Particle horizon in a power-law universe
= Particle horizon in a power-law universe
{title2=$R(t)=At^p,\quad D_p(t)=ct/(1-p),\quad0<p<1$}
The radial null integral from the <Big Bang> is $\chi_p=c\int_0^tdt'/R(t')=ct^{1-p}/[A(1-p)]$. Multiplication by the <scale factor> gives the proper radial horizon distance. It is $3ct$ for a flat matter-only model and $2ct$ for a flat radiation-only model. A finite initial <time> different from zero or an earlier expansion era changes the result.