Assumptions
The Friedmann equations start with the simplifying assumption that the universe is spatially homogeneous and isotropic, i.e. the Cosmological Principle; empirically, this is justified on scales larger than ~100 Mpc. The Cosmological Principle implies that the metric of the universe must be of the form:
where is a three dimensional metric that must be one of (a) flat space, (b) a sphere of constant positive curvature or (c) a hyperbolic space with constant negative curvature. The parameter discussed below takes the value 0, 1, -1 in these three cases respectively. It is this fact that allows us to sensibly speak of a "scale factor", .
Einstein's equations now relate the evolution of this scale factor to the pressure and energy of the matter in the universe. The resulting equations are described below.
Read more about this topic: Friedmann Equations
Famous quotes containing the word assumptions:
“Why did he think adding meant increase?
To me it was dilution. Where do these
Innate assumptions come from?”
—Philip Larkin (1922–1986)
“What a man believes may be ascertained, not from his creed, but from the assumptions on which he habitually acts.”
—George Bernard Shaw (1856–1950)
“Assumptions of male superiority are as widespread and deep rooted and every bit as crippling to the woman as the assumptions of white supremacy are to the Negro.... this is no more a man’s world than it is a white world.”
—Student Non-Violent Coordinating Committee, African American civil rights organization. SNCC Position Paper (Women in the Movement)