The science of the universe's origin, large-scale structure, evolution, and ultimate fate. This skill covers the standard cosmological model (LCDM), its observational foundations, open tensions, and alternative proposals.

## Key Points

- **1965**: Penzias and Wilson detect excess 3.5 K microwave noise with Bell Labs horn antenna; Dicke, Peebles, Roll, Wilkinson interpret it as relic radiation. Nobel Prize 1978.
- **COBE** (1989-1993): FIRAS confirms perfect blackbody at T = 2.7255 +/- 0.0006 K; DMR detects anisotropies at delta-T/T ~ 10^-5 level. Nobel Prize 2006 (Mather, Smoot).
- **WMAP** (2001-2010): Full-sky maps at 5 frequencies (23-94 GHz); determined cosmological parameters to percent-level precision; confirmed flat geometry, age 13.77 Gyr.
- **Planck** (2009-2013): ESA mission; 9 frequency bands (30-857 GHz); angular resolution to 5 arcmin; definitive measurement of power spectrum to l ~ 2500; polarization maps.
- **First acoustic peak** (l ~ 220, angular scale ~ 1 degree): confirms flat spatial geometry (Omega_total ~ 1)
- **Second peak** (l ~ 540): constrains baryon density Omega_b h^2
- **Third peak** (l ~ 800): constrains matter density Omega_m h^2
- **Damping tail** (l > 1000): Silk damping from photon diffusion
- **Sachs-Wolfe plateau** (l < 30): large-scale gravitational redshifts, nearly scale-invariant
- **E-modes**: gradient-type pattern from Thomson scattering at last scattering surface; well measured by Planck
- **B-modes**: curl-type pattern; two sources — gravitational lensing of E-modes (detected by SPTpol, POLARBEAR, ACT, Planck) and primordial gravitational waves from inflation (not yet detected)
- Tensor-to-scalar ratio r < 0.032 (BICEP/Keck 2024 upper limit); future targets: CMB-S4, LiteBIRD aim for r ~ 0.001

## Quick Example

```
v = H_0 * d
```

```
1 + z = a_0 / a_emit = lambda_obs / lambda_emit
```

Cosmology

The science of the universe's origin, large-scale structure, evolution, and ultimate fate. This skill covers the standard cosmological model (LCDM), its observational foundations, open tensions, and alternative proposals.

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Big Bang Timeline

The universe evolved through distinct epochs after the initial singularity (t = 0):

Epoch	Time After Bang	Temperature	Key Physics
Planck epoch	0 to ~5.4 x 10^-44 s	>10^32 K	Quantum gravity regime; all four forces unified; current physics breaks down
Grand unification	~10^-43 to ~10^-36 s	~10^29 K	Gravity separates; GUT symmetry holds for strong + electroweak
Inflation	~10^-36 to ~10^-32 s	—	Exponential expansion by factor ~10^26; seeds quantum fluctuations that become large-scale structure
Electroweak epoch	~10^-36 to ~10^-12 s	~10^28 to ~10^15 K	Strong force separates; electroweak symmetry intact
Quark epoch	~10^-12 to ~10^-6 s	~10^15 to ~10^12 K	Electroweak symmetry breaks (Higgs mechanism); quarks and gluons in plasma
Hadron epoch	~10^-6 to ~1 s	~10^12 to ~10^10 K	Quarks confine into protons and neutrons; matter-antimatter annihilation leaves baryon asymmetry (~1 in 10^9)
Lepton epoch	~1 to ~10 s	~10^10 to ~10^9 K	Neutrinos decouple (cosmic neutrino background, ~1.95 K today); electron-positron annihilation
Big Bang nucleosynthesis (BBN)	~10 s to ~20 min	~10^9 to ~10^8 K	Light nuclei form: ~75% H, ~25% He-4 by mass, trace D, He-3, Li-7; predicted abundances match observations — key pillar of Big Bang model
Photon epoch / radiation domination	~20 min to ~47,000 yr	—	Radiation energy density dominates; photons, electrons, baryons tightly coupled
Matter-radiation equality	~47,000 yr (z ~ 3400)	~10^4 K	Matter energy density overtakes radiation; structure growth accelerates
Recombination	~370,000 yr (z ~ 1100)	~3000 K	Electrons combine with nuclei to form neutral atoms; photons decouple — this is the CMB surface of last scattering
Dark ages	~370,000 yr to ~100-200 Myr	—	No luminous sources; neutral hydrogen pervades; density perturbations grow
Cosmic dawn / reionization	~100 Myr to ~1 Gyr (z ~ 20 to z ~ 6)	—	First stars and galaxies ionize intergalactic hydrogen; Gunn-Peterson trough in quasar spectra marks end of reionization
Structure formation	~1 Gyr onward	—	Galaxies, clusters, cosmic web assemble hierarchically
Dark energy domination	~9.8 Gyr (z ~ 0.4) to present	—	Expansion begins accelerating
Present	13.787 +/- 0.020 Gyr	2.7255 K (CMB)	Observable universe radius ~46.5 Gly (comoving)

