cosmological-observation

# Cosmological Observation

Modern cosmology is the shortest path from "what can I measure?" to "how old is the universe, what is it made of, and how does it end?" This skill covers the observational pillars: Hubble's law and redshift, the cosmic microwave background (CMB), Big Bang nucleosynthesis (BBN), large-scale structure, galaxy rotation curves as evidence for dark matter, Type Ia supernovae as evidence for dark energy, and the composition and parameters of the current concordance model (Lambda-CDM). It also covers the active frontier — the Hubble tension, the S8 tension, and the tests that could break or confirm Lambda-CDM in the next decade.

**Agent affinity:** hubble (expansion and distance), rubin (dark matter), burbidge (nucleosynthesis context)

**Concept IDs:** astro-big-bang, astro-dark-matter, astro-dark-energy, astro-cmb, astro-hubbles-law

## The Four Pillars of Big Bang Cosmology

1. **Hubble expansion** — galaxies recede with velocity proportional to distance
2. **Cosmic microwave background** — blackbody radiation at 2.725 K filling all space
3. **Big Bang nucleosynthesis** — observed primordial abundances of H, D, He-3, He-4, Li-7 match hot-early-universe predictions
4. **Large-scale structure** — galaxy distribution traces initial density fluctuations amplified by gravity

Any cosmological model that breaks one of these pillars is in serious trouble. Lambda-CDM — the current concordance model — was built to fit all four and has passed increasingly sharp tests from WMAP, Planck, BOSS, DES, and many others.

## Pillar 1 — Hubble's Law

In 1929 Edwin Hubble published a plot of galaxy distances (from Cepheid period-luminosity analysis) against their radial velocities (from spectroscopic redshift). He found:

    v = H_0 * d

with H_0 estimated at 500 km/s/Mpc. The slope was too steep by a factor of seven (the distance calibration had systematic errors that were later corrected), but the linear relation was real. Hubble had discovered that the universe is expanding.

**Modern H_0.** Local measurements (Cepheid + SN Ia): 73.0 +/- 1.0 km/s/Mpc. CMB + Lambda-CDM (Planck 2018): 67.4 +/- 0.5 km/s/Mpc. The 4-5 sigma discrepancy is the **Hubble tension**.

**Redshift.** For nearby galaxies, v = c z is a good approximation with z << 1. At cosmological distances, redshift is better interpreted as scale-factor expansion:

    1 + z = a_observed / a_emitted

where a is the cosmic scale factor. A redshift of z = 1 means the universe has doubled in size since the light was emitted; z = 1100 (the CMB redshift) means the universe was 1101 times smaller.

**Hubble flow vs. peculiar motion.** For galaxies within ~50 Mpc, local gravitational infall toward mass concentrations (the Virgo cluster, the Great Attractor) contributes velocities comparable to the Hubble flow. Cosmological H_0 measurements must avoid this regime or correct for it.

## Pillar 2 — The Cosmic Microwave Background

**Discovery.** Arno Penzias and Robert Wilson (Bell Labs, 1965) detected a 2.73 K excess signal in their horn antenna that they could not eliminate — not pigeons, not anything terrestrial. Simultaneously, Robert Dicke's group at Princeton had predicted such a signal would exist if the Big Bang were real: a blackbody radiation fossil from the era of recombination, cooled by cosmic expansion. The identification was immediate. Nobel Prize in Physics, 1978.

**Spectrum.** COBE FIRAS (Mather et al. 1994) measured the CMB spectrum to exquisite precision. It is a blackbody at T = 2.725 K with deviations smaller than 50 parts per million — the most perfect blackbody ever measured.

**Anisotropy.** The CMB is remarkably uniform but not perfectly so. After removing the dipole (from Earth's motion through the CMB rest frame) and the galactic plane foreground, anisotropies of order 10^-5 remain. These are the seeds from which all structure in the universe grew.

**Power spectrum.** Decompose the temperature anisotropies into spherical harmonics. The resulting power spectrum C_l has a series of **acoustic peaks** corresponding to sound waves in the photon-baryon plasma at recombination. The positions and heights of the peaks encode:

- **First peak angular scale:** total energy density / curvature (flat universe)
- **Relative heights of first and second peaks:** baryon density
- **Third peak:** matter density including dark matter
- **Damping tail:** helium fraction, neutrino background

WMAP (2001-2010) and Planck (2009-2013) have measured the CMB power spectrum from l ~ 2 to l ~ 2500 with percent-level precision, giving the parameters of Lambda-CDM to a few percent.

**Polarization.** The CMB is polarized at ~10% the level of the temperature anisotropies. E-mode polarization is produced by scalar density perturbations. B-mode polarization at large scales could come from primordial gravitational waves — a generic prediction of inflation — and its detection is a major target.

## Pillar 3 — Big Bang Nucleosynthesis (BBN)

At 1 second to 3 minutes after the Big Bang, the universe was hot enough for nuclear reactions but cooling rapidly. Protons and neutrons fused into light elements before the window closed. The predicted abundances depend on the baryon density:

- **He-4:** about 24% by mass
- **Deuterium (D):** D/H about 2.5 x 10^-5
- **He-3:** He-3/H about 10^-5
- **Li-7:** Li/H about 10^-10

These abundances are measured today in low-metallicity systems (to avoid stellar contamination) and the observed values match the BBN predictions when the baryon density is set to the value that the CMB also prefers. The agreement is one of the strongest confirmations that we understand the first few minutes of the universe.

**Lithium problem.** The observed Li-7 in metal-poor stars is lower than BBN predicts by about a factor of three. This is an unresolved tension — possibly stellar depletion, possibly new physics.

## Pillar 4 — Large-Scale Structure

Galaxies are not distributed randomly. Large redshift surveys (2dF, SDSS,