Kavli Affiliate: Masahiro Takada
| First 5 Authors: Ryo Terasawa, Ryuichi Takahashi, Takahiro Nishimichi, Masahiro Takada,
| Summary:
The spatial curvature ($Omega_K$) of the Universe is one of the most
fundamental quantities that could give a link to the early universe physics. In
this paper we develop an approximate method to compute the nonlinear matter
power spectrum, $P(k)$, for "non-flat" $Lambda$CDM models using the separate
universe (SU) ansatz which states that the effect of the curvature on structure
formation is equivalent to that of long-wavelength density fluctuation
($delta_{rm b}$) in a local volume in the "flat" $Lambda$CDM model, via the
specific mapping between the background cosmological parameters and redshifts
in the non-flat and flat models. By utilizing the fact that the normalized
response of $P(k)$ to $delta_{rm b}$ (equivalently $Omega_K$), which
describes how the non-zero $Omega_K$ alters $P(k)$ as a function of $k$, is
well approximated by the response to the Hubble parameter $h$ within the flat
model, our method allows one to generalize the prediction of $P(k)$ for flat
cosmologies via fitting formulae or emulators to that for non-flat cosmologies.
We use $N$-body simulations for the non-flat $Lambda$CDM models with
$|Omega_K|leq 0.1$ to show that our method can predict $P(k)$ for non-flat
models up to $k simeq 6,h{rm Mpc}^{-1}$ in the redshift range $zsimeq
[0,1.5]$, to the fractional accuracy within $sim 1$% that roughly corresponds
to requirements for weak lensing cosmology with upcoming surveys. We find that
the emulators, those built for flat cosmologies such as EuclidEmulator, can
predict the non-flat $P(k)$ with least degradation.
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