Understanding the relativistic overdensity of galaxy surveys. (arXiv:1606.00712v5 [astro-ph.CO] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Duniya_D/0/1/0/all/0/1">Didam Duniya</a> (BIUST, Cape Town, AIMS, Western Cape)
The main goal of galaxy surveys is to map the distribution of the galaxies,
for the purpose of understanding the properties of this distribution and its
implications for the content and the evolution of the universe. However, in
order to realise the full potential of these surveys, we need to ensure that we
are using the correct analysis: a relativistic analysis, which has been widely
studied recently. In this work, the known relativistic overdensity of galaxy
surveys is re-examined. Unlike in previous works, a consistent approach for
incorporating both the relativistic number-count overdensity and the
relativistic cosmic magnification overdensity in the total observed overdensity
of a generic survey, is presented. Since in practice, analyses are often done
for specific sample types (flux-limited or volume-limited) the approach in this
work allows for the total observed overdensity to be easily reduced to either
of the individual overdensities by applying the same limiting conditions as for
extracting the corresponding data samples. This is not obvious, or in some
cases not possible, with the results of previous works. Thus, the calculations
in this work serve to generalise the expression for the total observed
overdensity. However, care must be taken to apply it appropriately: the type of
the data sample in consideration needs to be taken into account.
The main goal of galaxy surveys is to map the distribution of the galaxies,
for the purpose of understanding the properties of this distribution and its
implications for the content and the evolution of the universe. However, in
order to realise the full potential of these surveys, we need to ensure that we
are using the correct analysis: a relativistic analysis, which has been widely
studied recently. In this work, the known relativistic overdensity of galaxy
surveys is re-examined. Unlike in previous works, a consistent approach for
incorporating both the relativistic number-count overdensity and the
relativistic cosmic magnification overdensity in the total observed overdensity
of a generic survey, is presented. Since in practice, analyses are often done
for specific sample types (flux-limited or volume-limited) the approach in this
work allows for the total observed overdensity to be easily reduced to either
of the individual overdensities by applying the same limiting conditions as for
extracting the corresponding data samples. This is not obvious, or in some
cases not possible, with the results of previous works. Thus, the calculations
in this work serve to generalise the expression for the total observed
overdensity. However, care must be taken to apply it appropriately: the type of
the data sample in consideration needs to be taken into account.
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