12.4 Big Bang Theory and Cosmic Microwave Background

The Big Bang Theory

Fundamental Concepts and Key Features

The Big Bang theory proposes that the universe began from an extremely hot, dense state approximately 13.8 billion years ago and has been expanding ever since. All matter, energy, space, and time originated from a singularity that rapidly expanded. This isn't an explosion into existing space; space itself was created and stretched in the process.

A critical early phase called cosmic inflation involved rapid exponential expansion during the first fraction of a second. Inflation explains two otherwise puzzling observations: why the universe appears so uniform in every direction, and why its geometry is so close to flat.

During the first few minutes after the Big Bang, a process called Big Bang nucleosynthesis produced the lightest elements:

• Hydrogen (about 75% by mass)
• Helium (about 25%)
• Trace amounts of lithium and deuterium

These predicted abundances match what we actually observe in the universe today, which is strong evidence for the theory.

On the largest scales, the universe's expansion is accelerating. This is attributed to dark energy, a poorly understood component that counteracts gravity's attractive pull. Dark energy makes up roughly 68% of the universe's total energy content.

Theoretical Implications and Consequences

The Big Bang carries several important consequences:

• The universe has a finite age rather than existing eternally.
• All regions of the observable universe were once close enough to exchange energy and information, despite being vastly separated today. Inflation stretched these once-connected regions apart.
• The theory predicts a relic glow from the early universe: the cosmic microwave background radiation.
• Distant galaxies show redshift proportional to their distance, which is a direct result of the expansion of space itself.
• Initial quantum fluctuations in the early universe grew over billions of years into the galaxies and galaxy clusters we see now.
• Olbers' paradox asks: if the universe is infinite and full of stars, why is the night sky dark? The Big Bang resolves this because the universe has a finite age and is expanding, so light from the most distant sources hasn't reached us or has been redshifted out of the visible range.

Evidence for the Big Bang

Observational Support

Several independent lines of evidence converge to support the Big Bang:

• Expansion of the universe: Distant galaxies are redshifted, meaning their light is stretched to longer wavelengths. The farther away a galaxy is, the faster it recedes. This is exactly what an expanding universe predicts.
• Cosmic microwave background (CMB): Discovered in 1964 by Arno Penzias and Robert Wilson, this faint microwave glow fills the entire sky. It's the cooled remnant of the hot plasma that filled the early universe.
• Light element abundances: The observed ratio of hydrogen to helium (and trace deuterium and lithium) across the universe closely matches what nucleosynthesis calculations predict for the first few minutes after the Big Bang.
• Large-scale structure: The distribution of galaxies and galaxy clusters across the sky matches what simulations predict when starting from small density fluctuations in an expanding universe.
• Olbers' paradox: The darkness of the night sky is naturally explained by a universe with a finite age and ongoing expansion.
• Gravitational waves: Detections in recent years are consistent with violent events predicted by general relativity, and certain signatures could provide additional support for the inflationary period.

Detailed Analysis of Evidence

• The CMB exhibits a nearly perfect blackbody spectrum at a temperature of about $2.7 \text{ K}$. No known process other than the cooling of a hot, dense early universe can produce such a precise blackbody over the entire sky.
• Hubble's law describes the linear relationship between a galaxy's distance $d$ and its recessional velocity $v$: $v = H_0 \, d$, where $H_0$ is the Hubble constant.
• The primordial abundance of deuterium is especially useful because deuterium is fragile and easily destroyed in stars. Its observed abundance acts as a sensitive probe of conditions during nucleosynthesis.
• Baryon acoustic oscillations (BAOs) are regular patterns in the distribution of galaxies. They originated as sound waves in the early universe plasma and were frozen in place at recombination, providing a "standard ruler" for measuring cosmic distances.
• The Lyman-alpha forest, a series of absorption lines in quasar spectra, traces the distribution of neutral hydrogen along the line of sight, consistent with Big Bang predictions for how matter is distributed.
• High-redshift quasars and galaxies confirm that structure was already forming in the first billion years, as the theory predicts.

