Power-Law Inflation from the Rolling Tachyon

Modeling the potential by an inverse square law in terms of the tachyon field (V (T ) = βT−2) we find exact solution for spatially flat isotropic universe. We show that for β > 2 √ 3/3 the model undergoes power-law inflation. A way to construct other exact solutions is specified and exemplified. Several interesting attempts to reconcile the inflationary paradigm with string theories have resulted recently in much work ( see for example [1]). These efforts, however, did not produce a completely successful union between the string theory and cosmology. It is fair to say, at this stage, that string inspired cosmologies are not a match to standard inflation. Yet, since many believe that superstrings or their generalisations provide an adequate description of fundamental interactions including gravity, it is worthwhile to pursue exploring the connections between the string theories and cosmology. Much has been written and emphasised about the role of the fundamental dilaton field in the context of string cosmology. Less is known about tachyon component of the string theory. Recently, several works have appeared studying such a field in the cosmological context [2], [3]. The main purpose of this note is to show that under the assumption that the tachyon potential behaves as an inverse square in terms of the field, the Einstein equations lead to simple exact analytic solutions in the case of spatially flat isotropic universe. These solutions undergo the so-called power-law inflationary expansion if the “slope” of the potential β > 2 √ 3/3, and decelerate otherwise. We also indicate and exemplify as to how more general solutions can be constructed. To this end we consider spatially flat FRW line element given by: ds = dt − a(t)(dx + dy + dz) (1) As shown by Sen [4], [5] a rolling tachyon condensate may be described by an effective fluid with energy density and pressure given by