Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 53 / 1 / ii / a

A physical positive scale factor here requires $t>1/C$. In that domain $\dot{a}=1/t>0$ but $\ddot{a}=-1/t^2<0$. There is no inflationary expansion. The range $0<t<1/C$ has a negative printed scale factor and cannot supply a positive expanding branch of this model.