 
Summary: Volume 120B, number 1,2,3 PHYSICSLETTERS 6 January 1983
A COSMOLOGICAL BOUND ON THE INVISIBLE AXION
L.F. ABBOTT 1
Physics Department, Brandeis University, Waltham,MA 02254, USA
and
P. SIKIVIE 2
Particle Theory Group, Universityof Florida, Gainesville,FL 32611, USA
Received 14 September 1982
The production of axions in the early universe is studied. Axion models which break the U(1)pQ symmetry above 1012
GeV are found to produce an unacceptably large axion energy density.
The absence of CP violation in the strong interac
tions can be explained naturally by incorporating the
U(1)pQ symmetry of Peccei and Quinn [1] into the
standard model. A consequence of this symmetry is
the axion [2], a spin 0 boson of mass
m a ,~ mJJv, (1)
where v is the magnitude of the vacuum expectation
value which breaks the U(1)pQ symmetry. An axion
of mass (1) with v of order the weak interaction scale
has not been observed. However, it has been pointed
