Friedmann Equation Solutions. A the maximum value of a occurs at θ π and is amax 8πgǫ0r2 0 3c4. Matter only κ 0 einstein de sitter 0 5 0 0 5 1 1 5 2 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2 einstein de sitter h 0 t.
Solutions of the friedmann equation we now understand the origin of the friedmann equation a a 2 8πg 3 ǫ t c2 kc2 r2 0 1 a2 t and the dependence of energy density ǫ t on the expansion factor a t for various forms of matter and energy. ð2þ the friedmann acceleration equation is a a 4pg 3 qþ 3p c2 ð3þ while the fluid equation is q þ3 a a p c2 0. Matter only κ 0 einstein de sitter 0 5 0 0 5 1 1 5 2 0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2 einstein de sitter h 0 t.
At his time it was believed that the universe was static but he found dynamical equations that involved acceleration terms.
The friedmann equations can be solved exactly in presence of a perfect fluid with equation of state p w ρ c 2 displaystyle p w rho c 2 where p displaystyle p is the pressure ρ displaystyle rho is the mass density of the fluid in the comoving frame and w displaystyle w is some constant. ð2þ the friedmann acceleration equation is a a 4pg 3 qþ 3p c2 ð3þ while the fluid equation is q þ3 a a p c2 0. The term friedmann equation is usually reserved for the first one. ð4þ the solutions of these equations are three fundamental parameters the scale factor a.
