(© Ángel Torregrosa Lillo) relatividad.org
One of the most important astronomical observations we must consider is the redshift of light from distant galaxies, first discovered by Edwin Hubble in the 1920s.
This redshift can be explained by a Doppler effect: galaxies are moving away from us, and their recession velocity is directly proportional to their distance. This phenomenon is known as the expansion of the universe.
Hubble (although others had observed the redshift earlier, and Hubble mainly correlated it with distance) derived the famous relation:
v = H × D
where:
- v = recession velocity
- D = distance to the galaxy
- H = Hubble’s constant (the proportionality factor)
From early graphs, a value of around 65 km/s/Mpc was obtained, but distance measurements had large errors. Over the decades, values between 50 and 80 km/s/Mpc were accepted. More precise satellite measurements (Hubble Space Telescope, Spitzer, NASA’s WMAP, and ESA’s Planck mission for the cosmic microwave background) have refined it further.
For now, we’ll use an approximate value close to the WMAP9 result: ≈ 69.6 (km/s)/Mpc. New measurements are published almost every year, so the exact value remains under discussion.
(Note: 1 Mpc = 1 megaparsec ≈ 3 × 10¹⁹ km ≈ 3.26 million light-years)
The dominant theory to explain this expansion is the Big Bang (first proposed by Georges Lemaître in 1931), which posits that in the distant past all matter in the universe was concentrated in a single point or “primordial egg” that exploded, giving rise to the ongoing expansion.
Gravitational attraction between galaxies should, in principle, slow this expansion—possibly even stopping it and leading to a future collapse known as the Big Crunch.
If we assume the expansion rate has been constant, calculating the time since the Big Bang is straightforward: just divide distance by velocity, which is the inverse of the Hubble constant:
T ≈ 1/H ≈ 13.7 billion years (roughly 13,700 million years)
This would be the age of the universe if the expansion rate were constant. However, if gravity has been slowing the expansion, the true age would be slightly less. Other methods (e.g., the evolution of the oldest stars or radioactive decay in globular clusters) exist, but the Hubble expansion remains the most widely used.
Another key concept is the observable universe. Since the universe has a finite age, light from beyond a certain distance simply hasn’t had time to reach us. The maximum observable distance (the radius of the observable universe) is roughly:
Dₘₐₓ ≈ c / H ≈ 13.7 billion light-years
However, because of expansion, the current proper distance to objects at the edge of the observable universe is actually much larger—around 46 billion light-years.
Distant galaxies seen by Hubble The Hubble Space Telescope pointed at apparently empty, dark regions of sky for many days and revealed thousands of extremely distant galaxies. Some of the tiny red ones have such a large redshift that their light was emitted ≈13 billion years ago. (Cropped image courtesy of NASA)
A potential issue with Hubble’s law is that, at very large distances, recession velocities appear to exceed the speed of light. This has led some to question whether the law holds at cosmological scales. The observed quantity is actually the redshift z, defined as:
z = (λₒ − λₑ) / λₑ
or
1 + z = λₒ / λₑ
In classical mechanics we approximate low redshifts with v ≈ c z, but the special-relativistic formula (which never exceeds c) is:
v = c × √(1 − 1/(1 + z)² ) (or similar forms)
Even so, many cosmologists argue that neither formula fully applies globally, because galaxies aren’t moving through space with a true velocity. Instead, the space between them is expanding—the expanding space paradigm.
As Edward Harrison (University of Massachusetts) wrote in his 1993 paper “The redshift-distance and velocity-distance laws”:
“The expanding space paradigm arose during the formative years of modern cosmology… In an influential paper enunciating the paradigm, Eddington (1930) said of the galaxies: ‘They are like spots on the surface of an inflating rubber balloon’… In modern cosmology the universe does not expand into space; rather the universe consists of expanding space… In all expanding isotropic homogeneous cosmological models, the linear velocity-distance law is the fundamental relation, valid at all distances, whereas the linear redshift-distance law is only an approximate relation valid for small redshifts.”
This and other aspects of Hubble’s law and cosmic expansion are explored in more detail on the next page of the site (Spanish).
Cite this article: Torregrosa Lillo, Ángel (2024). “Relatividad, Agujeros Negros y Universo”. ISBN 979-833822845-6
