Does Gravity Slow the Expansion of the Universe?

Yes—but the answer depends on what you mean by “slow.” The universe can continue expanding while the rate of expansion decreases. In the standard model of cosmology, matter and radiation have gravitational effects that decelerate the expansion. Dark energy, which currently dominates the cosmic energy budget, has the opposite effect on the expansion’s acceleration.

Expansion rate versus acceleration

Cosmologists describe the changing average size of the universe with a scale factor, $a(t)$. As space expands, $a$ increases. The expansion rate is often expressed as the Hubble parameter,

$$H(t)=\frac{\dot a}{a},$$

where a dot means a derivative with respect to time. The acceleration of the expansion is described by $\ddot a$.

These are not the same thing. If $\dot a$ is positive but $\ddot a$ is negative, the universe is still expanding, but its scale factor is growing more slowly than it would if the expansion were not decelerating. Negative acceleration does not mean that expansion has stopped or reversed.

How gravity affects cosmic expansion

In general relativity, the average cosmic expansion is governed by equations that depend on the universe’s energy density and pressure. One form of the acceleration equation is

$$\frac{\ddot a}{a}=-\frac{4\pi G}{3}\left(\rho+\frac{3p}{c^2}\right)+\frac{\Lambda c^2}{3}.$$

Here, $G$ is the gravitational constant, $c$ is the speed of light, $\rho$ is the mass-equivalent energy density of matter and radiation, $p$ is their pressure, and $\Lambda$ represents the cosmological constant. The equation shows why it is incomplete to say that only matter’s “pull” matters: pressure also contributes to cosmic acceleration. Ordinary matter and radiation have positive energy density and nonnegative pressure, so their contribution tends to make $\ddot a$ negative. A cosmological constant contributes positively and can make $\ddot a$ positive.

More generally, dark energy can be represented by an energy density and pressure rather than a cosmological constant. Its observed behavior is close to that of a cosmological constant: it has negative pressure, which can drive accelerated expansion.

A simple example of slowing expansion

Suppose the universe contains only pressureless matter, with no dark energy. In a spatially flat model, the scale factor grows as $a(t)\propto t^{2/3}$. Ignoring an overall constant, take

$$a(t)=t^{2/3}.$$

Then

$$\dot a=\frac{2}{3}t^{-1/3}>0, \qquad \ddot a=-\frac{2}{9}t^{-4/3}<0.$$

The first result says the universe is expanding; the second says that expansion is decelerating. For instance, from $t=1$ to $t=2$ in any consistent time units, the scale factor grows from $1$ to about $1.59$. It has grown, even though its acceleration is negative.

This is the sense in which gravity slows expansion: in a matter-dominated universe, the gravitational effect of matter reduces the expansion’s acceleration. It does not act like friction against space or necessarily bring the expansion to a halt.

What happens in our universe?

The standard cosmological model, called $\Lambda$CDM, includes ordinary matter, dark matter, radiation, and a cosmological constant. Early in cosmic history, matter and radiation were much denser, so their decelerating influence was stronger. As the universe expanded, matter became less dense. The density associated with a cosmological constant stays constant as space expands, so its influence eventually became dominant.

Observations indicate that the universe is accelerating today. In the standard model, the transition from decelerating to accelerating expansion occurred several billion years ago—roughly five to six billion years ago, with the precise estimate depending on the cosmological parameters used. Matter still gravitates; it has simply become less influential on the overall expansion than dark energy.

This statement concerns the universe’s large-scale average. Gravity also holds together galaxies, solar systems, and other bound structures. Those systems do not expand along with the general cosmic expansion in the same way as the large-scale distances between unbound galaxies.

Common mistakes

• “Slowing expansion” means the universe is shrinking. No. A negative $\ddot a$ can occur while $\dot a$ remains positive.
• The Hubble parameter and acceleration are interchangeable. They are different quantities: $H=\dot a/a$, while acceleration depends on $\ddot a$.
• Gravity must always make the expansion decelerate. Matter and radiation have a decelerating effect, but in general relativity pressure matters too. Dark energy’s negative pressure can produce acceleration.
• Galaxies expanding apart means every object expands. Cosmic expansion describes the large-scale average. Bound systems such as the solar system do not simply stretch with the universe.

For the distinction between the expansion rate and its change, see how fast the universe expands. For the role of negative pressure, see how pressure relates to cosmological expansion.