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The Big Bang

- Lemaitre was the first to point out that if the Universe is expanding, it must have been much hotter and denser in the past
- This was first called the big bang by steady-state cosmologist Fred Hoyle as a term of ridicule
- Now all cosmological models with an evolving Universe are called “big bang cosmologies”

Three fundamental questions in cosmology are:

• Can we explain the observed structures in the universe in a self-consistent cosmological model?

• Can we explain the observed cosmic background radiation?

• Can we explain the abundances of light elements within the same model?

Yes, for a hot big bang model (adiabatically expanding, monotonically cooling undergoing a series of phase transitions with structure defined by RW metric and Friedmann equations).

Timeline for the evolution of the Universe

(109 K)

- Direct observations limited to t > 372 kyrs (recombination or decoupling)
- Nucleosynthesis constraints extend to timescales of ~1 s
- Contains several categories of events (force unification, evolution of particle species, radiation-matter equality, formation and evolution of large scale structure)

Before exploring the thermal history of the universe in the big bang model, we first need to know how the temperature scales with redshift (or scale factor). Consider matter and radiation temperatures when the two are thermally decoupled and evolving independently. Also, assume both are approximated by adiabatically expanding ideal fluid in local thermodynamic equilibrium.

Relativistic matter and Radiation

photon density decreases with a3 but photons loose energy due to cosmological redshifting (extra factor of 1+z), so

Non-relativistic matter

E

Before recombination, both go as T = To(1+z)

Radiation-Matter Equality and a Matter Dominated Universe

Similarly, the thermal history of the Universe reveals a change from radiation to matter dominated.

Energy density (matter) ~ ρmc2

ρm ~ 1/a3

# density (photons) ~ 1/a3

But, the redshifting means that energy per photon ~ 1/a. Thus, energy density (radiation) ~ 1/a4

Energy density of radiation drops more quickly than matter as scale factor increases.

The time when radiation and matter contributed equally in the Universe occurred at:

zeq = 3454 when temp was about 9400 K

Consensus (or Concordance) Model

Friedmann equation (now including radiation density term and assuming flat curvature)

- Since the three components have different dependences on scale factor, there are long stretches of history when one component dominates. First radiation, then matter, then Λ…
- matter and radiation energy densities equal arm = 0.00029 (z=3454)
- Λ and matter energy densities equal amΛ = 0.75 (z=0.33)

Photon - Baryon Number Density Ratio

Present density of baryons is

Photon’s obey Bose-Einstein statistics and integrating over the applicable distribution function give their number density:

mostly CMB (only 10% from starlight)

(see discussion on page 57 - 59 in Cosmology Notes for derivation)

The photon-baryon ratio (with = 0.024 (WMAP CMB values))

= 1.6 x 109

There are far more photons than baryons in the present Universe

noϒ

nob

Epoch when charged electrons and protons first became bound to form neutral hydrogen atoms - a snapshot of the universe when temp was around 3000K

At recombination, the mean free path of a photon rapidly goes from being very short to essentially infinite as the probability for scattering off an electron becomes negligible. Thus, this epoch is often called the surface of last scattering or the time of decoupling – when radiation and matter became decoupled.

Cosmic Microwave Background: Gamow, Alpher and Herman(1948) suggested that the Universe should have been filled with radiation shortly after the Big Bang. A remnant of this radiation should still be detectable today as low intensity background microwaves.

- About one second after the Big Bang, the Universe had temperatures of a few MeV – emitting gamma-rays
- This radiation has redshifted due to the expansion of the Universe so that the peak is currently at microwave wavelengths with T = 2.7 K.

Radiation density decreases as (1+z)4

Free-free emission, Compton scattering and other processes occur frequently enough for photons to have Planck distribution

The initial black body spectrum retains its shape as the temperature cools.

- First observed (inadvertently) in 1965 by Arno Penzias andRobert Wilson at the Bell Telephone Laboratories in Murray Hill, NJ.
- Detected excess noise in a radio receiver peak emission at BB temp = 3 degrees
- In parallel, researchers at Princeton were preparing an experiment to find the CMB.
- When they heard about the Bell Labs result they immediately realized that the CMB had been detected.

- The result was a pair of papers in the Physical Review: one by Penzias and Wilson detailing the observations, and one by Dicke, Peebles, Roll, and Wilkinson giving the cosmological interpretation.
- Penzias and Wilson shared the 1978 Nobel prize in physics.
- Almost immediately after its detection, the Steady State theory was dead.

