Monopoles, Axions and Intermediate Mass Dark Matter

We present a solution to the cosmological problem encountered in (supersymmetric) grand unified theories due to copious monopole production at the end of hybrid inflation. By employing thermal inflation “driven” by the U(1) axion symmetry, the superheavy monopole flux can be naturally suppressed to values that should be accessible to dedicated large scale experiments. The U(1) axion symmetry also helps generate the right magnitude for the μ term of the minimal supersymmetric standard model. An important by-product is the predicted existence of stable or very longliving fermions possessing intermediate scale masses of order 1012 GeV. Their presence is required for implementing thermal inflation, and their stability is due to a Z2 symmetry. They may constitute a sizable fraction of cold dark matter, and possibly help explain the ultra-high energy cosmic ray events. The rest of cold dark matter may consist of axions. Although our discussion is carried out within the framework of supersymmetric SU(4)c × SU(2)L × SU(2)R , it can be extended to other grand unified gauge groups such as SU(3)c × SU(3)L × SU(3)R or SO(10). [email protected] [email protected] The great advantage of hybrid inflation [1] is that, in contrast to previous inflationary schemes, it can reproduce the observed temperature fluctuations of the cosmic microwave background radiation with natural values of the relevant coupling constant. Moreover, this inflationary scenario is almost automatically realized [2,3] in supersymmetric (SUSY) grand unified theories (GUTs). However, in trying to apply it to GUTs which predict the existence of magnetic monopoles, a cosmological disaster is encountered. Hybrid inflation is terminated abruptly when the system reaches an instability point on the inflationary trajectory and is followed by a ‘waterfall’ regime during which the spontaneous breaking of the GUT gauge symmetry takes place. The appropriate Higgs fields develop their vacuum expectation values (vevs) starting from zero and they can end up at any point of the vacuum manifold with equal probability. As a consequence, monopoles are copiously produced [4] by the Kibble mechanism [5] leading to a cosmological catastrophe. Possible solutions to this monopole problem have been proposed [4,6]. They rely on introducing the leading non-renormalizable term in the standard superpotential [2] for hybrid inflation. (For different resolutions of the problem see Ref. [7].) In Ref. [4], the trilinear coupling of this standard superpotential was eliminated by a discrete symmetry and was replaced by the leading non-renormalizable term. The system, from the beginning of inflation, follows a particular valley and ends up at a particular point of the vacuum manifold. Thus, no monopoles can be produced. The inflationary trajectory possesses a classical inclination driving the inflaton towards the SUSY vacua and the termination of inflation is smooth. In Ref. [6], both the trilinear and the leading non-renormalizable couplings were kept revealing a quite different picture. The inflationary trajectory is classically flat and, thus, radiative corrections [3] are needed for driving the inflaton. The termination of inflation is abrupt. Nevertheless, there is no monopole production since the GUT gauge symmetry is already broken during inflation. Both models predict complete absence of monopoles which may be disappointing for the experimenters. In this letter, we propose an alternative solution to the monopole problem of hybrid inflation which may yield a measurable monopole flux in our galaxy. The idea is to keep the original SUSY hybrid inflationary scenario unaltered and try to dilute the monopoles by invoking a subsequent thermal inflation [8,9] associated with an intermediate mass scale. (The main ideas underlying thermal inflation have been presented in Ref. [8]. The