23

CMB Cosmic Microwave Background time

Thermal History scale r p+e  H B=13.6 eV horizon H-1=ct T~ 4000K 2.7K ionized neutral Saha equation: p+e  H B=13.6 eV x=1/2 at Trec~ 4000 K teq trec t0 scale r 1+z~ 104 103 1 t~ 104y 5x105y 1.5x1010y H-1=ct horizon ma-3 ra-4 radiation matter 3x10-30 g/cm3 5x10-34 g/cm3

CMB: Recombination →Saha eq. X z H binding energy B=13.6 eV ~2.7 kT T~60,000 K but energetic tail of Plankian keeps it ionized In equilibrium, for kT<<mc2 (non-relat.), Maxwell-Boltzman for each component: g=2 for p and e →Saha eq. solve for X(T,η) For η=5.5x10-10 have X=0.5 at kTrec=0.3eV=B/40 Trec=3740K zrec=1370 trec=2.4x105y 1.0 0.9 0.5 0.1 0.0 1300 1400 1500 X z

Decoupling Rate of photon scattering: Decoupling when Γ=H zdec=1100 Tdec=3000K Optical depth: Last scattering at τ~1 z~zdec

Cosmic Microwave Background Radiation 1965

COBE 1992 Plank black-body spectrum I=energy flux per unit area, solid angle, and frequency interval Spectrum of the CMB

Origin of Cosmic Microwave Background horizon big-bang t=0 last-scattering surface Thomson scattering trec~380 kyr T~4000K ct0 T~2.7K c(t0-tdec) here & now t0~14 Gyr horizon at trec ~100 comoving Mpc ~1o transparent neutral H ionized p+e- opaque

horizon at last scattering Characteristic Scale time here & now space past light cone last scattering horizon at last scattering horizon big bang singularity

CMB Temperature Maps isotropy T2.725K T/T~10-3 dipole WMAP 2003 COBE 1992 WMAP 2003 resolution ~10o resolution ~ 10’ T/T~10-5

CMB Temperature Fluctuations COBE 1992 BOOMERANG 2002

Boomerang

WMAP: Wilkinson Microwave Anisotropy Probe δT/T~10-5 10 arcmin Charles Bennett

CMB anisotropy – density fluctuations black body: adiabatic fluctuations:

Curvature closed flat open

Curvature closed flat open

Angular Power Spectrum initial conditions acoustic peaks curvature baryons dark matter dissipation T  angle =2/ 

1st peak Curvature 1st peak closed open flat

Origin of Fluctuations in CMB Temperature Large angles l<180: Sachs-Wolf gravitational redshift On scales of the horizon at decoupling (l~180) and below: acousitic oscilations of photon-baryon fluid in the dark-matter potential wells. in eq. of state w = 0 (cold baryons) to 1/3 (photons), depending on nb/nγ maximum T where the oscilation is at maximum compression: minimum T at maximun expansion. Peak angular scale at l~180. At this scale max compression at tdec. Exact lmax tells Ωk . Peak amplitude depends on sound speed

Origin of Peaks  / t horizon scale M H-1=ct teq trec t0 radiation matter horizon scale M ionized neutral H-1=ct Horizon: M enters the horizon M1 M2 Comoving sphere: teq trec t0 t  / M1 M2 Fluctuations grow after entering the horizon 1st peak 2nd peak

Acoustic Peaks In the early hot ionized universe, photons and baryons are coupled via Thomson scattering off free electrons. Initial fluctuations in density and curvature (quantum, Inflation) drive acoustic waves, showing as temperature fluctuations, with a characteristic scale - the sound horizon cst. At z~1,090, T~4,000K, H recombination, decoupling of photons from baryons. The CMB is a snapshot of the fluctuations at the last scattering surface. Primary acoustic peak at rls ~ ctls ~ 100 co-Mpc or θ~1˚ (~200) – the “standard ruler”. Secondary oscillations at fractional wavelengths.

CMB Acoustic Oscillations explore all parameters compression kctls=π curvature velocity max dark matter initial conditions dissipation rarefaction kcstls=2π baryons

Pre-WMAP CMB Anisotropy spectrum

The ΛCDM model is very successful Accurate parameter determination curvature dark matter initial fluctuations dissipation baryons

The ΛCDM model is very successful Accurate parameter determination Planck 2015

Curvature The Universe is nearly flat: Open? Closed? Surely much larger than our horizon!

large universe – small curvature small universe -- large curvature large universe – small curvature עקמומיות גדולה וקטנה

Baryons 2nd peak

Dark Matter 3rd peak

Late Re-ionization → Polarization of CMB horizon big-bang t=0 last-scattering surface trec~380 kyr T~4000K ct0 T~2.7K c(t0-tdec) here & now t0~14 Gyr transparent neutral H ionized p+e- opaque

Anisotropy power spectrum by WMAP T/T late reionization Polarization precision

Polarization by scattering off free e-

Polarization by scattering off free e-

Polarization by scattering off electrons; re-ionization by stars & quasars at z~10

Polarization by scattering off electrons; re-ionization by stars & quasars at z~10 Planck 2015

T late reionization

Anisotropy power spectrum by WMAP T/T Polarization late reionization First stars at 180 Myr precision

WMAP Polarization reionization precision  First stars at 180 Myr

Cosmic History galaxy formation dark ages big bang last scattering t=380 kyr reionization t=430 Myr today t=13.7 Gyr

Cosmological Epochs recombination last scattering dark ages 380 kyr z~1000 recombination last scattering dark ages 180 Myr z=8.81.5 first stars reionization galaxy formation today 13.8 Gyr

Inflation Problems with standard hot-big-bang: 1. horizon-causality 2. flattness 3. origin of expansion 4. origin of fluctuations Inflation

Horizon Causality Problem big bang singularity conformal time  comoving space u here & now d  dt/a(t) d=du for light 103/2 a t2/3 comoving shell of matter arec~10-3 a0=1 scale rh=ct horizon past light cone horizon last scattering

Flattness problem Friedman equation: density parameter  a1-2 a tot r, m 1 a

Inflation  Causality scale a eHt a t2/3 rh=ct 103/2 arec~10-3 a0=1 big bang singularity last scattering conformal time  comoving space u here & now past light cone horizon d  dt/a(t) d=du for light  - scale a t2/3 comoving shell of matter rh=ct 103/2 horizon a eHt arec~10-3 a0=1

Inflation  Flattness Friedman equation: density parameter a tot  r, m 1 a

Inflation with  FRW: if Energy conservation:  p dV repulsion possible Quintessence: for inflation need to exceed

Dark Energy by SN

Inflation in field theory From Lagrangian and energy-momentum tensor : potential fluctuations V() inf scalar field  0 (inflaton) →Equation of motion: When slow roll? Fluid eq. for inflaton field in FRW: slow roll approximation: “friction” leads to terminal constant “velocity” FRW (k=0): End of inflation Reheating Scale-invariant large-scale density fluctuations from small quantum fluctuations in 

Planck Scale Quantum gravity when αG ~1 In the early universe gravity dominates (asymptotic freedom for GUTs) Strength of gravity compared to quantum effects: In analogy to strength of E&M interaction compared to quantum effects: Quantum gravity when αG ~1

יקומים רבים? Local big-bangs זמן