Cosmic Background Explorer Satellite (COBE) launched in 1989 and revealed precise spectrum of CMB – best fit BB peaks at 2.725K. At what z would CMB have formed then?

CMB should be generally isotropic but high sensitivity observations with COBE revealed small anisotropies

Major source of anisotropy is Earth’s (Sun, galaxy, cluster) motion wrt Hubble flow – Dipole Anisotropy

Galactic Plane

All sky plot of CMB radiation with bright regions (yellow) being hotter and dark regions being cooler than Tavg

Wilkinson Microwave Anisotropy Probe (WMAP)

Comparison of WMAP and COBE results minus dipole anisoptropy

Launched in 2001

First all-sky maps released in 2003

Last data release Jan 2011

WMAP orbits at the L2 lagrange point

Planck

Small scale fluctuations in the CMB map are ~10-5 the strength of the radiation itself.

The Planck mission released their map of the CMB in March of 2013

- geometry of universe – flat
- seeds of various scales of structure that we see
- measure of several cosmological parameters
- (Jarosik et al. 2010)

Power spectrum reveals relative intensities of fluctuations on different angular scales

The dominant angular scale fluctuation is the angle subtended by the sonic horizon at CMB. In a flat universe, where light will move in a straight line, this scale is roughly one degree. The relative amplitude of the second peak constrains the baryon density, while the third peak can be used to measure the total matter density. Meanwhile, the damping tail provides a cross-check on the above measurements.

Open Universe: photons move on diverging paths in a negatively curved space. Our ruler would appear to have a smaller angular size - location of the first peak would appear at smaller angular scales (grey line)

Closed Universe: Angle would appear larger (first peak shifted to the left)

Flat Universe: A flat universe – undistorted (red line)

http://map.gsfc.nasa.gov/mission/sgoals_parameters_geom.html for movie!

- dark matter and atoms become less dense as the universe expands
- photon and neutrino particles lose energy as the universe expands, so their energy density decreases faster than the matter.
- dark energy density does not appear to decrease
- it now dominates the universe even though it was a tiny contributor 13.7 billion years ago

- Another source of small scale anisotropy in the CMB that is not cosmological
- Compton scattering - gamma-ray strikes a low energy electron and becomes a lower frequency photon with excess energy going to the electron.
- Inverse Compton scattering - low energy photon scatters off a high energy electron, with the photon gaining energy and the electron losing it.
- SZ effect occurs when low energy CMB photons strike the hot gas within a cluster of galaxies and inverse Compton scattering takes some of the photons from the low energy side of the CMB blackbody and transfers them to the high energy side.

CMB Isotropy and Causality (the horizon problem)

Is the background radiation too isotropic?

Conditions should only be identical at different locations if they have some way of communicating with each other. Two objects separated by a distance greater than that which light can traverse cannot affect each other – Causality problem

θo = (1/a)*(t/to) is the maximum current separation between 2 points that could have been causally connected before decoupling.

What is the maximum angular separation for causality if the Universe is 13.7 Gyr old and was 372,000 years old at decoupling? (recall relationship between scale factor and temperature for radiation)

In the first three minutes, the Universe was hot enough for nuclear reactions to take place.

Protons and neutrons formed 2H (deuterium), 3He and 4He.

4He is most stable and, within 3 minutes, made up 25% of the Universe.

What determined the abundance of 4He? need to know Universal conditions (density, relative number of neutrons and protons) at T=109 K (about t ~ 200s). In a hot universe, equilibrium between protons and neutrons maintained by weak interactions:

Ratio of neutrons to protons is set when T < 1010K (less than 1s after BB when neutrinos decouple). Protons favored over neutrons because they are slightly lighter. Weak interactions stop and nn/np fixed at about 1/5.

Decay of free neutron (half-life 10.6 min)

Because 2H is so reactive, most neutrons in 2H will end up in 4He

In these terms, mass fraction of 4He is

Mass fraction in 4He is

Y = 2nn/(np+nn) = 2(nn/np)(1+nn/np)-1

Proton to neutron ratio set at 1/5 which yields Y ~ 0.3.

Actual value lower because D forming reaction is suppressed by the high photon to baryon ratio.

NL is number of light particles, like neutrinos. Best model fit for a relativistic gas (dominated by neutrino motions) is 3.

