On model independent cosmic determinations of $H_0$. (arXiv:2101.08565v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Colgain_E/0/1/0/all/0/1">E. Ó Colgáin</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Sheikh_Jabbari_M/0/1/0/all/0/1">M.M. Sheikh-Jabbari</a>
Motivated by Hubble tension, we have recently witnessed a number of “model
independent” $H_0$ determinations at cosmological scales. Here we compare two
“model independent” techniques, Taylor expansion and Gaussian Processes (GP).
While Taylor expansion is truly model independent in a limited range, we show
that one can reduce the $H_0$ errors by increasing the range of the expansion,
but the approximation suffers. For GP, we confirm for the Mat’ern class
kernels that the errors on $H_0$ decrease as the parameter $nu rightarrow
infty$, where we recover the Gaussian kernel. The errors from GP are typically
smaller than Taylor and by mapping the GP analysis back into the Taylor
expansion, we show that GP explores a smaller portion of the parameter space.
In a direct comparison of GP with the CPL model, the simplest model of
dynamical dark energy, we see that correlations are suppressed by GP relative
to CPL. Therefore, GP cannot be model independent. We emphasise that if a truly
model independent statement of Hubble tension exists, then it will have serious
consequences for the FLRW framework.
Motivated by Hubble tension, we have recently witnessed a number of “model
independent” $H_0$ determinations at cosmological scales. Here we compare two
“model independent” techniques, Taylor expansion and Gaussian Processes (GP).
While Taylor expansion is truly model independent in a limited range, we show
that one can reduce the $H_0$ errors by increasing the range of the expansion,
but the approximation suffers. For GP, we confirm for the Mat’ern class
kernels that the errors on $H_0$ decrease as the parameter $nu rightarrow
infty$, where we recover the Gaussian kernel. The errors from GP are typically
smaller than Taylor and by mapping the GP analysis back into the Taylor
expansion, we show that GP explores a smaller portion of the parameter space.
In a direct comparison of GP with the CPL model, the simplest model of
dynamical dark energy, we see that correlations are suppressed by GP relative
to CPL. Therefore, GP cannot be model independent. We emphasise that if a truly
model independent statement of Hubble tension exists, then it will have serious
consequences for the FLRW framework.
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