9.1 Primordial nucleosynthesis

Primordial nucleosynthesis shaped the early universe, creating the building blocks of matter. This process, occurring shortly after the Big Bang, formed most of the universe's hydrogen and helium, along with trace amounts of lithium.

The timeline of nucleosynthesis spans several epochs, from the Planck epoch to the photon epoch. Each stage played a crucial role in setting the conditions for element formation and the universe's eventual structure.

Origin of primordial nucleosynthesis

• Primordial nucleosynthesis is the process by which light elements were formed in the early universe, shortly after the Big Bang
• It is responsible for the production of the vast majority of the universe's hydrogen and helium, as well as trace amounts of lithium
• The process began when the universe had cooled sufficiently for protons and neutrons to combine into atomic nuclei without being immediately broken apart by high-energy photons

Timeline of nucleosynthesis

Planck epoch

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• The Planck epoch represents the earliest stage of the universe, lasting from time zero to approximately $10^{-43}$ seconds after the Big Bang
• During this period, the universe was an extremely hot and dense state where the four fundamental forces (gravity, electromagnetism, strong and weak nuclear forces) were unified
• The physics of this epoch is not well understood as it requires a theory of quantum gravity to fully describe

Grand unification epoch

• The grand unification epoch followed the Planck epoch and lasted until around $10^{-36}$ seconds after the Big Bang
• During this time, the strong nuclear force separated from the other fundamental forces, while the electroweak force (a unification of electromagnetism and the weak nuclear force) remained unified
• The universe underwent a period of exponential expansion called cosmic inflation, which helped explain the observed homogeneity and flatness of the universe

Electroweak epoch

• The electroweak epoch spans from the end of the grand unification epoch to about $10^{-12}$ seconds after the Big Bang
• In this period, the electroweak force split into the electromagnetic and weak nuclear forces as the universe continued to cool and expand
• The Higgs field, responsible for giving particles their mass, became non-zero during this epoch

Quark epoch

• The quark epoch lasted from the end of the electroweak epoch until approximately $10^{-6}$ seconds after the Big Bang
• Quarks, the fundamental building blocks of matter, were the dominant particles during this time
• As the universe cooled, quarks began to form hadrons, such as protons and neutrons, through a process called hadronization

Hadron epoch

• The hadron epoch occurred between $10^{-6}$ and $1$ second after the Big Bang
• During this period, hadrons (including protons and neutrons) were the most abundant particles in the universe
• The universe was still too hot for hadrons to form stable atomic nuclei, as they would be immediately broken apart by high-energy photons

Lepton epoch

• The lepton epoch lasted from the end of the hadron epoch to around $10$ seconds after the Big Bang
• Leptons, such as electrons and neutrinos, were the most abundant particles during this time
• The universe continued to cool, allowing for the formation of stable protons and neutrons

Photon epoch

• The photon epoch began at the end of the lepton epoch and lasted until approximately 380,000 years after the Big Bang
• During this period, photons were the dominant form of energy in the universe
• As the universe expanded and cooled, nucleosynthesis began, allowing for the formation of the first atomic nuclei

Conditions for nucleosynthesis

Temperature

• Nucleosynthesis could only occur once the universe had cooled sufficiently, to around $10^9$ K (1 billion degrees Kelvin)
• At higher temperatures, the energy of photons was too great, preventing the formation of stable atomic nuclei
• As the universe expanded and cooled, the average energy of photons decreased, allowing nuclei to form without being immediately broken apart

Density

• The density of the universe during nucleosynthesis was much higher than it is today, approximately $10^{-5}$ g/cm³ (0.00001 grams per cubic centimeter)
• This high density was necessary to ensure that protons and neutrons collided frequently enough to form atomic nuclei
• As the universe expanded, the density decreased, eventually becoming too low for further nucleosynthesis to occur

Expansion rate

• The expansion rate of the universe during nucleosynthesis was a critical factor in determining the relative abundances of elements produced
• A faster expansion rate would have resulted in a higher proportion of hydrogen, as there would have been less time for heavier elements to form before the density and temperature became too low
• The observed abundances of light elements provide evidence for the expansion rate of the universe during this period

Elements produced by nucleosynthesis

Hydrogen

• Hydrogen is the most abundant element in the universe, making up approximately 75% of the universe's baryonic matter by mass
• During nucleosynthesis, most free protons remained uncombined due to the rapid expansion and cooling of the universe
• These protons later combined with electrons to form neutral hydrogen atoms during the epoch of recombination

