Cosmology

Relativistic cosmological model, expansion, early universe, CMB, dark matter, and dark energy.

General idea of the topic

Cosmology investigates the origin, large-scale structure, and ultimate fate of the universe using General Relativity, thermodynamics, and quantum field theory. The concordance model ( $\Lambda$ CDM) models a statistically homogeneous and isotropic spacetime described by the Friedmann-Lemaître-Robertson-Walker (FLRW) metric, driven by dark matter and dark energy.

This node covers the Friedmann equations, Big Bang nucleosynthesis (BBN), Cosmic Microwave Background (CMB) anisotropies, cosmic inflation, and accelerated expansion.

What you will truly understand

You will understand how cosmic energy components (relativistic radiation, cold matter, vacuum energy) dictate the time evolution of the scale factor $a(t)$ and spatial curvature $k$ .

You will calculate hydrogen recombination thermodynamics ( $T \approx 3000\text{ K}$ , $z \approx 1100$ ), the formation of the CMB surface of last scattering, and the angular power spectrum of acoustic peaks.

Recommended learning route

FLRW metric and cosmic kinematics: scale factor $a(t)$ , cosmological redshift $z$ , luminosity distance, and particle horizons.
Friedmann dynamics: critical density $\rho_c$ , density parameters $\Omega_m, \Omega_r, \Omega_\Lambda$ , and cosmic cosmic era transitions.
Early Universe and Inflation: flatness and horizon problems, inflaton scalar field dynamics, and quantum origin of primordial perturbations.
CMB and large-scale structure: photon-baryon plasma decoupling, Baryon Acoustic Oscillations (BAO), and linear structure growth.

Physical criterion you must acquire

Understanding why dark energy requires a negative equation-of-state parameter $w = P/\rho \approx -1$ to drive cosmic gravitational acceleration.

Connection with real problems

Hubble tension ( $H_0$ discrepancy between local Cepheids/SNe Ia and high-z CMB).
Deep-field cosmological observations by Planck, JWST, and Euclid.
Primordial B-mode polarization searches for inflationary gravitational waves.

Final goal of the topic

Model and solve cosmological Friedmann equations to analyze CMB observables, dark matter distributions, and cosmic acceleration.

Topics in this section

Redshift and Cosmological Distances
Relation between redshift, expansion, and observable cosmological distances.
Cosmological Principle
Describes homogeneity and isotropy as the geometric basis of modern cosmology.
FLRW Metric
Homogeneous and isotropic geometry used to describe cosmological expansion.
Friedmann Equations
Relates cosmic expansion, density, curvature, and cosmological constant.
Thermal Big Bang
Thermal evolution of the early universe and cosmic microwave background origin.
Primordial Nucleosynthesis
Early formation of light nuclei and cosmological abundances. Theory, formulas, worked examples and interactive graphs.
Cosmic Microwave Background
Relic radiation used to measure cosmological temperature, spectrum, and anisotropies.
Expansion of the Universe
Cosmic expansion, Hubble law, scale factor, and redshift. Theory, formulas, worked examples and interactive graphs.
Dark Matter and Dark Energy
Cosmological model with dark matter, dark energy, and accelerated expansion.