Graduate
  1. Classical mechanics  1.1. Advanced Kinematics  1.1.1. Generalized coordinate systems  1.1.2. Parametric equations of motion  1.1.3. Non-inertial frames and fictitious forces  1.1.4. Covariant formulation of momentum  1.1.5. Action-angle variable  1.2. Lagrangian and Hamiltonian mechanics  1.2.1. Principle of minimum action  1.2.2. Euler–Lagrange equations  1.2.3. Noether's theorem and conservation laws  1.2.4. Normalized Speed  1.2.5. Canonical conversion  1.2.6. Poisson bracket and Hamilton–Jacobi theory  1.2.7. Hamiltonian chaos and integrability  1.3. Rigid body mobility  1.3.1. Euler's equations of motion  1.3.2. Principal moments of inertia  1.3.3. Gyroscopic motion and precession  1.3.4. Inertia tensor  1.3.5. Stability of rotational speed  1.4. Nonlinear dynamics and chaos  1.4.1. Phase space and stability analysis  1.4.2. Poincaré sections and bifurcation theory  1.4.3. Strange Attractors and Fractals  1.4.4. Lyapunov exponent  1.4.5. KAM theorem and quasi-periodic motion
  2. Electromagnetism  2.1. Advanced Electrodynamics  2.1.1. Green's function and potential theory  2.1.2. Multipole expansion  2.1.3. Image charging method  2.1.4. Boundary conditions and uniqueness theorem  2.2. Electromagnetic wave propagation  2.2.1. Plane waves in dielectrics and conductors  2.2.2. Waveguides and cavity resonators  2.2.3. Radiation pressure and optical tweezers  2.2.4. Polarization and Jones calculus  2.3. Relativistic electrodynamics  2.3.1. Covariant formulation of electrodynamics  2.3.2. Lienard–Wiechert potentials  2.3.3. Synchrotron radiation and bremsstrahlung  2.3.4. Electromagnetic field tensor and Lorentz transformations  2.4. Plasma physics  2.4.1. Magnetohydrodynamics  2.4.2. Debye shielding and plasma oscillations  2.4.3. Alfvén waves and tokamak confinement  2.4.4. Plasma instabilities and turbulence
  3. Statistical mechanics and thermodynamics  3.1. Advanced Thermodynamics  3.1.1. Legendre transforms and thermodynamic potentials  3.1.2. Fluctuation–dissipation theorem  3.1.3. Onsager interpersonal relations  3.1.4. Critical events and phase transitions  3.2. Quantum statistical mechanics  3.2.1. Density Matrix and Ensemble Theory  3.2.2. Bose–Einstein condensates  3.2.3. Quantum phase transition  3.2.4. Fermi–Dirac and Bose–Einstein statistics  3.2.5. Partition functions and grand canonical ensembles
  4. Quantum mechanics  4.1. Advanced wave mechanics  4.1.1. WKB approximation  4.1.2. Path integral formulation  4.1.3. Quantum harmonic oscillator and coherent states  4.2. Angular momentum and spin  4.2.1. Spherical Harmonics  4.2.2. Clebsch–Gordan coefficient  4.2.3. Wigner–Eckart theorem  4.2.4. Spin–orbit coupling  4.3. Quantum scattering theory  4.3.1. Born approximation  4.3.2. Partial wave analysis  4.3.3. Optical theorem  4.3.4. S-matrix theory  4.4. Quantum field theory  4.4.1. Second Quantization  4.4.2. Feynman diagrams and propagators  4.4.3. Renormalization theory  4.4.4. Gauge theory and Yang–Mills fields  4.4.5. Spontaneous symmetry breaking and the Higgs mechanism
  5. General relativity and cosmology  5.1. Tensor calculus and differential geometry  5.1.1. Einstein field equations  5.1.2. Schwarzschild and Kerr metrics  5.1.3. Geodesics and Christoffel symbols  5.2. Cosmology and the Universe  5.2.1. The FLRW metric and cosmic inflation  5.2.2. Dark energy and structure formation  5.2.3. Cosmic microwave background radiation
  6. Condensed matter physics  6.1. Band structure and transport theory  6.1.1. Block theorem and the Kronig–Penney model  6.1.2. Fermi surface topology  6.1.3. Quantum Hall Effect  6.2. Superconductivity  6.2.1. BCS theory and Cooper pairs  6.2.2. Meissner effect and flux quantization  6.2.3. The Josephson Effect and SQUIDs  6.3. Topological phases of matter  6.3.1. Topological Insulators  6.3.2. Majorana fermions in topological phases of matter
  7. Nuclear and Particle Physics  7.1. Quantum Chromodynamics (QCD)  7.1.1. Quark–gluon plasma  7.1.2. Asymptotic freedom  7.1.3. Confinement and hadronization  7.2. Beyond the Standard Model  7.2.1. Grand Unified Theories  7.2.2. Supersymmetry and extra dimensions  7.2.3. Neutrino oscillations

Graduate → General relativity and cosmology → Cosmology and the Universe ↓


Cosmic microwave background radiation


The cosmic microwave background radiation (CMB) is one of the most important discoveries in cosmology and a powerful evidence for the Big Bang theory. It is the afterglow radiation from the hot, dense state of the universe, now cooled by the expansion of the universe and stretched to microwave wavelengths. In this lesson, we will explore the significance, discovery, characteristics, and implications of the CMB in the context of cosmology and the framework of general relativity.

