Big Bang and Cosmic Microwave Background Radiation

Universe: Matter, Geometry, Big Bang, and Inflation

Overview of the Big Bang

• The Big Bang is characterized as the beginning of the Universe, a phase that was very hot, dense, and compact.

• Since that time, the Universe has been cooling and expanding.

• The Big Bang theory does not explain what triggered the event itself.

Main Observations Explained by the Big Bang Theory

• The Big Bang theory is supported by several key observations which are considered pillars of the theory, including:
    - Expansion of the Universe:
      - Edwin Hubble's observations in the 1920s regarding the distances to galaxies and Slipher's measurements of redshifts led to the conclusion of the Universe's expansion.
      - Einstein's General Theory of Relativity supports this as it suggests that the universe is in motion.
      - In 1927, Georges Lemaître found solutions to Einstein's equations that described an expanding space.
  
    - Primordial Nucleosynthesis:
      - In the 1940s, George Gamow, a Russian physicist, sought to explain how foundational elements were formed.
      - He proposed a very hot phase during the early Universe's development, leading to nuclear reactions that formed heavier nuclei from protons and neutrons.
      - The Big Bang model posits that during this phase, matter was crunched together at high density and temperature.
      - This model is known as the "Hot Big Bang".
      - The predictions include the formation of hydrogen, helium, deuterium, and lithium.
  
    - Cosmic Background Radiation (CMB):
      - This is the residual radiation from the Big Bang, providing strong evidence for the Big Bang theory.

Expansion of the Universe

• The expansion of the Universe implies that galaxies are moving away from each other.

• Key figures:
    - Hubble's Law describes the rate of this expansion.
    - The observed redshift in spectra from distant galaxies correlates with their speed away from us.

Primordial Nucleosynthesis

• Occurred roughly 3 minutes after the Big Bang, when temperatures rapidly cooled from roughly $10^{32}$ K to $10^{9}$ K.

• Nucleosynthesis refers to the production of light elements during this brief period. This process included:
    - The combination of protons and neutrons to form deuterium ($D$):
      - $D$ = 1 proton + 1 neutron
    - Deuterium then combined with other protons and neutrons to produce helium and a small amount of tritium (1 proton + 2 neutrons).
    - Lithium-7 formations can arise from the fusion of tritium and deuterium:
      - $Li_7$ = 1 tritium + 2 deuterium nuclei

Predictions of Element Abundances

• The Big Bang theory predicts about 75% hydrogen and 25% helium by mass.

• These predictions match observations of nearly primordial gases.

• The amount of deuterium produced in this early phase depends on the Universe's density.

• High density leads to complete conversion of deuterium into helium, while in a low-density Universe, some deuterium remains.

Evidence for the Big Bang Theory

1. Abundance of Light Elements:
      - The predictions regarding hydrogen, helium, and deuterium abundances align closely with observations.

2. Cosmic Microwave Background Radiation (CMB):
      - Detected as leftover radiation from the Big Bang.

Photon Behavior in Early Universe

• In the early Universe, energy levels were so high that photons could convert into particle-antiparticle pairs, and vice versa.

• The early Universe was an energetic soup of particles and radiation due to its high temperature.

Production of Elements

• Nucleosynthesis at about three minutes post-Big Bang is crucial for the formation of stable helium nuclei when the Universe was approximately three minutes old.

• The density of the Universe at that phase influences the amount of deuterium versus helium formed.

Quasar Observations

• Quasars are used to measure primordial deuterium abundances as a test of the Big Bang theory.

• Detections imply a cosmic background temperature consistent with standard Big Bang cosmology.

• Measurements via the Sloan Digital Sky Survey reflect the conditions of the Universe at approximately 800 million years old.

Formation of Stable Atoms

• Initially, the Universe contained free protons, electrons, and other particles.

• The cooling of the Universe allowed stable atoms to form through the capture of electrons.

• This process marked a fundamental change in the Universe, allowing radiation to travel freely, making the Universe transparent.

Cosmic Microwave Background Radiation

• The CMB represents the radiation released after the Universe became cool enough for electrons and protons to combine into neutral atoms.

• Detected in 1965 by Arno Penzias and Robert Wilson at Bell Labs, earning them a Nobel Prize.

• The CMB is characterized by a blackbody spectrum at approximately 2.725 K.

• Originally, it emitted from a temperature of about 3000 K, redshifted over time to current levels.

Key Characteristics of CMB

• The wavelengths of CMB have been stretched due to the expansion of the Universe.

• The blackbody spectrum predicted by Gamow and Alpher was confirmed by CMB observations.

Uniformity and Fluctuations

• The CMB is uniform across the sky with tiny fluctuations that provide insights into the Universe's composition and structure.

• Instruments like COBE, WMAP, and Planck detect these fluctuations, offering clues about the early Universe's density and matter distribution.

Understanding Universe Expansion

• The universe expands into itself.

• Two-dimensional models, such as the balloon analogy, illustrate how the Universe does not need a pre-existing void or a center to expand from.

Closed, Open, and Flat Universe Models

• Closed Universe:
    - No center or edge, curves back onto itself.

• Open Universe:
    - Expands indefinitely without boundaries or a defined center.

• Flat Universe:
    - Demonstrated by the distribution of galaxies and CMB fluctuations, suggesting an infinite future of expansion.