Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Astrophysics and cosmology → Cosmology ↓


Cosmic microwave background


The cosmic microwave background (CMB) is an important topic in the field of cosmology. It is one of the most compelling evidence for the Big Bang theory. The CMB is a faint glow of light that fills the universe, which falls in the microwave region of the electromagnetic spectrum. It is essentially a snapshot of the oldest light in our universe, emitted about 380,000 years after the Big Bang, when the universe had cooled enough that protons and electrons could combine to form neutral hydrogen atoms. This era is known as 'recombination', and the CMB is a relic of this time.

Understanding the Big Bang and the creation of the universe

To understand the importance of the CMB, let's first get into the framework of the Big Bang theory. According to this theory, the universe began from an incredibly hot and dense state about 13.8 billion years ago and has been expanding ever since. Initially, it was filled with a plasma of photons, electrons, and baryons. During this early stage, the universe was opaque, as photons were constantly scattered off free electrons in a phenomenon called Thomson scattering.

As the universe expanded, it cooled and eventually it reached a point where the ambient temperature dropped to about 3000 Kelvin. This allowed electrons to combine with protons to form neutral hydrogen atoms. With fewer free electrons to scatter, photons could travel freely, turning the universe from opaque to transparent. This separation of matter and radiation is what we now see as the CMB.

Features of the cosmic microwave background

The CMB is nearly uniform, with temperature fluctuations of the order of 1 part in 100,000. These tiny variations are important because they represent the seeds of all existing structures in the universe: galaxies, clusters, and cosmic webs.

A distinctive feature of the CMB is its black body spectrum. A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The CMB closely follows this radiation curve, with the intensity peaking at a temperature of about 2.7 Kelvin - hence classified in the microwave band.

This thermal nature of the CMB is reflected in the following formula for the black body spectrum: 

B(ν, T) = (2hν³/c²) / (e^(hν/kT) - 1)
where: ν is the frequency, h is the Planck constant, c is the speed of light, k is the Boltzmann constant, T is the temperature.

Discovery of the cosmic microwave background

The CMB was discovered by chance in 1965 by Arno Penzias and Robert Wilson while they were working with microwave receivers at Bell Labs in New Jersey. They detected an extra noise that was isotropic and still present even after all possible sources of interference were taken into account. This noise matched the predictions of the Big Bang theory about thermal radiation left over from the early universe.

This discovery proved to be a major turning point, strengthening the Big Bang theory over rival explanations such as the steady state theory, and earning Penzias and Wilson the Nobel Prize in Physics in 1978.

Oddities in the cosmic microwave background

While the CMB is remarkably uniform, with an average temperature of about 2.725 Kelvin, careful observations reveal slight asymmetries, or spatial variations, in the temperature. These asymmetries are extremely important because they provide evidence of the initial conditions from which large-scale structures in the universe formed.

These temperature fluctuations can be visualized as follows: 

(ΔT/T) ≈ 10⁻⁵

These fluctuations are thought to have originated from quantum fluctuations in the very early universe, which amplified during a period of rapid expansion known as inflation. The detailed patterns of these variations encode information about the universe's structure, expansion rate, and even its size.

Cosmic Background Explorer (COBE)

In 1989, the Cosmic Background Explorer (COBE) satellite was launched, carrying instruments that were able to measure the CMB across the entire sky with unprecedented accuracy. COBE's results provided the first detailed maps of CMB asymmetries and confirmed the black body nature of the CMB radiation. This discovery provided new information about the large-scale properties of the early universe.

Wilkinson Microwave Anisotropy Probe (WMAP) and Planck mission

Later missions, such as the Wilkinson Microwave Anisotropy Probe (WMAP), launched in 2001, improved on COBE's observations, providing maps of the CMB with much greater resolution and sensitivity. Data from WMAP have made precise measurements of the age, structure, and curvature of the universe possible.

Later, the European Space Agency's Planck satellite, launched in 2009, refined these measurements with even more fine detail. The Planck mission has mapped the CMB with such precision that it has become one of the cornerstone datasets of cosmology.

Implications of the cosmic microwave background

Studying the CMB provides a glimpse into the early state of the universe and serves as a powerful tool for testing cosmological models. The CMB provides information about the age of the universe, its current rate of expansion (Hubble constant), and its geometry (flat, open or closed).

The angular scale of the first acoustic peak in the CMB power spectrum suggests that our universe is flat: 

l_peak ≈ 200

This insight is consistent with the predictions of inflationary models and has important implications for theories about the ultimate fate of the universe.

Visualization example of the CMB pattern

When observing the CMB, consider the following simplified pattern representation, where each small dot indicates a temperature fluctuation:

This simplified version is just to show that the pattern of the cosmic microwave background is made up of many small variations spread across the sky.

Current research and future directions

Today, research continues into the fine details of the CMB, to detect phenomena such as the effects of gravitational lensing, isotropy on small scales, and the presence of any non-Gaussianity, which may point to new physics beyond the standard cosmological model.

In addition, efforts are focused on measuring the polarization of the CMB, which could provide more information about primordial gravitational waves and provide evidence for the theory of inflation.

Conclusion

The cosmic microwave background is crucial to understanding the beginning, structure, and fate of the universe. As one of the most important discoveries in astrophysics, it challenges and inspires the pursuit of knowledge about our universe.


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Cosmic microwave background

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