The Cosmic Microwave Bacground Pt Said 2020 Amr El-Zant (CTP, BUE, - - PowerPoint PPT Presentation

Plasma & Cosmology The Cosmic Microwave Bacground Pt Said 2020

Amr El-Zant (CTP, BUE, Cairo)

Useful refs: Liddle: Introduction to Cosmology (Newtonian) Ferreira: Lectures on General Relativity and Cosmology (simple intro with essentials) http://wwwastro.physics.ox.ac.uk/~pgf/B3..pdf Peacock: Cosmological Physics (Newtonian + GR).

Cosmic Distance Scale

• Earth-Moon ~ 1 light second
• Earth-Sun ~ 8 light minutes
• Nearest stars

>~ 5 light yrs

The Milky Way Galaxy

Distance from sun to centre ~ 20 000 light years Farthest individual stars seen by naked eye ~ 1000 light years

Galactic Characteristics

 Nearest large galaxy > Million light years ~ Mpc  Time scales ~ 100 million years; speeds ~ 100 km/s  Mass scale ~ 107 to 1013 solar masses (most apparently dark!)  Average Density ~ 10-24 kg/m3

(larger near centre)

 Compare with 5000 for Earth and 1 kg/m3 for air

Larger scales (and back in time)

• Clusters of galaxies

1-10 Million light years 

• Large scale structure
• > few 100 Million light years

Cosmo molo logical l horizon

~13 Billion years

Gravity governs

very weak  Long time scales

BUT

 ONLY ATTRACTIVE (NO POSITIVE AND NEGATIVE)  Long range

 Wins on cosmic scales



Makes and holds together stars and galaxies and determines the cosmological evolution

Newtonian Derivation of Cosmological Evolution Equations

• Consider universe with uniform energy density
• If scale large  need GR as Newtonian gravity

assumes instantaneous interaction

• Take instead a patch that is small compared to the

‘horizon’ (distance light travels since ‘beginning’).

• Because of homogeneity  all patches same

Newton-Birkhoff theorem

• Take said patch to be spherical

(isotropy)

• Equation of motion

‘Energy Integral’ and interpretation

• Integrate e. motion keeping enclosed mass constant
• ‘Energy’ E  universe forever expands (E>0) or eventually recontracts (E<0).
• No equilibrium solutions (as in systems with random or

rotational mean motion)!

 similar to a ball thrown vertically upward!

1 2 𝑒 𝑠 𝑒 𝑢 2

− 𝐻 𝑁 (<𝑠)

𝑠

= E

Dynamics of Different Universes

 Need to know:  Rate of expansion as fn of cosmic history  most directly via distance and ‘redshift’

Light from galaxies redshifted

Nobel 2011  acceleration!

Expansion and its Acceleration: Dark Energy and Dark Matter

Current acceleration  Dark energy Past deceleration rate  Dark matter

e.g., Supernovae ‘standard candles’

The Cosmic Microwave Background

• Tells us of prior thermal equilibrium
• Current temperature of spectrum: 2.728 Kelvin
• Current energy density of CMB:
• The average energy per photon

~ k T ~ h ν

(since distn ~ 𝐟− 𝑭

𝒍𝑼 )

 photon number density ~

Compare with < one proton per cubic meter!

Era of Tightly Coupled Plasma (exercise)

• Currently interaction rate of CMB photons with matter negligible, but
• As universe expands scale a increases 

 energy per photon ~ h ν ~ 1/λ ~1/a ~ k T

Back in time  higher density and temperature  universe ionised Fraction of neutral atoms (~Hydrogen) suppre ressed by factor 𝑪𝒑𝒎𝒖𝒜𝒏𝒃𝒐𝒐 𝒈𝒃𝒅𝒖𝒑𝒔 𝒇−𝑪𝑰

𝑼

(𝐶𝐼 = 13.6 eV is Hydrogen’s binding energy) There are ~ 10

9 photons per proton  Trec~ 14/ln 10 9

= 0.7 eV (used 109𝑓−𝐶𝐼

𝑈 ~1; proper calcgives 0.3)

3600 Kelvin  a (rec ) =1/ / 13 1300  z (rec.) = 1300  t (rec) ) ~ 300 000 yr yr for

Cosmic Plasma Coupling

• Gas fully ionized  strongly interacts with photons by Thompson

scattering:

• Electron placed in EM field 

 oscillates

• radiates back

Crossection ~ power radiated / mean incident energy flux ~ Square of classical electron radius

interaction rate

(note relative vely ~ c = 1 here!)

Sound Waves in a Photon Fluid

• Remember recombination?
• Before that Baryons tightly coupled with photon gas.
• The latter behaves as ideal fluid with 𝑄 =

1 3 𝜍

(c = 1).

• It obeys a continuity equation for photon number ~ T

3

++ a momentum conservation equation.  Wave Eq. for Temp. Perturbations: (with sol. Θ = Θ 0 Cos (cs k 𝑢), if small Θ (0)) ** Transformed wave equation obtained earlier  acoustic waves travelling at

𝟐 𝟒 c

**If system expanding, equation remains with t   Valid in terms of this ‘conformal time’ (comoving dist light travels since t=0)

Acou

• ustic Peaks
• Photon fluid is permeated by sound waves
• Frozen at recombination

 Temperature fluctuations: where and 𝑡∗ indicates recomb. era. ** Peaks indicate 𝑙 =

𝑜𝜌 𝑡∗

(𝐥 𝐭∗ = 𝒐 𝝆)

First peak  1st Compression Second  1st Rarefication Third  2nd Compression more oscillations damping

From Wayne Hu pages

Location

• n of the Peaks as

s Stand ndard d Ruler

• Object of commoving size 𝜇 appears of angular size

𝜄 at 𝑢𝑠𝑏𝑜𝑡𝑤𝑓𝑠𝑡𝑓 𝑑𝑝𝑛𝑝𝑤𝑗𝑜𝑕 𝑒𝑗𝑡𝑢𝑏𝑜𝑑𝑓 𝐸: So If 𝜄 =

𝜇 𝐸 , and 𝑙 = 𝑜 𝜌 𝑡∗  𝜄 = 2 𝑜 𝑡∗ 𝐸

Distance sound of photon wave travels can easily be calculated  Given angle measured  Euclidean distance D inferred! ….or angle calculated given assumptions about model! Given a = a (t) and knowing a ~ 1/T , current T and T (Rec)!

Curvatur ure and d Cosm smological Con

• nstant
• In a closed universe objects appear

closer  peaks shifted to larger angles as where R is the radius of curvature In an open universe things will appear further away (the sin  sinh) Also in a universe with Λ since

Baryon Loading

• Perturbations exist even if there’s no initial temperature fluctuation (due to potential

fluctuations from Inflation)

• Adding baryons  additional source (gravitational potential) term in wave Eq.

 compression larger than rarefaction (but no collapse as Jeans scale is of order of horizon for coupled baryons)

Radi diation n Driving and d DM fraction n

𝜲𝑬𝑵

 a 𝒃𝒇𝒓

Summary of CMB Parameter Sensitivity Gives again ~70 % DE ~ 20 20 % DM

Fundamental Aspect of Gravity : Clustering Instability Gravity: i) always attractive ii) Long range

I) ‘Normal’ sound wave

Gravity against Pressure

ii) Gravi

vity y beats pr pressure  Collapse!

Fluctuations in the CMB  seeding structure