---

Cosmic Microwave Background (CMB)

Discovery and Missions

• 1965: Penzias and Wilson detect excess 3.5 K microwave noise with Bell Labs horn antenna; Dicke, Peebles, Roll, Wilkinson interpret it as relic radiation. Nobel Prize 1978.
• COBE (1989-1993): FIRAS confirms perfect blackbody at T = 2.7255 +/- 0.0006 K; DMR detects anisotropies at delta-T/T ~ 10^-5 level. Nobel Prize 2006 (Mather, Smoot).
• WMAP (2001-2010): Full-sky maps at 5 frequencies (23-94 GHz); determined cosmological parameters to percent-level precision; confirmed flat geometry, age 13.77 Gyr.
• Planck (2009-2013): ESA mission; 9 frequency bands (30-857 GHz); angular resolution to 5 arcmin; definitive measurement of power spectrum to l ~ 2500; polarization maps.

Power Spectrum

The angular power spectrum C_l as a function of multipole moment l encodes:

• First acoustic peak (l ~ 220, angular scale ~ 1 degree): confirms flat spatial geometry (Omega_total ~ 1)
• Second peak (l ~ 540): constrains baryon density Omega_b h^2
• Third peak (l ~ 800): constrains matter density Omega_m h^2
• Damping tail (l > 1000): Silk damping from photon diffusion
• Sachs-Wolfe plateau (l < 30): large-scale gravitational redshifts, nearly scale-invariant

Polarization

• E-modes: gradient-type pattern from Thomson scattering at last scattering surface; well measured by Planck
• B-modes: curl-type pattern; two sources — gravitational lensing of E-modes (detected by SPTpol, POLARBEAR, ACT, Planck) and primordial gravitational waves from inflation (not yet detected)
• Tensor-to-scalar ratio r < 0.032 (BICEP/Keck 2024 upper limit); future targets: CMB-S4, LiteBIRD aim for r ~ 0.001

---

Expansion of the Universe

Hubble's Law

v = H_0 * d

• v: recession velocity of a galaxy
• H_0: Hubble constant (present-day expansion rate)
• d: proper distance

Hubble Constant Tension

This is one of the most significant open problems in cosmology:

Method	Value (km/s/Mpc)	Basis
Planck CMB (2018)	67.36 +/- 0.54	Early universe, assuming LCDM
SH0ES Cepheid-calibrated SNe Ia (2022)	73.04 +/- 1.04	Local distance ladder
CCHP TRGB (2024)	~69.8 +/- 1.7	Tip of red giant branch calibration
TDCOSMO strong lensing time delays	~74 +/- 1.7	Gravitational lensing
DESI BAO + CMB (2024)	~67.97 +/- 0.38	Baryon acoustic oscillations

The ~5 sigma discrepancy between early-universe (CMB) and late-universe (distance ladder) values may indicate new physics beyond LCDM or unresolved systematic errors.

Redshift

Cosmological redshift z: wavelength stretching from expansion.

1 + z = a_0 / a_emit = lambda_obs / lambda_emit

For z << 1: v ~ c * z (Hubble flow). For higher z, use full Friedmann cosmology.

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Dark Matter

Observational Evidence

1. Galaxy rotation curves (Rubin & Ford, 1970s): flat rotation curves at large radii imply M(r) proportional to r, far exceeding visible mass
2. Gravitational lensing: strong lensing arcs in clusters; weak lensing shear maps reveal mass distributions exceeding baryonic content
3. CMB power spectrum: relative heights of acoustic peaks constrain Omega_DM h^2 ~ 0.120
4. Bullet Cluster (1E 0657-56): X-ray gas (baryonic) offset from lensing mass (dark matter) after cluster collision — direct evidence dark matter is collisionless and distinct from baryons
5. Structure formation: simulations require cold dark matter to reproduce observed galaxy clustering; baryons alone cannot form structure fast enough
6. BBN: baryon density from light element abundances is only ~5% of critical density; total matter is ~31%