The Universe's Timeline

Early Epochs and Fundamental Forces

The earliest moments of the universe involved extreme conditions where the fundamental forces separated one by one:

1. Planck era ($0$ to $10^{-43}$ s): The earliest conceivable period. Temperatures and densities are so extreme that current physics breaks down. A theory of quantum gravity would be needed to describe this era.
2. Grand Unification era ($10^{-43}$ to $10^{-36}$ s): Gravity separates from the other three fundamental forces, which remain unified.
3. Inflationary epoch ($10^{-36}$ to $10^{-32}$ s): The universe undergoes rapid exponential expansion, increasing in size by a factor of at least $10^{26}$. This smooths out irregularities and sets the stage for later structure formation.
4. Electroweak era ($10^{-32}$ to $10^{-12}$ s): The strong nuclear force separates from the electroweak force.
5. Quark confinement ($10^{-12}$ to $10^{-6}$ s): As the universe cools, quarks can no longer exist freely. They combine to form hadrons, including protons and neutrons.

Later Stages and Structure Formation

After the first second, the timeline stretches out dramatically:

• Big Bang nucleosynthesis (3 to 20 minutes): Protons and neutrons fuse into light nuclei. The universe produces roughly 75% hydrogen and 25% helium by mass, with traces of deuterium and lithium.
• Recombination (~380,000 years): The universe cools enough (to about $3000 \text{ K}$) for electrons to combine with nuclei and form neutral atoms. Photons decouple from matter and stream freely across space. This is the light we now detect as the CMB.
• Dark Ages (380,000 years to ~400 million years): No stars exist yet. The universe is filled with neutral hydrogen gas, slowly cooling and expanding.
• Reionization (~400 million to 1 billion years): The first stars and galaxies ignite, and their ultraviolet radiation ionizes the surrounding neutral hydrogen.
• Galaxy formation and evolution (1 billion years to present): Structures grow through hierarchical clustering, with smaller galaxies merging to form larger ones.
• Solar System formation (~4.6 billion years ago): Our solar system forms within the Milky Way from a collapsing cloud of gas and dust.
• Present day (13.8 billion years): The universe continues to expand at an accelerating rate.

Cosmic Microwave Background Radiation

Characteristics and Significance

The cosmic microwave background (CMB) is a snapshot of the universe at the moment of recombination, roughly 380,000 years after the Big Bang. Before this point, the universe was an opaque plasma of charged particles. Once neutral atoms formed, photons could travel freely, and those photons have been streaming through space ever since, cooling as the universe expanded.

Key properties of the CMB:

• It has a nearly perfect blackbody spectrum at $T \approx 2.725 \text{ K}$, confirming that the early universe was hot and dense.
• Tiny temperature fluctuations of about 1 part in $10^5$ reveal slight density variations in the early universe. These small over-densities eventually grew, under gravity, into galaxies and galaxy clusters.
• The angular size of these fluctuations tells us about the geometry of the universe. The observed pattern is consistent with a spatially flat universe.
• Polarization patterns in the CMB carry additional information. E-mode polarization has been measured and confirms the standard model. B-mode polarization, if detected from the inflationary era, would provide direct evidence for primordial gravitational waves.
• The remarkable uniformity of the CMB across the entire sky supports cosmic inflation. Without inflation, regions on opposite sides of the sky would never have been in thermal contact, yet they share nearly identical temperatures.

Analysis and Cosmological Implications

Detailed analysis of the CMB power spectrum (a plot of temperature fluctuation strength versus angular scale) allows cosmologists to pin down fundamental parameters of the universe:

• Age: $13.8$ billion years
• Composition: ~4.9% ordinary (baryonic) matter, ~26.8% dark matter, ~68.3% dark energy
• Expansion rate: Hubble constant $H_0 \approx 67.4 \text{ km/s/Mpc}$

Beyond these parameters, the CMB reveals several additional features:

• Acoustic oscillations in the early universe plasma left characteristic peaks in the power spectrum. These peaks correspond to sound waves that were "frozen" at recombination.
• The Sunyaev-Zel'dovich effect occurs when CMB photons scatter off hot electrons in galaxy clusters, slightly distorting the CMB spectrum in those directions. This allows detection of galaxy clusters even at great distances.
• CMB lensing, the subtle bending of CMB photons by intervening mass, maps out the distribution of dark matter along the line of sight.
• The CMB shows no significant large-scale non-Gaussianity, which supports the simplest models of inflation (single-field, slow-roll).
• Precise measurements of the CMB spectrum tightly constrain deviations from the standard $\Lambda$CDM model (Lambda Cold Dark Matter), which remains the best-fit description of our universe.