= Open slicing of anti-de Sitter spacetime
{title2=$a(t)=\alpha^{-1}\sin(\alpha t),\quad k=-1$}
An <FLRW metric> with $p=-\varrho_0$ and constant negative <energy density> $\varrho_0$ has $\alpha^2=-8\pi G\varrho_0/3>0$ and obeys $\dot a^2+k=-\alpha^2a^2$. Positive solutions exist only for $k=-1$. They are $a=\alpha^{-1}\sin[\alpha(t-t_B)]$ on $0<\alpha(t-t_B)<\pi$. This is an open slicing of <Anti-de Sitter spacetime>, whose <Ricci scalar> is $-12\alpha^2$ and <Kretschmann scalar> is $24\alpha^4$. The zeros mark boundaries of this slicing rather than <curvature singularities>.
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