Non-linear matter power spectrum without screening dynamics modelling in $f(R)$ gravity. (arXiv:2001.09229v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Ruan_C/0/1/0/all/0/1">Cheng-Zong Ruan</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Zhang_T/0/1/0/all/0/1">Tong-Jie Zhang</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Hu_B/0/1/0/all/0/1">Bin Hu</a>
Halo model is a physically intuitive method for modelling the non-linear
power spectrum, especially for the alternatives to the standard $Lambda$CDM
models. In this paper, we exam the Sheth-Tormen barrier formula adopted in the
previous texttt{CHAM} method citep{2018MNRAS.476L..65H}. As an example, we
model the ellipsoidal collapse of top-hat dark matter haloes in $f(R)$ gravity.
A good agreement between Sheth-Tormen formula and our result is achieved. The
relative difference in the ellipsoidal collapse barrier is less than or equal
to $1.6%$. Furthermore, we verify that, for F4 and F5 cases of Hu-Sawicki
$f(R)$ gravity, the screening mechanism do not play a crucial role in the
non-linear power spectrum modelling up to $ksim1[h/{rm Mpc}]$. We compare two
versions of modified gravity modelling, namely with/without screening. We find
that by treating the effective Newton constant as constant number ($G_{rm
eff}=4/3G_N$) is acceptable. The scale dependence of the gravitational coupling
is sub-relevant. The resulting spectra in F4 and F5, are in $0.1%$ agreement
with the previous texttt{CHAM} results. The published code is accelerated
significantly. Finally, we compare our halo model prediction with N-body
simulation. We find that the general spectrum profile agree, qualitatively.
However, via the halo model approach, there exists a systematic
under-estimation of the matter power spectrum in the co-moving wavenumber range
between $0.3 h/{rm Mpc}$ and $3 h/{rm Mpc}$. These scales are overlapping
with the transition scales from two halo term dominated regimes to those of one
halo term dominated.
Halo model is a physically intuitive method for modelling the non-linear
power spectrum, especially for the alternatives to the standard $Lambda$CDM
models. In this paper, we exam the Sheth-Tormen barrier formula adopted in the
previous texttt{CHAM} method citep{2018MNRAS.476L..65H}. As an example, we
model the ellipsoidal collapse of top-hat dark matter haloes in $f(R)$ gravity.
A good agreement between Sheth-Tormen formula and our result is achieved. The
relative difference in the ellipsoidal collapse barrier is less than or equal
to $1.6%$. Furthermore, we verify that, for F4 and F5 cases of Hu-Sawicki
$f(R)$ gravity, the screening mechanism do not play a crucial role in the
non-linear power spectrum modelling up to $ksim1[h/{rm Mpc}]$. We compare two
versions of modified gravity modelling, namely with/without screening. We find
that by treating the effective Newton constant as constant number ($G_{rm
eff}=4/3G_N$) is acceptable. The scale dependence of the gravitational coupling
is sub-relevant. The resulting spectra in F4 and F5, are in $0.1%$ agreement
with the previous texttt{CHAM} results. The published code is accelerated
significantly. Finally, we compare our halo model prediction with N-body
simulation. We find that the general spectrum profile agree, qualitatively.
However, via the halo model approach, there exists a systematic
under-estimation of the matter power spectrum in the co-moving wavenumber range
between $0.3 h/{rm Mpc}$ and $3 h/{rm Mpc}$. These scales are overlapping
with the transition scales from two halo term dominated regimes to those of one
halo term dominated.
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