Thawing k-essence dark energy in the PAge space
  A broad class of dark energy models can be written in the form of k-essence,
whose Lagrangian density is a two-variable function of a scalar field $\phi$
and its kinetic energy $X\equiv \frac{1}{2}\partial^\mu\phi \partial_\mu\phi$.
In the thawing scenario, the scalar field becomes dynamic only when the Hubble
friction drops below its mass scale in the late universe. Thawing k-essence
dark energy models can be randomly sampled by generating the Taylor expansion
coefficients of its Lagrangian density from random matrices \cite{thaws}. Ref.
\cite{thaws} points out that the non-uniform distribution of effective equation
of state parameters $(w_0, w_a)$ of thawing k-essence model can be used to
improve the statistics of model selection. The present work studies the
statistics of thawing k-essence in a more general framework that is
Parameterized by the Age of the universe (PAge) \cite{PAge}. For fixed matter
fraction $\Omega_m$, the random thawing k-essence models cluster in a narrow
band in the PAge parameter space, providing a strong theoretical prior. We
simulate cosmic shear power spectrum data for the Chinese Space Station
Telescope optical survey, and compare the fisher forecast with and without the
theoretical prior of thawing k-essence. For an optimal tomography binning
scheme, the theoretical prior improves the figure of merit in PAge space by a
factor of $3.3$.
