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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