Stars as Laboratories for Fundamental Physics - MPP Theory Group

190 Chapter 5
than about 10 −9 of a given neutrino species may show up in the form
of decay photons (Fig. 12.9) if the spectral distribution is taken to be
characterized by T ≈ 30 MeV. Therefore, one finds a limit of g 4 10 ∼ <
10 −4 or g aγ ∼ < 10 −11 GeV −1 , applicable if the particle mass is below
about 10 −10 eV. This is more restrictive than Carlson’s original limit,
and of the same order as the PSR 1937+21 birefringence limit quoted
after Eq. (5.36).
5.5.4 Polarimetry of Distant Radio Sources
Nambu-Goldstone bosons a are by definition the result of a spontaneously
broken global symmetry. The cosmic evolution from a very
hot initial phase begins with the unbroken symmetry; as the universe
expands and cools a phase transition will occur where the field responsible
for the spontaneous breakdown must find its new minimum. As
this process occurs independently in each causally connected region of
the universe at that time, the universe today will be characterized by
different orientations of the ground state, i.e. by different values of a
classical background a field. If no inflation occurred in the universe
after the phase transition, and if the Nambu-Goldstone bosons remain
truly massless (in contrast with axions), the background field will not
have relaxed to a common ground state everywhere.
In this scenario a radio signal from a distant source travels through
regions with different values of the classical a field, and thus through
regions of gradients ∇a which act as an optically active medium according
to Eq. (5.35). Therefore, linearly polarized light will experience a
random rotation of its plane of polarization.
This effect is also expected from the Faraday rotation caused by
intervening magnetic fields which induce optical activity in the cosmic
background plasma. As this effect is frequency dependent it can be
removed by observing a given object at different wavelengths. The
effect induced by pseudoscalars, on the other hand, is independent of
frequency.
A systematic correlation between the geometric shape of distant
radio sources and the linear polarization of the emitted radiation has
been observed. This correlation proves that no random rotation of
the plane of polarization occurs over cosmic distances, except for the
Faraday effect which can be removed from the data. Therefore, the
maximum allowed coupling strength of photons to a random cosmic
Nambu-Goldstone field can be constrained. Harari and Sikivie (1992)
found that C < aγ ∼ 50 in Eq. (5.5), independently of the symmetry break-