Friedmann equationsequation
Imagine that the Universe is a giant balloon with galaxies living on its surface. The Friedmann equations are instructions for how this balloon inflates or deflates over time. They say: 'If you know how much matter and energy is inside, you can predict how fast the balloon expands, and even find out whether it will expand forever or collapse back.' These equations are the foundation of modern ideas about the Big Bang.
How it works
The equations work in cosmology, describing the evolution of a homogeneous and isotropic Universe. For example, according to modern data, the Universe is expanding with acceleration, which in the equations reflects the presence of dark energy (lambda term). They are used to calculate the age of the Universe, its composition, and the geometry of space.
💡 Alexander Friedmann himself was a mathematician and meteorologist. He loved solving complex equations and even participated in launching stratospheric balloons. His boldness in applying general relativity to the entire Universe initially displeased Einstein, who at the time believed in an eternal and unchanging Universe.
\left(\frac{\dot{a}}{a}\right)^2 = \frac{8\pi G}{3}\rho - \frac{kc^2}{a^2} + \frac{\Lambda c^2}{3}
ȧ — derivative of the scale factor a with respect to time, G — gravitational constant, ρ — energy density, k — curvature parameter (-1, 0, +1), c — speed of light, Λ — cosmological constant
\frac{\ddot{a}}{a} = -\frac{4\pi G}{3}\left(\rho + \frac{3p}{c^2}\right) + \frac{\Lambda c^2}{3}
ä — second derivative of a, p — pressure; shows how the expansion rate changes