Axion Cosmology with its Scalar Superpartner

In supersymmetric theories, the Peccei-Quinn symmetry has a complex extension as a symmetry of the superpotential, so that the scalar potential always has an almost flat direction, the dilaton. We discuss how coherent oscillation of the dilaton affects axion cosmology. We stress that the dilaton decay, if its dominant mode is not into axions, releases large entropy at a late epoch of the Universe’s evolution to dilute axion energy density and the upperbound of the decay constant is raised up to about 10 GeV. The case of the M-theory axion is also discussed. ∗Research Fellow of the Japan Society for the Promotion of Science. Although the standard model describes interactions of elementary particles remarkably well, its extension is demanded by some fine tuning problems in it. One of such fine tuning problems is the strong CP problem [1] and another is the Higgs mass hierarchy problem. So far, the most attractive solution to the latter problem is supersymmetry [2], whereas the Peccei-Quinn (PQ) mechanism solves the former one in a beautiful way [3]. The standard arguments based on astrophysics and cosmology constrain the PQ symmetry breaking scale to lie between 10 GeV and 10 GeV [4, 5]. In this paper, we shall consider the PQ mechanism in the framework of supersymmetry. Then the axion forms a supermultiplet. We shall discuss cosmological effects of the scalar superpartner of the axion and show that it can drastically change the standard axion cosmology. In supersymmetry, the PQ U(1)PQ symmetry is extended to its complex form U(1)PQ as a symmetry of the superpotential [6]. To illustrate this point, let us consider a linear realization of the U(1)PQ symmetry, in which a field transforms as φ → eiφ, (1) where α is a real parameter of the U(1)PQ transformation and Qi the U(1)PQ charge of the field. The point is that the superpotential W (φ), a holomorphic function of the complex fields φ, is invariant under the U(1)PQ transformation with α being now an arbitrary complex number. When α is pure imaginary, the transformation corresponds to a dilatational one. Under the assumption of unbroken supersymmetry, this U(1)PQ symmetry leads to the existence of a non-compact flat direction in the scalar potential, associated with this dilatational transformation. We shall call, in this paper, the field along this flat direction a “dilaton” field, which will be denoted by φ. Supersymmetry breaking generates the potential for the dilaton field and thus the dilaton mass. In the gravity-mediated supersymmetry breaking scenario, the dilaton mass, mφ, is of the order of the gravitino mass, m3/2, which should be in the TeV range. Existence of the weakly-interacting scalar field, the dilaton, can drastically change axion cosmology. In the early Universe the coherent mode of the dilaton field is in general displaced from its true minimum. As the expansion rate of the Universe becomes comparable to the dilaton mass mφ, the field starts damped oscillation. As we will see, the coherent oscillation of the dilaton and its subsequent decay may play important roles in the history