Final mixture of elements from BB depends on density at t = 1s when reactions started

4He is stable and depends more on the p/n ratio than the baryon density

- Deuterium drops sharply with density because greater density yields more particles to react with
- 3He has slightly less density dependence
- 7Li is heavier – higher density provides more reactions for building heavier elements. At very low density, Li is more abundant as well because it relies on reactions involving deuterium and there is more of that at the lowest densities.
- C, N and O increase for ρ > ρcrit (but still well below current observed values – most produced via stars )

Best density estimate from abundance data

Density of baryons

Much effort has gone into determining the ratio of D/H as a way to determine the density of baryons in the Universe. Current abundances of D are from BBN and stellar nucleosynthesis (which destroys D). Taking this into account, baryons make up ~5% of ρcrit.

Fundamental Particles and Forces Primer

- Leptons– do not interact by strong force – no internal structure
- Hadrons – strongly interacting – made of quarks
- Baryons – massive (n and p); composite fermions; made of 3 quarks
- Mesons– less massive; composite bosons; made of 2 quarks (don’t obey PE)

4 fundamental forces in nature by which particles interact

- Short range forces felt on scales of nuclei
- Long range forces fall as 1/r2
- Particles (bosons) carry the forces
- QED theory - photonscarry EM force (can be real or virtual photons)
- Massless graviton thought to carry gravity (so far undetected)
- Strong force (color force; QCD) carried by pion (gluons) and its mass is determined by the force range
- Weak force carried by massive W and Z particles (80 and 90 x proton mass))

Unification of Forces – are all forces a manifestation of one larger force?

Maxwell unified electricity and magnetic forces

Nobel prize in physics in 1979

Predictions of GUTs:

Decay of proton and magnetic monopole (not observed yet)

Energies must be even greater to unite the electroweak and strong forces

At higher energies forces are more unified

For the electroweak force to exist, the photon (massless) and W (or Z) particle (massive) must be indistinguishable. This can only happen when particle energy is greater than the difference in mass (nature is symmetric as long as there is enough energy). This occurred briefly in the early Universe....

Re-examining the Universe timeline…

- Begin at Planck Time (light travel time across a Planck length where Rs is equivalent to particle wavelength), GR breaks down – cannot probe history further
- High temps allow for GUT. Particles, anti-particles and photons are created and annihilated. Baryon number was not conserved.
- Symmetry breaking as the Universe cools produces slight excess of matter over antimatter - one excess particle for every 1010 particle-antiparticle pairs produced (explains ~1010 photons for every baryon in the Universe).
- Universe cools (at 10-36 s after BB) to temp where color (strong) and electroweak forces separate (end of GUT). Baryon number now conserved.

During time of GUTs, the vacuum of the Universe was not really a vacuum

It is theorized that the nature of vacuum changed during this time (like a phase transition from liquid to gas state of water)

Resulted in extremely rapid expansion of vacuum. Scale factor underwent exponential growth (1026 growth in 10-32 s)

Solves flatness problem - inflation drives the universe towards critical density - stretches any initial curvature of the universe to near flatness.

Solves causality/horizon problem – everything within horizon was closer together in the past and in causal contact.

Re-examining the Universe timeline…

- By 10-12 s, Universe cools to temp allowing for separation of EM and weak forces (average energy is comparable to mass of W particle ~ 100 GeV).
- Hot Universe allows quarks to move as in a fluid until 10-5 s. Then quarks are confined to hadrons.
- Lepton Era – when Universe is dominated by leptons (electrons, neutrinos)
- Weak force continues to weaken w.r.t. EM force. At 1s it is weak enough that neutrinos are rarely absorbed by matter (matter-neutrino decoupling – sets proton/neutron ratio). This occurs during BB nucleosynthesis.

Why do we believe the Big Bang model?

1. provides a natural explanation for the observed expansion of the universe

2. explains the observed abundance of helium via cosmological production of light elements. Indeed, the high helium abundance cannot be explained via stellar nucleosynthesis, but explained well if one assumes that it was produced at early times when the universe was hot enough for fusion.

3. explains the cosmic microwave background. The CMB is a natural consequence of the cooling expansion.

4. provides a framework for understanding structure formation. Initial fluctuations (from whatever origin) remain small until recombination, after which they grow via gravity to produce stars, galaxies, and other observed structure. Numerical simulations show that this works remarkably well given (a) a prescription for the power spectrum of the initial fluctuations, and (b) inclusion of non-baryonic dark matter.

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