Top Equations in Cosmology
The mathematical foundations of our understanding of the universe
Cosmology seeks to understand the origin, evolution, and ultimate fate of the Universe as a whole. These equations form the mathematical backbone of modern cosmological theory, helping us explain everything from the overall expansion of the cosmos to the behavior of the smallest particles within it.
Rather than just focusing on the mathematical symbols, try to understand what each equation reveals about our universe—its birth, composition, and evolution over billions of years.
Friedmann Equation
H² = (ȧ/a)² = (8πG/3)ρ - k/a² + Λ/3
Governs the universe's expansion and evolution; predicts the Big Bang, future fate, and role of dark energy.
Hubble's Law
v = H₀d
Established that the universe is expanding; recessional velocity of galaxies is proportional to their distance.
Planck's Law
E = hf
Describes quantized energy; explains photon energy for photoelectric effect and blackbody radiation (e.g., CMB).
Doppler Shift / Redshift
z = Δλ/λ ≈ v/c
Measures recessional velocity of stars and galaxies; key evidence for expanding universe.
Einstein's Field Equations
Gμν + Λgμν = (8πG/c⁴)Tμν
Describes gravity as spacetime curvature; foundation for models of universe's structure.
Mass-Energy Equivalence
E = mc²
Explains energy source in stars and nuclear processes; matter and energy are interchangeable.
Stefan-Boltzmann Law
L = 4πR²σT⁴
Relates a star's luminosity to temperature and size; crucial for calculating stellar energies.
Fluid Equations
∂ρ/∂t + ∇·(ρv) = 0
Model evolution of cosmic structures (e.g., galaxies) from gas and dark matter density perturbations.
Newton's Law of Gravitation
F = G(m₁m₂/r²)
Foundation for understanding orbital motions (planets, stars, galaxies) and gravitational dynamics.
Schrödinger Equation
iℏ(∂Ψ/∂t) = ĤΨ
Governs behavior of quantum systems; essential for atomic and subatomic processes shaping the universe.
No comments:
Post a Comment