Big Bang Theory & Cosmology — Comprehensive Study Notes

• The Big Bang Theory posits that the universe began as a singular point approximately 13.8 billion years ago, and has been expanding ever since.

• Key evidence for this theory includes the Cosmic Microwave Background Radiation (CMBR), which is the afterglow of the initial explosion, and the observed redshift of distant galaxies.

Inspirational Quotation (Stephen Hawking)

• "One may think that time had a beginning at the Big Bang … One can imagine that God created the universe at literally anytime in the past… if the universe is expanding, there may be physical reasons why there had to be a beginning."
  • Brings in philosophical/theological reflection on time, creation, and cosmology.

Early Astronomical Observations

• Early 20th-century telescopes showed “fuzzy patches”—now known to be other galaxies.

• 1920: Edwin Hubble used a 2.5\,\text{m} telescope at Mt. Wilson to confirm these were separate “island universes.”

• Hubble’s spectroscopic studies led to the redshift–distance relationship (galaxies recede faster the farther away they are).

Formulation of the Big Bang Idea

• 1948: George Gamow, Ralph Alpher, Hans Bethe (often nick-named the “αβγ paper”) proposed that the universe began in a gigantic explosion from a hot, dense state.

• Pre-Bang state: “tiny volume,” “unimaginably hot,” “burning fireball of radiation mixed with minute particles of matter.”

• Cooling enabled atoms to form; gravity later clumped these atoms into billions of galaxies.

Evidence Supporting Gamow’s Hypothesis

1. Universal Expansion
   • Spectroscopic redshift data.
   • Direct imaging with large ground telescopes and later the Hubble Space Telescope (HST).

2. Cosmic Microwave Background Radiation (CMBR)
   • Predicted relic of the hot early universe, now cooled to about T \approx 3\,\text{K} (\approx -270^{\circ}\text{C}).
   • 1964: Arno Penzias & Robert Wilson (Bell Labs) accidentally measured microwaves with \lambda = 7.35\,\text{cm} coming uniformly from all directions ⇒ isotropic background.
   • Later space missions (WMAP, Planck) mapped tiny anisotropies (\Delta T/T \sim 10^{-5}).

3. Primordial Element Abundances
   • Dominance of hydrogen (H) and helium (He).
   • 1995: Ultraviolet spectra of a distant quasar (>10^{10} light-years) showed absorption by singly-ionized He, confirming its early-epoch presence.
   • Rationale for H nondetection: H has only one electron; quasar photons easily ionize it (photo-ionization), making neutral H scarce along the line of sight.

Cosmic Microwave Background Radiation (CMBR) Details

• Any object above 0\,\text{K} emits thermal radiation; the universe itself is the object.

• CMBR spectrum is an almost perfect blackbody; peak wavelength \lambda{\text{max}} satisfies \lambda{\text{max}} T \approx 2.9\times10^{-3}\,\text{m·K} (Wien’s Law).

• Uniformity across the sky supports an early, hot, well-mixed universe; slight anisotropies seed large-scale structure.

Big Bang Nucleosynthesis (BBN): Formation of Light Elements

• Timeframe: \sim 10^{-2} s to \sim 10^{3} s after t=0.

• Key steps:
  • p^+ + n^0 \leftrightarrow D + \gamma (deuterium formation).
  • Helium-3, helium-4, and trace lithium-7 subsequently produced by fusion pathways.

• Predicted mass fractions:
  X{\text{H}} \approx 0.75, Y{\text{He}} \approx 0.25, Z_{\text{others}} < 10^{-2}.

• Matches modern observations (next section).

Current Elemental Composition of the Universe

• Atom number abundance (sciencenotes.org slide):
  • \approx 92\% hydrogen, 7.1\% helium.

• Mass fraction slide:
  • Hydrogen \approx 75\%, Helium \approx 23\%.
  • Heavier elements ("metals" in astronomy): oxygen 1\%, carbon 0.5\%, neon 0.1\%, iron 0.1\%, nitrogen 0.1\%, all others 0.2\%.

Formation of Heavier Elements (preview for assignment)

• Not created in BBN because density & time too small once T dropped.

• Stellar nucleosynthesis: stars fuse H → He → C, O, etc.

• Supernova nucleosynthesis and neutron-star mergers forge elements heavier than Fe via s- and r-processes.

• Heavy elements are crucial for rocky planets, biochemistry (C-based life), and technological materials (Fe, Si, etc.).

Sample Review Questions (from Q&A Session)

1. Hubble’s observation of galaxies moving away implies the universe is expanding (answer b).

2. Gamow’s origin model: hot, dense state → Big Bang (answer c).

3. Evidence set: a, b, c are correct; d is incorrect because heavier elements were not formed simultaneously with H & He.

4. Afterglow of the Big Bang: cosmic background radiation (answer d).

5. Detection difficulty for H: it has one electron easily stripped off (answer b).

Ethical, Philosophical & Theological Considerations

• Hawking quote juxtaposes scientific need for an initial singularity with possibility of divine creation “at any time.”

• Benedictine context encourages viewing science and faith as complementary, fostering responsible stewardship of knowledge.

• Humility before cosmic vastness; responsibility to use scientific insight for peace (aligns with PAX).

Numerical & Statistical References (consolidated)

• Telescope aperture: 2.5\,\text{m} (Mt. Wilson).

• CMBR temperature: T = 2.725\,\text{K} (approx 3\,\text{K}).

• Wavelength detected by Penzias & Wilson: \lambda = 7.35\,\text{cm}.

• Look-back time of quasar study: >10^{10}\,\text{yr}.

• CMBR anisotropy: \Delta T/T \sim 10^{-5}.

• Hydrogen mass fraction: X \approx 0.75; Helium: Y \approx 0.23.

Glossary

• Redshift (z) – Dimensionless measure of wavelength stretching z = (\lambda{\text{obs}}-\lambda{\text{emit}})/\lambda_{\text{emit}}.

• CMBR – Cosmic Microwave Background Radiation, the thermal relic at \approx 3\,\text{K}.

• Big Bang Nucleosynthesis (BBN) – Era of element formation within first minutes.

• Quasar – Extremely luminous active galactic nucleus used as a cosmic backlight.

• Ionization – Removal of an electron (e.g., \text{H} \to p^+ + e^-).

Study Tips

• Relate each piece of evidence to a specific prediction of the Big Bang model.

• Practice converting between Kelvin and Celsius using T(^{\circ}\text{C}) = T(\text{K}) - 273.15.

• Draw a timeline: 10^{-43}\,\text{s} (Planck), 10^{-4}\,\text{s} (BBN onset), 380{,}000\,\text{yr} (CMBR release), \sim 10^{8}\,\text{yr} (first galaxies).

• Prepare to explain why heavier elements require stellar environments (Coulomb barrier & longer timescales).