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