Hubble's constant is estimated at 15km/s at a distance of million light years, without considering effects of mutual gravity, relativity, etc. I am trying to calculate the characteristic expansion time of the universe. Its formula is given as reciprocal of the Hubble constant, because time is distance by velocity. But:
This implies that velocity and distance are exponential functions of time and so time cannot simply be calculated by dividing 1 million light years by 15km/s. So what am I missing? Why is the characteristic expansion time simply the reciprocal of Hubble's constant?