R-Invariant Topological Inflation

We propose a topological inflation model in the framework of supergravity with R invari-ance. This topological inflation model is not only free from the initial value problem of the inflaton field but also gives a low reheating temperature, which is favored in supergravity, since in this case the overproduction of gravitinos is avoided. Furthermore, the predicted spectrum of the density fluctuations is found to be generally tilted. This result can be tested by future observations concerning CMB anisotropies and the large scale structure of the universe. The topological 1), 2) and chaotic 3) inflation models are very attractive among various inflation models considered to this time, since they do not suffer from the initial value problem 3) for the inflaton field ϕ. That is, within these models the inflationary universe is a natural consequence of the system. The chaotic inflation model assumes large initial values ϕ0 1, where we set the gravitational scale M = 2.4 × 1018 GeV to unity. It is, however, unlikely that this is realized in the framework of supergravity. 4) Thus, we are led to consider the topological inflation model.∗