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


Cosmology is a branch of astronomy that involves the study of the origin and ultimate fate of the universe. It includes the largest scales of spacetime and everything that occurs within it. The field is a fundamental part of astrophysics and physics, where scientists develop theories and models to understand the makeup, structure, and origin of the universe.

The Big Bang Theory

One of the fundamental concepts of cosmology is the Big Bang Theory. This theory holds that the universe began with an extremely hot and dense state and has been expanding ever since. The Big Bang is not an explosion in the classic sense, but an expansion of space.

Evidence for the Big Bang includes the discovery of the cosmic microwave background radiation, the abundance of light elements, and Hubble's law of the expanding universe. Hubble's observations showed that galaxies are moving away from us, which shows that the universe is expanding.

        Hubble's Law: v = H₀ × d

Where v is the velocity of the outgoing galaxy, H₀ is the Hubble constant, and d is the distance to the galaxy.

Cosmic microwave background radiation

The cosmic microwave background radiation (CMB) is a key piece of evidence for the Big Bang theory. It is a faint glow left over from the early hot stages of the universe. The CMB is roughly uniform in all directions, indicating isotropy of the universe on large scales.

This radiation is observed as a uniform radiation field in the microwave spectrum that encompasses the entire universe.

CMB Radiation

Inflation theory

To solve various problems of the original Big Bang model, in the 1980s, scientists introduced the concept of cosmic inflation. This theory states that the universe expanded exponentially just after the Big Bang. This rapid expansion explains the uniformity of the CMB and the distribution of galaxies across vast regions of space.

The inflationary epoch lasted only a fraction of a second, but during this time, the size of the universe increased enormously, smoothing out the initial irregularities.

The fate and size of the universe

Cosmology also investigates the various possible shapes of the universe and its ultimate fate. The geometry of the universe is determined by the amount of matter and energy present. There are three primary proposals for the shape of the universe:

  • Closed universe: If there is enough matter in the universe, its gravity will eventually stop and the expansion will reverse, causing a big crunch.
  • Flat universe: If the amount of density in the universe is just right, the expansion will gradually slow down, but will never stop completely.
  • Open universe: If the density of the universe is less than the critical density, it will continue to expand forever, and the rate of expansion will slow down but will never reach zero.
Open universe Closed universe Flat universe

Dark matter and dark energy

An important and mysterious component in cosmology is dark matter and dark energy. Observations show that these elements make up about 95% of the total energy content of the universe, with dark matter accounting for about 27% and dark energy accounting for about 68%.

Dark matter

Dark matter does not emit, absorb, or reflect light, making it invisible and only detectable through its gravitational effects. It plays a key role in the formation of large structures in the universe, such as galaxies and galaxy clusters. The presence of dark matter was first suggested to explain the speed of stars rotating in galaxies, which was faster than could be explained by visible matter alone.

Dark energy

Dark energy is thought to be responsible for the acceleration of the universe's expansion. Unlike dark matter, which tends to clump together, dark energy appears to be a uniform field that pervades all of space, affecting the universe on the largest scales.

Anthropic principle

The anthropic principle investigates why the universe has the necessary conditions for the existence of intelligent life forms capable of observing it. The principle explains that the laws and constants of the universe appear to be fine-tuned and precise enough to allow the development of life.

This theory can give rise to philosophical ideas, as it holds that the structure of the universe is not coincidental or random from a purely existential point of view.

Multiverse theory

Some cosmologists explore the possibility of the multiverse, which suggests that our universe is only one of a potentially infinite number of universes with different properties. These different universes may have other physical constants, dimensions, and rules.

This concept could help explain why our universe allows for life, since it is possible that we are simply in one of the regions where life is possible. However, this idea is highly speculative and challenging to test or measure scientifically.

Conclusion

Cosmology is an ongoing journey to understand the universe. As our observational capabilities and theoretical frameworks evolve, our understanding of the universe, its origins, structure, and ultimate destiny continues to grow and change. The field is concerned with fundamental questions about reality, the nature of existence, and our place within the universe.

Theories such as the Big Bang, cosmic inflation, and the existence of dark matter and dark energy reshape our view of the universe every day. Ultimately, cosmology seeks to unravel the complexities of the universe and our myriad connections to it.


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Cosmology

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