1. Standard ΛCDM Model Parameters
2015: Planck (+BAO+SN)
Hubble constant H0=67.8  0.9 km s-1 Mpc-1
Total density Ωm+λ =  0.005
Dark energy density ΩΛ=0.692  0.012
Mass density Ωm=0.308  0.012
Baryon density Ωb= 
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

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

3. CMB
Cosmic Microwave Background
time

4. Thermal History scale r p+e  H B=13.6 eV horizon H-1=ct
T~ K K
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~
t~ y 5x105y x1010y
H-1=ct
horizon
ma-3
ra-4
radiation matter
3x10-30 g/cm3
5x10-34 g/cm3

5. 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=5.5x have X=0.5 at kTrec=0.3eV=B/40 Trec=3740K zrec= trec=2.4x105y
1.0
0.9
0.5
0.1
0.0 X z

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

7. Cosmic Microwave Background Radiation
1965

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

9. 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

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

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

12. CMB Temperature Fluctuations
COBE 1992
BOOMERANG 2002

13. Boomerang

14. WMAP: Wilkinson Microwave Anisotropy Probe
δT/T~ arcmin
Charles Bennett

15. CMB anisotropy – density fluctuations
black body:
adiabatic fluctuations:

16. Curvature
closed
flat
open

17. Curvature
closed
flat
open

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

19. 1st peak
Curvature
1st peak
closed
open
flat

20. 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

21. 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

22. 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.

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

24. Pre-WMAP CMB Anisotropy spectrum

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

26. The ΛCDM model is very successful Accurate parameter determination
Planck 2015

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

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

29. Baryons
2nd peak

30. Dark Matter
3rd peak

31. 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

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

33. Polarization by scattering off free e-

34. Polarization by scattering off free e-

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

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

37. T
late reionization

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

39. WMAP Polarization
reionization
precision
 First stars at 180 Myr

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

41. 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

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

43. 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~ a0=1
scale
rh=ct
horizon
past light cone
horizon
last scattering

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

45. 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~ a0=1

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

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

48. Dark Energy by SN

49. 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 

50. 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

51. יקומים רבים?
Local big-bangs
זמן