Monopole Fluctuation of the CMB and its Gauge Invariance. (arXiv:2012.03968v2 [astro-ph.CO] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Baumgartner_S/0/1/0/all/0/1">Sandra Baumgartner</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Yoo_J/0/1/0/all/0/1">Jaiyul Yoo</a> (Zürich)
The standard theoretical description $Theta(hat n)$ of the observed CMB
temperature anisotropies is gauge-dependent. It is, however, well known that
the gauge mode is limited to the monopole and the higher angular multipoles
$Theta_l$ ($lgeq1$) are gauge-invariant. Several attempts have been made in
the past to properly define the monopole fluctuation, but the resulting values
of the monopole power $C_0$ are infinite due to the infrared divergences. The
infrared divergences arise from the contribution of the uniform gravitational
potential to the monopole fluctuation, in violation of the equivalence
principle. Here we present the gauge-invariant theoretical description of the
observed CMB temperature anisotropies and compute the monopole power
$C_0=1.66times10^{-9}$ in a $Lambda$CDM model. While the gauge-dependence in
the standard calculations originates from the ambiguity in defining the
hypersurface for the background CMB temperature $bar T$ today, it is in fact
well defined and one of the fundamental cosmological parameters. We argue that
once the cosmological parameters are chosen, the monopole fluctuation can be
unambiguously inferred from the angle-average of the observed CMB temperature,
making it a model-dependent ”observable”. Adopting simple approximations for
the anisotropy formation, we derive a gauge-invariant analytical expression for
the observed CMB temperature anisotropies to study the CMB monopole fluctuation
and the cancellation of the uniform gravitational potential contributions on
large scales.
The standard theoretical description $Theta(hat n)$ of the observed CMB
temperature anisotropies is gauge-dependent. It is, however, well known that
the gauge mode is limited to the monopole and the higher angular multipoles
$Theta_l$ ($lgeq1$) are gauge-invariant. Several attempts have been made in
the past to properly define the monopole fluctuation, but the resulting values
of the monopole power $C_0$ are infinite due to the infrared divergences. The
infrared divergences arise from the contribution of the uniform gravitational
potential to the monopole fluctuation, in violation of the equivalence
principle. Here we present the gauge-invariant theoretical description of the
observed CMB temperature anisotropies and compute the monopole power
$C_0=1.66times10^{-9}$ in a $Lambda$CDM model. While the gauge-dependence in
the standard calculations originates from the ambiguity in defining the
hypersurface for the background CMB temperature $bar T$ today, it is in fact
well defined and one of the fundamental cosmological parameters. We argue that
once the cosmological parameters are chosen, the monopole fluctuation can be
unambiguously inferred from the angle-average of the observed CMB temperature,
making it a model-dependent ”observable”. Adopting simple approximations for
the anisotropy formation, we derive a gauge-invariant analytical expression for
the observed CMB temperature anisotropies to study the CMB monopole fluctuation
and the cancellation of the uniform gravitational potential contributions on
large scales.
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