Hubble's law and the expanding universe

Galaxy redshifts

In the early twentieth century, astronomers found that many galaxies have spectral lines shifted toward longer wavelengths. This redshift was interpreted as evidence that distant galaxies are receding.

Edwin Hubble and others found a relationship between galaxy distance and recession speed. More distant galaxies generally recede faster. This is Hubble's law:

$v=H_0d$

where $H_0$ is the Hubble constant.

Expansion, not explosion into space

The expanding universe is not best imagined as galaxies flying away from a central explosion into empty space. Instead, space itself expands, increasing distances between galaxies not gravitationally bound to each other.

Every observer in a homogeneous expanding universe sees distant galaxies receding. There is no special center of expansion within space.

Scale factor

Cosmologists describe expansion using the scale factor $a(t)$. Distances between comoving galaxies scale as

$d(t)=a(t)d_0$

where $d_0$ is a fixed comoving separation. The Hubble parameter is

H(t)=rac{dot{a}}{a}

The current value is $H_0$.

Interpreting Hubble's law

For nearby galaxies where speeds are small compared with $c$, Hubble's law can be interpreted as recession velocity proportional to distance. At very large distances, general relativity is needed, and recession speeds can exceed $c$ without violating special relativity because this is expansion of space, not motion through local space faster than light.

Local peculiar velocities, caused by gravitational interactions, can also affect observed redshifts.

Hubble time

The inverse Hubble constant gives a rough cosmic timescale:

t_H=rac{1}{H_0}

If the expansion rate had always been constant, this would estimate the universe's age. In reality, the expansion rate changes over time, so detailed cosmological models are needed.

Homogeneity and isotropy

Modern cosmology is built on the cosmological principle: on large enough scales, the universe is homogeneous and isotropic. Homogeneous means no preferred location. Isotropic means no preferred direction.

The universe is clumpy on small scales, but galaxy surveys and the cosmic microwave background support large-scale uniformity.

Hubble constant tension

Different methods of measuring $H_0$ do not fully agree. Measurements based on the early universe, such as the cosmic microwave background, and measurements based on local distance ladders have shown tension. This may indicate unknown systematic errors or new physics.

The big idea

Hubble's law reveals that the universe is expanding. The scale factor describes how cosmic distances grow, while the Hubble parameter gives the expansion rate. Expansion is a property of spacetime itself, not an explosion from a central point.