Critical density
The critical density is the average density of matter and &energy that the universe must have in order to be geometrically flat — that is, for the geometry of space to be Euclidean on a large scale. If the actual density is equal to the critical density, the universe is flat. If it is greater, the universe is positively curved (like a sphere). If it is less, it is negatively curved (like a horse saddle).
A very small value
The critical density of the current universe is approximately 9.47 × 10⁻²⁷ kilograms per cubic meter, which is equivalent to about 5 to 6 protons per cubic meter. This is an extraordinarily low density—far lower than the best vacuum produced in a laboratory. Yet, spread across the immensity of the universe, it determines its overall geometry.
The Omega parameter
The ratio of the actual density of the universe to the critical density is denoted by Ω. If Ω = 1, the universe is flat. If Ω > 1, it is closed. If Ω < 1, it is open. Observations of the cosmic microwave background indicate that Ω is extremely close to 1—the universe is flat to within 0.4%. This result is one of the confirmed predictions of cosmic inflation.
Significance in Astronomy
The critical density is a central parameter in modern cosmology. It allows us to compare the relative contributions of ordinary matter, dark matter, and dark energy to the composition of the universe. Current measurements indicate approximately 5% ordinary matter, 27% dark matter, and 68% dark energy—for a total of Ω close to 1, confirming that the universe is flat.
Concrete example
If we add up only visible matter (stars, gas), we obtain only about 1% of the critical density. If we add dark matter, we reach about 32%. It is only by adding dark energy that we reach the total critical density—a striking illustration of the dominance of the invisible components of the universe.
Frequently Asked Questions
If the universe is flat, does that mean it is infinite?
Not necessarily. A geometrically flat universe can be infinite (extending indefinitely) or finite with a particular topology (such as a torus), depending on its overall structure. Flatness constrains only the local geometry, not the global topology.
Does the critical density change over time?
Yes. It decreases as the universe expands, because it is proportional to the square of the Hubble constant, which changes over time. The actual density also decreases, but the two evolve in tandem to keep Ω close to 1 in the Standard Model.
Can we measure the density of the universe?
Yes, indirectly. Analysis of the cosmic microwave background, the distribution of galaxies, and measurements of the Hubble constant allow us to constrain the total density with good precision. The measured value is in remarkable agreement with the critical density.