1. What is cosmic microwave background radiation?

The CMB is an omnipresent electromagnetic radiation that fills the universe. It is a remnant of the universe's earliest phase, also known as the "afterglow of the Big Bang." When the universe was about 380,000 years old, it was filled with a hot, dense plasma of photons, electrons and protons. As the universe expanded and cooled, these particles combined to form neutral hydrogen, allowing photons to travel freely for the first time in a process called "recombination."

Transition from opaque to transparent

Before recombination, the universe was opaque because free electrons scattered photons the same way fog scatters light. Once these electrons combined with protons to form neutral hydrogen, the universe became transparent, leaving photons free to travel through space, creating what we now see as the CMB.

The universe before recombination Recombination (photon released) The Journey of a Photon

2. Discovery of cosmic microwave background radiation

The existence of the CMB was accidentally discovered in 1965 by American radio astronomers Arno Penzias and Robert Wilson. They were experimenting with a radio receiver and detected a background noise that was isotropic and unambiguous. This radiation matched the theoretical predictions of Ralph Alpher and Robert Herman about the heat left over from the early universe, which coincided with Big Bang cosmology.

Penzias and Wilson's discovery earned them the Nobel Prize in Physics in 1978. The discovery was a watershed moment in cosmology, providing empirical evidence for the Big Bang theory.

3. Characteristics of cosmic microwave background radiation

3.1 Temperature

The temperature of the CMB is remarkably uniform, about 2.725 Kelvin, although it has small variations (temperature fluctuations) on the level of one part in 100,000. These variations in temperature are important because they are reflected in the evolution of the large-scale structure of the universe, including galaxies and galaxy clusters.

3.2 Spectrum

The CMB radiation exhibits an ideal black-body spectrum, meaning that it exactly obeys Planck's law of black-body radiation. The spectrum peaks at microwave wavelengths, about 1 millimeter, which corresponds to a blackbody temperature of about 2.7 K.

[ E(nu, T) = frac{8pi hnu^3}{c^3} frac{1}{e^{(hnu/kT)} - 1} ] 
    Where:
    E(ν, T) = energy density
    ν = frequency
    T = temperature in Kelvin
    h = Planck's constant
    c = speed of light
    k = Boltzmann constant

4. Importance of cosmic microwave background radiation in cosmology

4.1 Support for the Big Bang theory

The uniformity and spectrum of the CMB strongly support the Big Bang theory. According to this model, the universe began as an incredibly hot and dense point about 13.8 billion years ago and has been expanding ever since. The presence of this background radiation aligns with the concept of a hot origin that continues to cool and expand over the ages.

Visual example of the expansion of the universe over time

Early Universe Current Universe

4.2 Measuring the age and structure of the universe

By analyzing the CMB, cosmologists can obtain important information about the age, structure, and geometry of the universe. Variations in the CMB provide data on the density of different components of the universe, such as dark matter, normal matter, and dark energy.

4.3 Construction of large-scale structures

The tiny fluctuations seen in the CMB are the seeds of all existing structures. They expose differences in density that will eventually grow under the influence of gravity to form galaxies, clusters, and the cosmic web network.

5. General relativity and the cosmic microwave background radiation

Einstein's theory of general relativity plays a key role in understanding the CMB because it provides a framework for how gravity affects the large-scale structure of the universe. The equations of general relativity describe how expansion over time affects CMB photons traveling through space.

5.1 Friedman equation

The equations governing cosmology derived from general relativity are the Friedmann equations. They relate the rate of expansion of the universe to its energy content.

[ left( frac{dot{a}}{a} right)^2 = frac{8pi G}{3} rho - frac{kc^2}{a^2} + frac{Lambda c^2}{3} ] 
    Where:
    a = scale factor
    G = Gravitational constant
    ρ = energy density
    k = spatial curvature
    Λ = cosmological constant

5.2 Gravitational redshift

According to general relativity, light traveling in the expanding universe experiences redshift. The CMB, which was initially released at a redshift of 1100, has spread out to longer wavelengths over time, an example of gravitational redshift.

6. Modern experiments and observations of the CMB

A number of satellite missions and experiments have been launched to study the CMB in detail. Perhaps the most famous is the Wilkinson Microwave Anisotropy Probe (WMAP), which mapped the temperature fluctuations in unprecedented detail, leading to refined cosmological models.

Another important mission is the Planck satellite, which provided the most precise measurements ever made of the CMB fluctuations, helping to better understand the age of the universe, its rate of expansion, and overall matter composition.

6.1 Cosmological parameters

Observations from CMB experiments help scientists calculate essential cosmological parameters, such as the Hubble constant, the density of dark matter, and baryonic matter.

Conclusion

The cosmic microwave background radiation is a hallmark of the Big Bang theory, providing a doorway into the early stages of the universe. It has been a cornerstone for cosmological research, providing insight into the structure and evolution of the universe. Through the lens of general relativity, the CMB connects the microscopic world of particles to the macroscopic expanse of the universe, underscoring the interconnection of the universal laws that govern physics and reality.


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Cosmic microwave background radiation

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