Candidates

• WIMPs (Weakly Interacting Massive Particles): mass ~10 GeV to ~10 TeV; motivated by WIMP miracle (thermal relic abundance naturally gives correct Omega_DM); increasingly constrained by null results
• Axions: mass ~10^-6 to 10^-3 eV; originally proposed to solve strong CP problem; searched via microwave cavity experiments (ADMX)
• Sterile neutrinos: mass ~keV range; warm dark matter candidate; X-ray line searches (3.5 keV anomaly debated)
• Primordial black holes: constrained across most mass ranges but windows remain (~10^-12 to 10^-11 solar masses; asteroid mass)

Detection Experiments

• Direct detection: LUX-ZEPLIN (LZ), XENONnT — liquid xenon time projection chambers; world-leading spin-independent WIMP-nucleon cross-section limits (~10^-48 cm^2 at 30 GeV); PandaX-4T (China)
• DAMA/LIBRA: claims annual modulation signal consistent with dark matter wind; not reproduced by any other experiment; controversial
• Indirect detection: Fermi-LAT gamma-ray searches; IceCube neutrinos from Sun/galactic center; AMS-02 positron excess (astrophysical explanations compete)
• Collider searches: LHC searches for missing transverse energy events; no confirmed dark matter production

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Dark Energy

Discovery

In 1998, two teams independently found that Type Ia supernovae at z ~ 0.5 were ~25% fainter than expected in a decelerating universe, implying accelerating expansion:

• Supernova Cosmology Project (Perlmutter et al.)
• High-z Supernova Search Team (Riess, Schmidt et al.)
• Nobel Prize in Physics 2011

Cosmological Constant (Lambda)

Einstein's cosmological constant: Lambda term in field equations acts as constant vacuum energy density.

rho_Lambda = Lambda * c^2 / (8 * pi * G) ~ 5.96 x 10^-27 kg/m^3

• Constitutes ~68% of total energy density today
• Cosmological constant problem: quantum field theory predicts vacuum energy ~10^120 times larger than observed
• Coincidence problem: why are Omega_m and Omega_Lambda of similar magnitude now?

Equation of State

Dark energy equation of state parameter:

w = P / (rho * c^2)

• Cosmological constant: w = -1 exactly (constant in time)
• Quintessence models: w varies with time; -1 < w < -1/3
• Phantom energy: w < -1 (leads to Big Rip)

DESI Results (2024-2025)

The Dark Energy Spectroscopic Instrument released BAO measurements across redshift bins 0.1 < z < 4.2 using >5.7 million galaxies and quasars:

• Hints that w may evolve with time (w_0 w_a parameterization: w(a) = w_0 + w_a(1-a))
• w_0 ~ -0.55, w_a ~ -1.6 (combined with CMB + SNe) — >2 sigma deviation from cosmological constant
• If confirmed, would rule out simple Lambda; suggests dynamical dark energy or modified gravity
• More data releases expected to clarify

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Cosmological Parameters (Planck 2018 + BAO)

Parameter	Symbol	Value
Hubble constant	H_0	67.36 +/- 0.54 km/s/Mpc
Total matter density	Omega_m	0.3153 +/- 0.0073
Baryon density	Omega_b	0.0493 +/- 0.0006
Dark energy density	Omega_Lambda	0.6847 +/- 0.0073
Dark matter density	Omega_c h^2	0.1200 +/- 0.0012
Amplitude of fluctuations	sigma_8	0.8111 +/- 0.0060
Scalar spectral index	n_s	0.9649 +/- 0.0042
Optical depth to reionization	tau	0.0544 +/- 0.0073
Age of the universe	t_0	13.787 +/- 0.020 Gyr

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Cosmic Inflation

Problems Solved

• Horizon problem: regions on opposite sides of the CMB sky (separated by >2 degrees) were never in causal contact in standard Big Bang — inflation stretches a causally connected patch to encompass the entire observable universe
• Flatness problem: without inflation, Omega must be fine-tuned to 1 part in 10^60 at the Planck time; inflation drives Omega toward 1 dynamically
• Monopole problem: GUT phase transitions produce magnetic monopoles; inflation dilutes them to undetectable density

Theory

• Alan Guth (1981): proposed old inflation (first-order phase transition); bubble nucleation problem
• New inflation (Linde; Albrecht & Steinhardt, 1982): slow-roll down a potential — solves graceful exit
• Chaotic inflation (Linde, 1983): inflation from generic initial conditions with large-field potentials
• Inflaton field phi rolls slowly: slow-roll parameters epsilon and eta << 1
• Quantum fluctuations in phi become density perturbations (scalar) with nearly scale-invariant power spectrum (n_s ~ 0.96)
• Tensor perturbations (gravitational waves): amplitude parameterized by tensor-to-scalar ratio r

