9.3 Recombination and decoupling

Recombination and decoupling marked a pivotal moment in the early universe. As the cosmos cooled, electrons and protons combined to form neutral hydrogen, allowing photons to travel freely for the first time.

This event, occurring about 380,000 years after the Big Bang, gave birth to the cosmic microwave background radiation. The CMB provides a snapshot of the early universe, offering crucial insights into its composition and evolution.

Recombination in the early universe

• Recombination is a critical event that occurred approximately 380,000 years after the Big Bang, marking a significant transition in the evolution of the universe
• During this period, the universe had cooled sufficiently to allow electrons and protons to combine, forming neutral hydrogen atoms
• This process had far-reaching consequences for the structure and observability of the universe, setting the stage for the formation of the first stars and galaxies

Cosmic microwave background radiation

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• Cosmic microwave background (CMB) radiation is the remnant heat from the Big Bang, which permeates the entire universe
• As the universe expanded and cooled, the CMB photons red-shifted to microwave wavelengths, corresponding to a temperature of about 2.7 Kelvin
• The CMB provides a snapshot of the universe at the time of recombination, offering invaluable insights into the early universe and the distribution of matter and energy

Photon decoupling

• Photon decoupling occurred during the epoch of recombination, when the universe became transparent to photons
• Prior to recombination, photons were tightly coupled to the plasma of electrons and protons through Thomson scattering
• As neutral hydrogen formed, the mean free path of photons increased dramatically, allowing them to travel freely through the universe without further interaction with matter

Stages of recombination

• Recombination is a multi-stage process that involves the progressive capture of electrons by protons, leading to the formation of neutral hydrogen atoms
• The stages of recombination are governed by the interplay between the expansion and cooling of the universe, as well as the interactions between photons, electrons, and protons
• Understanding the stages of recombination is crucial for interpreting the observed properties of the cosmic microwave background and the large-scale structure of the universe

Saha equation for ionization fraction

• The Saha equation describes the ionization fraction of a gas in thermal equilibrium, taking into account the balance between ionization and recombination processes
• In the context of the early universe, the Saha equation is used to calculate the fraction of free electrons and protons as a function of temperature and density
• The ionization fraction plays a key role in determining the timing and duration of the recombination epoch, as well as the opacity of the universe to photons

Electron capture by protons

• Electron capture by protons is the primary mechanism for the formation of neutral hydrogen during recombination
• As the universe cools, free electrons are captured by protons through radiative recombination, releasing photons in the process
• The rate of electron capture depends on the temperature, density, and the availability of free electrons and protons

Formation of neutral hydrogen

• The formation of neutral hydrogen marks the end of the recombination epoch and the beginning of the neutral universe
• Neutral hydrogen atoms are stable against ionization by the ambient radiation field, allowing them to persist and accumulate over time
• The formation of neutral hydrogen sets the stage for the subsequent evolution of the universe, including the formation of the first stars and galaxies through gravitational collapse

Temperature evolution during recombination

• The temperature of the universe plays a crucial role in the recombination process, as it determines the energy of photons and the kinetic energy of particles
• As the universe expands, it undergoes adiabatic cooling, with the temperature decreasing as a power law with the scale factor
• The temperature evolution during recombination is closely tied to the expansion history of the universe and the relative contributions of matter and radiation to the total energy density

Expansion and cooling of the universe

• The expansion of the universe is driven by the combined effects of matter, radiation, and dark energy
• As the universe expands, it undergoes adiabatic cooling, with the temperature decreasing inversely with the scale factor
• The cooling of the universe during recombination is a gradual process, with the temperature dropping from around 3000 Kelvin to 3 Kelvin over a period of about 100,000 years

Matter-radiation equality

• Matter-radiation equality is the epoch at which the energy densities of matter and radiation are equal
• This occurs at a redshift of approximately 3400, corresponding to a temperature of around 9000 Kelvin
• The matter-radiation equality marks a transition in the expansion history of the universe, with matter dominating the energy density at later times and radiation dominating at earlier times

Effects of recombination on the universe

• Recombination had profound effects on the structure and observability of the universe, setting the stage for the formation of the first stars and galaxies
• The formation of neutral hydrogen during recombination allowed the universe to become transparent to photons, enabling the propagation of light across vast distances
• Recombination also marked the end of the dark ages, a period during which the universe was opaque to visible light and dominated by neutral hydrogen

Transparency of the universe

• Prior to recombination, the universe was opaque to photons due to the high density of free electrons, which scattered photons through Thomson scattering
• As neutral hydrogen formed during recombination, the mean free path of photons increased dramatically, allowing them to travel freely through the universe
• The transparency of the universe after recombination enabled the formation and observation of the cosmic microwave background, as well as the propagation of light from distant galaxies

End of the dark ages

• The dark ages refer to the period between the time of recombination and the formation of the first stars and galaxies
• During the dark ages, the universe was filled with neutral hydrogen and devoid of visible light sources
• Recombination marked the end of the dark ages, as the formation of neutral hydrogen set the stage for the gravitational collapse of matter and the ignition of the first stars

Birth of the cosmic microwave background

• The cosmic microwave background (CMB) is the remnant heat from the Big Bang, which was released at the time of recombination
• As the universe became transparent to photons during recombination, the CMB photons were able to propagate freely through the universe
• The CMB provides a snapshot of the universe at the time of recombination, encoding information about the distribution of matter and energy, as well as the geometry and expansion history of the universe

Observational evidence of recombination

• The observational evidence for recombination comes primarily from the cosmic microwave background (CMB) radiation, which provides a direct probe of the universe at the time of recombination
• The CMB has been extensively studied by satellite missions such as COBE, WMAP, and Planck, providing unprecedented insights into the properties of the early universe
• The observational evidence of recombination supports the standard model of cosmology and provides stringent constraints on the parameters describing the universe

Cosmic microwave background spectrum

• The CMB spectrum follows a nearly perfect black-body distribution, with a temperature of 2.725 ± 0.001 Kelvin
• The black-body nature of the CMB spectrum is a direct consequence of the thermal equilibrium between photons and matter in the early universe
• Deviations from the black-body spectrum, such as the Sunyaev-Zel'dovich effect, provide additional information about the intervening matter between the CMB and observers

Anisotropies in the cosmic microwave background

• The CMB is not perfectly uniform, but exhibits small temperature fluctuations on the order of 1 part in 100,000
• These anisotropies arise from quantum fluctuations in the early universe, which were amplified by cosmic inflation and imprinted on the CMB at the time of recombination
• The angular power spectrum of the CMB anisotropies encodes information about the geometry, content, and evolution of the universe, providing a powerful probe of cosmological parameters

Cosmological parameters from the cosmic microwave background

• The CMB anisotropies can be used to constrain a wide range of cosmological parameters, including the age, geometry, and composition of the universe
• Precise measurements of the CMB power spectrum by satellite missions such as Planck have provided the most accurate determinations of parameters such as the Hubble constant, the baryon density, and the dark energy equation of state
• The consistency between CMB-derived parameters and those obtained from other cosmological probes, such as galaxy surveys and gravitational lensing, provides strong support for the standard model of cosmology