Expanding Universe
The expanding universe is the observational discovery that the fabric of space itself is stretching over time, causing galaxies that are not gravitationally bound to each other to recede from one another at velocities proportional to their separating distances. First confirmed observationally by Edwin Hubble in 1929 through measurements of galaxy redshifts, this expansion is described by the Friedmann–Lemaître–Robertson–Walker (FLRW) metric in general relativity. The rate of expansion, parameterised by the Hubble constant H₀ ≈ 67–73 km/s/Mpc, has been measured to be accelerating due to dark energy.
Key Formula
v = H₀ × d
LaTeX: v = H_0 \, d
| Symbol | Meaning | Unit |
|---|---|---|
| v | Recession velocity of a galaxy | km/s |
| H₀ | Hubble constant | km/s/Mpc |
| d | Proper distance to the galaxy | Megaparsecs (Mpc) |
Worked Example
Problem
A galaxy is observed at a distance of 500 Mpc. Using H₀ = 70 km/s/Mpc, calculate its recession velocity and the corresponding redshift z (for v << c).
Solution
Step 1 – Recession velocity: v = H₀ × d = 70 km/s/Mpc × 500 Mpc = 35,000 km/s Step 2 – Redshift (non-relativistic approximation, valid since v/c = 35000/300000 ≈ 0.117): z ≈ v/c = 35,000 / 300,000 = 0.117 Note: for a more accurate result at this velocity, use the relativistic Doppler formula: z = sqrt((1 + v/c)/(1 - v/c)) - 1 ≈ 0.124
Answer
Recession velocity ≈ 35,000 km/s; redshift z ≈ 0.12.
Scale Factor and Expansion History of the Universe
| Era | Dominant Component | Scale Factor a(t) | Expansion Rate |
|---|---|---|---|
| Radiation-dominated | Photons, neutrinos | a ∝ t^(1/2) | Decelerating |
| Matter-dominated | Dark + baryonic matter | a ∝ t^(2/3) | Decelerating |
| Dark energy-dominated | Cosmological constant | a ∝ e^(Ht) | Accelerating |
| Present epoch | Mixed matter + Λ | a = 1 (by convention) | Accelerating |
Interactive Tools
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Related Terms
Hubble's Law
Hubble's Law is the empirical observation that the recession velocity of a galaxy is directly proportional to its distance from the observer, expressed as v = H₀d, where H₀ is the Hubble constant. First published by Edwin Hubble in 1929 based on measurements of galaxy redshifts, it provided the first direct observational evidence for the expanding universe predicted by general relativity. The Hubble constant H₀, currently estimated at approximately 67–73 km/s/Mpc from different methods, also allows astronomers to estimate the age of the universe as roughly 1/H₀.
Dark Energy
Dark energy is a hypothetical form of energy that permeates all of space and is postulated to drive the accelerated expansion of the universe, constituting approximately 68% of the total energy content of the cosmos. It was first inferred from Type Ia supernova observations in 1998, which showed that distant supernovae were fainter than expected, implying the expansion of the universe is speeding up rather than slowing down. The simplest model for dark energy is the cosmological constant (Λ), representing a constant energy density of free space, though alternative models such as quintessence propose a dynamic scalar field.
Cosmological Redshift
Cosmological redshift is the increase in the wavelength of photons as they travel through an expanding universe, caused by the stretching of space itself rather than by the relative motion of source and observer (Doppler effect). Quantified by the redshift parameter z = (λ_observed − λ_emitted) / λ_emitted, it is directly related to the expansion factor of the universe: 1 + z = a(t_now) / a(t_emit). Cosmological redshift allows astronomers to determine the distance and lookback time to distant galaxies and serves as a primary tool for mapping the large-scale structure of the universe.
"Expanding" derives from Latin "expandere" (to spread out, ex- out + pandere to spread). "Universe" from Latin "universus" (whole, entire, all turned into one). The concept of universal expansion was theoretically predicted by Alexander Friedmann (1922) and Georges Lemaître (1927) before Hubble's 1929 observational confirmation.