Tasks on CMB by Prof. M.Bucher

Tasks on CMB by Prof. M.Bucher

New postby Maxim Khlopov on Sun 9 Jun 2019 13:03

Prof. M. Bucher proposes the following questions, which will be used as additional questions to ticket

1. In the framework of the conventional cosmological model, our present horizon is described as a sphere of radius $\approx 45$ Gyr in terms of co-moving units. According to this same model however, the age of the universe is only $13.8$ Gyr. Explain how these two numbers can be reconciled with the requirement of causality. Show how one would calculate the radius of our present horizon given the measured value of the present Hubble parameter $H_0=68 km s^{-1} Mpc ^{-1}$) and $\Omega _\Lambda =0.7$

2. Thomson scattering (i.e., the scattering of photons by electrons) is highly anisotropic and polarization dependent. If the universe instantaneously passed from a completely opaque state to a completely transparent state (as is implicit in the Sachs-Wolfe formula), the CMB would not be polarized at all, which is contrary to observation. For this problem please ignore the complications arising from the re-scattering from the late-time re-ionized electrons resulting from the first stars and quasars.) Explain how one would estimate the magnitude of the polarization anisotropy when one takes into account a finite width of the surface of last scatter rather than idealizing that decoupling took place instantaneously. (Make a plausible guess for the width of the surface
of last scatter.) For answering this question, a rough order of magnitude suffices. [N.B. The following may prove useful for this problem: $\sigma _{Thomson}=6.6\times 10^{-25} cm^2;$ the current critical density of the universe is $\approx 10^{-29}~g~cm^{-3}$ of which the baryonic density contributes $\approx 4\% $ ; the redshift of decoupling is $\approx 10^3$; and $m_{proton}=1.6\times 10^{-24}~g.$]
[i]Хлопов Максим Юрьевич
Maxim Khlopov[/i]
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Maxim Khlopov
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