This thesis sheds valuable new light on the second-order
cosmological perturbation theory, extensively discussing it in the
context of cosmic microwave background (CMB) fluctuations. It
explores the observational consequences of the second-order vector
mode, and addresses magnetic field generation and the weak lensing
signatures, which are key phenomena of the vector mode. The author
demonstrates that the second-order vector mode, which never appears
at the linear-order level, naturally arises from the non-linear
coupling of the first-order scalar modes. This leads to the
remarkable statement that the vector-order mode clearly contributes
to the generation of cosmological magnetic fields. Moreover, the
weak lensing observations are shown to be accessible to the vector
mode. On the basis of ongoing and forthcoming observations, the
thesis concludes that the second-order vector mode is detectable.
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