Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 62 / 3 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 15B / c / Solution

{c}

For the <de Sitter scale factor in flat slicing>
$$
a(t)=a_0e^{H_{\rm inf}t},
$$
choose the additive constant so that
$$
\tau=-\frac1{a_0H_{\rm inf}}e^{-H_{\rm inf}t}
=-\frac1{aH_{\rm inf}}.
$$
An eternal expanding patch has $-\infty<\tau<0$.

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 Incoming links: Conformal time during de Sitter expansion