Eternal Inflation and Multiverse

• In many models, inflation never ends globally — quantum fluctuations keep some regions inflating forever
• Produces a "multiverse" of causally disconnected pocket universes with potentially different physical constants
• Controversial: not directly testable; raises measure problem

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LCDM: Successes and Tensions

Successes

• Predicts CMB power spectrum with extraordinary precision (6 parameters fit thousands of data points)
• Correctly predicts BBN light element abundances
• Reproduces observed large-scale structure (BAO, galaxy clustering, weak lensing)
• Consistent with observed accelerating expansion

Tensions

• H_0 tension: 4-6 sigma discrepancy between CMB-inferred and local measurements; most significant challenge to LCDM
• S_8 tension: weak lensing surveys (KiDS, DES, HSC) measure S_8 = sigma_8 * sqrt(Omega_m/0.3) ~ 0.76, while Planck predicts ~0.83; 2-3 sigma discrepancy; possible evidence for less clumping than expected
• DESI dark energy hints: possible time-varying w challenges cosmological constant assumption
• Lithium problem: BBN predicts 3x more Li-7 than observed in old stars
• Sigma-8 / lensing anomaly: Planck internal lensing amplitude A_L prefers >1 at ~2-3 sigma

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Fate of the Universe

Scenario	Condition	Outcome
Big Freeze / Heat Death	w = -1 (Lambda); current best fit	Expansion accelerates forever; galaxies beyond Local Group become unreachable; stars burn out (~10^14 yr); black holes evaporate via Hawking radiation (~10^100 yr); maximum entropy state
Big Rip	w < -1 (phantom energy)	Dark energy density increases; eventually tears apart galaxy clusters, galaxies, solar systems, planets, atoms; finite time to singularity
Big Crunch	Omega > 1, no dark energy	Expansion reverses; universe collapses to singularity; ruled out by observations of acceleration
Big Bounce	Cyclic models	Universe oscillates between expansion and contraction; no true beginning or end

Current data favors the Big Freeze / heat death scenario.

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Alternative Cosmologies

• MOND (Modified Newtonian Dynamics; Milgrom, 1983): modifies gravity at low accelerations (a < a_0 ~ 1.2 x 10^-10 m/s^2) instead of invoking dark matter; explains galaxy rotation curves but struggles with cluster-scale observations and CMB without supplementary dark matter; relativistic extension TeVeS largely ruled out by gravitational wave speed measurement (GW170817)
• Cyclic models (Steinhardt & Turok): brane collisions in extra dimensions produce repeated Big Bang events; avoids initial singularity; no inflation needed; generates nearly scale-invariant perturbations via ekpyrotic contraction
• f(R) gravity: generalization of Einstein's equations; can produce late-time acceleration without dark energy; constrained by solar system tests and gravitational wave observations
• Emergent gravity (Verlinde): gravity as entropic force; dark matter as emergent phenomenon from entanglement entropy; not yet a complete theory

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Anti-Patterns

• Stating the Big Bang was an explosion in space: It was an expansion of space itself; there is no center or edge; every point was the Big Bang
• Claiming dark matter has been directly detected: No confirmed direct detection as of 2025; all evidence is gravitational/indirect; DAMA claims are not independently reproduced
• Treating the Hubble constant as precisely known: The H_0 tension is real and unresolved; always note the measurement method and value range (~67-73 km/s/Mpc)
• Conflating dark matter and dark energy: Fundamentally different phenomena — dark matter gravitates and clumps; dark energy is smooth and causes accelerating expansion
• Presenting inflation as confirmed fact: Inflation is the leading paradigm but remains unproven; primordial B-modes (smoking gun) have not been detected; alternatives exist
• Saying the universe is 13.8 billion light-years in radius: The observable universe has a comoving radius of ~46.5 billion light-years due to expansion; the age in years does not equal the radius in light-years
• Treating LCDM tensions as proof of new physics: They may reflect systematic errors in measurements; state them as tensions, not confirmed anomalies
• Confusing recombination with the end of the universe's opacity: Recombination made the universe transparent to photons but neutral hydrogen was opaque to UV until reionization
• Presenting the multiverse as scientific consensus: It is a theoretical prediction of some inflation models, not an observationally confirmed framework
• Ignoring error bars on cosmological parameters: Always cite uncertainties; cosmology is a precision science and the uncertainties matter