Question

(* In class I discussed the expansion of the universe and gave the formula 8тG Н2! where H is the expansion rate, G is Newton's gravitational constant, and p is the density of energy. Based on this equation, argue that that there was a point in the past when the density was infinite (this is the Big Bang). I am looking for a qualitative argument. To give such an argument, think about what expansion rate means, what energy density means and what happens to the energy density when you go back in time when the universe was smaller For those of you who have taken calculus, for extra credit you can solve the problem using calculus. You will need to use H(t)à/a

Answer 1

Since energy is not conserved in an expanding universe . Now according to the given Friedmann formula ,density of energy is directly proportional to H ,i.e. H² ,where H = (da/dt)/a

OX

since a is comoving coordinate ,it is nearly zero during big band ,and expansion rate (da/dt) should be constant ,so H should be infinity and so density of energy should also goes to infinity.