In class, we solved the friedmann equation for the critical case, where the constant of integration was set to k 0; this resulted in the einstein-de sitter model, where a ox p/3. now, let us consider the closed case (k = +1), where the universe starts with a big bang, reaches a maximum expansion, turns around, and eventually ends in a big crunch for the closed model, it is convenient to write the frieddmann equation as follows: 8 gpo (a-1) 3 where po is the present-day mass density. show that this equation can be solved with the following parametric expressions: a sin a a. and t a (a-sin a cos a) where a is a "development angle", such that a 0 corresponds to the big bang, a corresponds to the point of maximum expansion ("turn-around"), and a 27 to the big c crunch. find an expression for the constant a