Optimal constraints on the growth rate using the observed galaxy power spectrum. (arXiv:1907.02975v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Fonseca_J/0/1/0/all/0/1">José Fonseca</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Viljoen_J/0/1/0/all/0/1">Jan-Albert Viljoen</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Maartens_R/0/1/0/all/0/1">Roy Maartens</a>
The large-scale structure growth index $gamma$ provides a consistency test
of the standard cosmology and is a potential indicator of modified gravity. We
investigate the constraints on $gamma$ from next-generation spectroscopic
surveys, using the power spectrum that is observed in redshift space, i.e., the
angular power spectrum. The angular power spectrum avoids the need for an
Alcock-Packzynski correction. It also naturally incorporates cosmic evolution
and wide-angle effects, without any approximation. We develop a redshift
binning strategy that maximises the signal-to-noise on $gamma$ as a function
of bin width. We include the cross-correlations between redshift bins, using a
hybrid approximation when the total number of bins is computationally
unfeasible. Neglecting cross-bin correlations degrades the constraints by a
factor of $sim 1.5-2$. In our forecasts, we marginalise over the amplitude of
primordial fluctuations and other standard cosmological parameters, including
the dark energy equation of state parameter, as well as the clustering bias.
Using only linear scales, we find that at low redshifts, a DESI-like survey and
an SKA1 HI galaxy survey deliver similar errors of {$sim3-4%$}. This is
matched by an intensity mapping survey with the SKA1 precursor MeerKAT. The
high-redshift Euclid-like survey is at a similar level, while an intensity
mapping survey on SKA1 gives the best error of $sim2%$. Sub-percent errors
are predicted for the futuristic SKA2 HI galaxy survey.
The large-scale structure growth index $gamma$ provides a consistency test
of the standard cosmology and is a potential indicator of modified gravity. We
investigate the constraints on $gamma$ from next-generation spectroscopic
surveys, using the power spectrum that is observed in redshift space, i.e., the
angular power spectrum. The angular power spectrum avoids the need for an
Alcock-Packzynski correction. It also naturally incorporates cosmic evolution
and wide-angle effects, without any approximation. We develop a redshift
binning strategy that maximises the signal-to-noise on $gamma$ as a function
of bin width. We include the cross-correlations between redshift bins, using a
hybrid approximation when the total number of bins is computationally
unfeasible. Neglecting cross-bin correlations degrades the constraints by a
factor of $sim 1.5-2$. In our forecasts, we marginalise over the amplitude of
primordial fluctuations and other standard cosmological parameters, including
the dark energy equation of state parameter, as well as the clustering bias.
Using only linear scales, we find that at low redshifts, a DESI-like survey and
an SKA1 HI galaxy survey deliver similar errors of {$sim3-4%$}. This is
matched by an intensity mapping survey with the SKA1 precursor MeerKAT. The
high-redshift Euclid-like survey is at a similar level, while an intensity
mapping survey on SKA1 gives the best error of $sim2%$. Sub-percent errors
are predicted for the futuristic SKA2 HI galaxy survey.
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