Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Can we neglect relativistic temperature corrections in the Planck
  thermal SZ analysis?   Measurements of the thermal Sunyaev-Zel'dovich (tSZ) effect have long been
recognized as a powerful cosmological probe. Here we assess the importance of
relativistic temperature corrections to the tSZ signal on the power spectrum
analysis of the Planck Compton-$y$ map, developing a novel formalism to account
for the associated effects. The amplitude of the tSZ power spectrum is found to
be sensitive to the effective electron temperature, $\bar{T}_e$, of the cluster
sample. Omitting the corresponding modifications leads to an underestimation of
the $yy$-power spectrum amplitude. Relativistic corrections thus add to the
error budget of tSZ power spectrum observables such as $\sigma_8$. This could
help alleviate the tension between various cosmological probes, with the
correction scaling as $\Delta \sigma_8/\sigma_8 \simeq
0.019\,[k\bar{T}_e\,/\,5\,{\rm keV}]$ for Planck. At the current level of
precision, this implies a systematic shift by $\simeq 1\sigma$, which can also
be interpreted as an overestimation of the hydrostatic mass bias by $\Delta b
\simeq 0.046\,(1-b)\,[k\bar{T}_e\,/\,5\,{\rm keV}]$, bringing it into better
agreement with hydrodynamical simulations. It is thus time to consider
relativistic temperature corrections in the processing of current and future
tSZ data.

9
The categories of this paper are: nlin
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex