Chapter 25, Problem 35Q

(a)

To determine

The reason due to which the radiation temperature was $T_0=T\left(1+z\right)$ at the redshift z. Let, T denotes today’s temperature of the cosmic microwave background. It is given that a proton of wavelength ${\lambda }_0$ from the cosmic microwave background was emitted at redshift $z$. Today it’s wavelength is, $\lambda ={\lambda }_0\left(1+z\right)$.

(b)

To determine

The radiation temperature at $z=1$, if it is given that a proton of wavelength ${\lambda }_0$ from the cosmic microwave background was emitted at redshift $z$. Today it’s wavelength is, $\lambda ={\lambda }_0\left(1+z\right)$.

(c)

To determine

The redshift at which the radiation temperature is equal to 293 K, if it is given that a proton of wavelength ${\lambda }_0$ from the cosmic microwave background was emitted at redshift $z$. Today it’s wavelength is, $\lambda ={\lambda }_0\left(1+z\right)$.