Helium

• Helium is the second most abundant element, constituting about 25% of the universe's baryonic matter by mass
• Most of the universe's helium was produced during primordial nucleosynthesis through the fusion of deuterium (an isotope of hydrogen) and helium-3
• The formation of heavier elements was limited by the rapid expansion and cooling of the universe

Lithium

• Trace amounts of lithium, specifically the isotopes lithium-6 and lithium-7, were produced during primordial nucleosynthesis
• The abundance of lithium is much lower than that of hydrogen and helium, as the formation of lithium requires the fusion of more complex nuclei
• The observed abundance of lithium is lower than predicted by standard Big Bang nucleosynthesis models, a discrepancy known as the "lithium problem"

Heavier elements

• Elements heavier than lithium were not produced in significant quantities during primordial nucleosynthesis
• The formation of these elements requires higher temperatures and densities than those present in the early universe
• Most heavy elements were later synthesized in the cores of stars and during stellar explosions, such as supernovae

Abundance of elements

Hydrogen vs helium

• The relative abundances of hydrogen and helium produced during primordial nucleosynthesis are approximately 75% and 25% by mass, respectively
• This ratio is determined by the expansion rate of the universe and the number of protons and neutrons available for fusion
• The observed abundances of hydrogen and helium in the universe closely match the predictions of Big Bang nucleosynthesis, providing strong evidence for the theory

Lithium problem

• The observed abundance of lithium in the universe is lower than predicted by standard Big Bang nucleosynthesis models
• This discrepancy is known as the "lithium problem" and suggests that either the models are incomplete or there are additional processes that have depleted the primordial lithium abundance
• Possible explanations include the decay of unstable particles, variations in the fundamental constants, or the presence of stellar processes that have destroyed lithium

Evidence for nucleosynthesis

Cosmic microwave background

• The cosmic microwave background (CMB) radiation is the remnant heat from the early universe, observed as a nearly uniform background of microwave radiation
• The CMB provides information about the conditions of the universe approximately 380,000 years after the Big Bang, during the epoch of recombination
• The observed properties of the CMB, such as its temperature and small anisotropies, are consistent with the predictions of Big Bang nucleosynthesis

Primordial abundances

• The observed abundances of light elements (hydrogen, helium, and lithium) in the universe closely match the predictions of Big Bang nucleosynthesis
• These abundances have been measured in various astrophysical environments, such as distant galaxies, intergalactic gas, and old, metal-poor stars
• The agreement between the predicted and observed abundances provides strong evidence for the occurrence of primordial nucleosynthesis and supports the Big Bang theory

Role in structure formation

Jeans mass

• The Jeans mass is the minimum mass required for a gravitationally bound object to overcome internal pressure and collapse under its own gravity
• The value of the Jeans mass depends on the temperature and density of the object, which are influenced by the abundances of elements produced during primordial nucleosynthesis
• The presence of heavier elements, such as helium, increases the Jeans mass, as these elements are more efficient at cooling and allowing gas clouds to collapse

Cooling mechanisms

• The formation of structures in the universe, such as galaxies and stars, requires the cooling of gas clouds to allow for gravitational collapse
• The primary cooling mechanisms in the early universe were dependent on the abundances of elements produced during primordial nucleosynthesis
• Hydrogen and helium, the most abundant elements, cooled through radiative processes such as atomic line emission and recombination radiation, enabling the formation of the first stars and galaxies

Alternatives to Big Bang nucleosynthesis

Steady state theory

• The steady state theory proposes that the universe has always existed in a steady state, with no beginning or end
• In this model, matter is continuously created to maintain a constant average density as the universe expands
• The steady state theory has been largely discarded due to observations that contradict its predictions, such as the existence of the cosmic microwave background and the evolution of galaxies over time

Oscillating universe models

• Oscillating universe models suggest that the universe undergoes cycles of expansion and contraction, with each cycle beginning with a "Big Bang" and ending with a "Big Crunch"
• In these models, primordial nucleosynthesis would occur during the early stages of each expansion phase
• While oscillating universe models have been proposed as alternatives to the standard Big Bang theory, they face challenges in explaining observed features of the universe, such as the second law of thermodynamics and the apparent fine-tuning of cosmological parameters