Throughout this question, assume that the universe the universe only contain: s matter and a possible cosmological constant. i̇mat constant-d0hg given that in any realistic cosmology ωmat-1 at early times, compute the hubble parameter at decoupling (zdec 1000) as a fraction of its present value. as the only important characteristic scale in the young universe, the hubble length ch-1 gives the characteristic scale of the first peak in the microwave background. in a spatially-flat cosmology with a cosmological constant, the present physical distance to an object with z 1 is given approximately by 2cho