How do I use Solve to find a variable in the integral?

I have the following formula: $ $ t(a) = \frac{1}{H_0}\int_0^a \frac{da’}{\sqrt{\Omega_{r,0}a^{-2} + \Omega_{m,0}a^{-1}+\Omega_{\Lambda,0}a^2 + (1-\Omega_0)}}$ $ I want to go in the opposite direction. That is, I want to know what a is given t. $ $ a(t) = ??$ $ Can I use Solve to find this value?