Editing Dark Energy (section)

=== [[The Cosmological Constant (Λ)]] ===
One of the most straightforward ways to model Dark Energy mathematically is through the '''Cosmological Constant (Λ)''', originally introduced by Albert Einstein in his equations of General Relativity. The cosmological constant is often interpreted as the energy density of empty space, or vacuum energy, which drives the accelerated expansion of the universe.

The Einstein field equations with the cosmological constant are given by:

<math>
R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R + g_{\mu\nu} \Lambda = \frac{8 \pi G}{c^4} T_{\mu\nu}
</math>

where:
* <math>R_{\mu\nu}</math> is the Ricci curvature tensor,
* <math>g_{\mu\nu}</math> is the metric tensor,
* <math>R</math> is the Ricci scalar,
* <math>\Lambda</math> is the cosmological constant,
* <math>G</math> is the gravitational constant,
* <math>c</math> is the speed of light,
* <math>T_{\mu\nu}</math> is the stress-energy tensor.

In this equation, the term <math>\Lambda g_{\mu\nu}</math> represents the contribution of Dark Energy to the overall curvature of spacetime. When <math>\Lambda</math> is positive, it causes the universe to accelerate in its expansion.

The energy density associated with the cosmological constant can be expressed as:

<math>
\rho_\Lambda = \frac{\Lambda c^2}{8 \pi G}
</math>

This equation indicates that the energy density of Dark Energy is proportional to the cosmological constant, which has been observed to be small but positive.