Chapter 44, Problem 57E

(a)

To determine

To explain: Why at any time $\frac{dR/dt}{R}$ is the same for all points in the balloon in the spherical balloon model of two dimensional expanding universe.

(b)

To determine

To show: In the spherical balloon model of two-dimensional expanding universe $v=\frac{dr}{dt}$ is directly proportional to $r$ at any distance.

(c)

To determine

The expression for Hubble constant $H_0$ in terms of $R$ and $dR/dt$.

(d)

To determine

The dependence of $R$ on time for $H_0$ to be a constant in time.

(e)

To determine

Whether the dependence of $R$ as on time as $R\left(t\right)=R_0{e}^{H_{0}t}$ is consistent with the observed rate of expansion of the universe.