The intergalactic hydrogen atoms after recombination are in their ground state, which hyperfine-structure
splits into a singlet and a triple states ( with
and
respectively, see
Section III.B.1 of FCV [500
]). It was recently proposed [284
] that the observation of the 21 cm emission
can provide a test on the fundamental constants. We refer to [221
] for a detailed review on
21 cm.
The fraction of atoms in the excited (triplet) state versus the ground (singlet) state is conventionally
related by the spin temperature defined by the relation
It follows [284, 285] that the change in the brightness temperature of the CMB at the corresponding
wavelength scales as
, where the Einstein coefficient
is defined below. Observationally,
we can deduce the brightness temperature from the brightness
, that is the energy received in a given
direction per unit area, solid angle and time, defined as the temperature of the black-body radiation with
spectrum
. Thus,
. It has a mean value,
at various redshift where
. Besides, as for the CMB, there will also be fluctuation in
due
to imprints of the cosmological perturbations on
and
. It follows that we also have
access to an angular power spectrum
at various redshift (see [329
] for details on this
computation).
Both quantities depend on the value of the fundamental constants. Beside the same dependencies
of the CMB that arise from the Thomson scattering cross section, we have to consider those
arising from the collision terms. In natural units, the Einstein coefficient scaling is given by
. It follows that it scales as
. The brightness
temperature depends on the fundamental constant as
. Note that the signal can also be
affected by a time variation of the gravitational constant through the expansion history of the universe.
[284] (see also [221] for further discussions), focusing only on
, showed that this was the dominant
effect on a variation of the fundamental constant (the effect on
is much complicated to
determine but was argued to be much smaller). It was estimated that a single station telescope like
LWA9 or
LOFAR10
can lead to a constraint of the order of
, improving to 0.3% for the full LWA. The
fundamental challenge for such a measurement is the subtraction of the foreground.
The 21 cm absorption signal in a available on a band of redshift typically ranging from to
, which is between the CMB observation and the formation of the first stars, that is
during the “dark age”. Thus, it offers an interesting possibility to trace the constraints on the
evolution of the fundamental constants between the CMB epoch and the quasar absorption
spectra.
As for CMB, the knowledge of the cosmological parameters is a limitation since a change of 1% in the
baryon density or the Hubble parameter implies a 2% (3% respectively) on the mean bolometric
temperature. The effect on the angular power spectrum have been estimated but still require an in depth
analysis along the lines of, e.g., [329]. It is motivating since is expected to depend on the
correlators of the fundamental constants, e.g.,
and thus in principle allows to
study their fluctuation, even though it will also depend on the initial condition, e.g., power spectrum, of the
cosmological perturbations.
In conclusion, the 21 cm observation opens a observational window on the fundamental at redshifts ranging typically from 30 to 100, but full in-depth analysis is still required (see [206, 286] for a critical discussion of this probe).
http://www.livingreviews.org/lrr-2011-2 |
Living Rev. Relativity 14, (2011), 2
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