Cosmology and neutrino mass with the Minimum Spanning Tree. (arXiv:2111.12088v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Naidoo_K/0/1/0/all/0/1">Krishna Naidoo</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Massara_E/0/1/0/all/0/1">Elena Massara</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Lahav_O/0/1/0/all/0/1">Ofer Lahav</a>

The information content of the minimum spanning tree (MST), used to capture
higher-order statistics and other information from the cosmic web, is compared
to that of the power spectrum for a $nuLambda$CDM model. The measurements are
made in redshift space using haloes from the Quijote simulation of mass $geq
3.2times 10^{13},h^{-1}{rm M}_{odot}$ in a box of length $L_{rm
box}=1,h^{-1}{rm Gpc}$. The power spectrum multipoles (monopole and
quadrupole) are computed for Fourier modes in the range $0.006 < k < 0.5,
h{rm Mpc}^{-1}$. For comparison the MST is measured with a minimum length
scale of $l_{min}simeq13,h^{-1}{rm Mpc}$. Combining the MST and power
spectrum allows for many of the individual degeneracies to be broken; on its
own the MST provides tighter constraints on the sum of neutrino masses
$M_{nu}$, Hubble constant $h$, spectral tilt $n_{rm s}$, and baryon energy
density $Omega_{rm b}$ but the power spectrum alone provides tighter
constraints on $Omega_{rm m}$ and $sigma_{8}$. The power spectrum on its own
gives a standard deviation of $0.25,{rm eV}$ on $M_{nu}$ while the
combination of power spectrum and MST gives $0.11,{rm eV}$. There is similar
improvement of a factor of two for $h$, $n_{rm s}$, and $Omega_{rm b}$.
These improvements appear to be driven by the MST’s sensitivity to small scale
clustering, where the effect of neutrino free-streaming becomes relevant. The
MST is shown to be a powerful tool for cosmology and neutrino mass studies, and
therefore could play a pivotal role in ongoing and future galaxy redshift
surveys (such as DES, DESI, Euclid, and Rubin-LSST).

The information content of the minimum spanning tree (MST), used to capture
higher-order statistics and other information from the cosmic web, is compared
to that of the power spectrum for a $nuLambda$CDM model. The measurements are
made in redshift space using haloes from the Quijote simulation of mass $geq
3.2times 10^{13},h^{-1}{rm M}_{odot}$ in a box of length $L_{rm
box}=1,h^{-1}{rm Gpc}$. The power spectrum multipoles (monopole and
quadrupole) are computed for Fourier modes in the range $0.006 < k < 0.5,
h{rm Mpc}^{-1}$. For comparison the MST is measured with a minimum length
scale of $l_{min}simeq13,h^{-1}{rm Mpc}$. Combining the MST and power
spectrum allows for many of the individual degeneracies to be broken; on its
own the MST provides tighter constraints on the sum of neutrino masses
$M_{nu}$, Hubble constant $h$, spectral tilt $n_{rm s}$, and baryon energy
density $Omega_{rm b}$ but the power spectrum alone provides tighter
constraints on $Omega_{rm m}$ and $sigma_{8}$. The power spectrum on its own
gives a standard deviation of $0.25,{rm eV}$ on $M_{nu}$ while the
combination of power spectrum and MST gives $0.11,{rm eV}$. There is similar
improvement of a factor of two for $h$, $n_{rm s}$, and $Omega_{rm b}$.
These improvements appear to be driven by the MST’s sensitivity to small scale
clustering, where the effect of neutrino free-streaming becomes relevant. The
MST is shown to be a powerful tool for cosmology and neutrino mass studies, and
therefore could play a pivotal role in ongoing and future galaxy redshift
surveys (such as DES, DESI, Euclid, and Rubin-LSST).

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