2 00 4 A note on the structural stability of tachyonic inflation

We study the structural stability of tachyonic inflation against changes in the shape of the potential. Following Lidsey (Gen. Rel. Grav. 25, 399 (1993)), the concepts of rigidity and fragility are defined through a condition on the functional form of the Hubble factor. We find that the models are rigid in the sense that the attractor solutions never change as long as the conditions for inflation are met. The inflationary paradigm has received the support of WMAP data [1], but a completely satisfactory theoretical explanation remains nonexistent. Some works in this direction have attempted to find an answer in string theory, and as a result tachyonic inflation has been put forward [2]. The idea strongly relies in the possibility of describing tachyon condensates in string theories in terms of perfect fluids. Many papers have been devoted to the study of cosmological consequences of such fluids both in general relativity and brane-world cosmology [3, 4, 5]. Recently, tachyonic inflation has been criticized [6]. It seems though, that the situation is not so clear cut because potentials have been found which seem to circumvent the problem [5]. This area of cosmological modelling, as any other, involves a great deal of idealization; any conclusion or result may turn out to depend strongly on the chosen values and number of free parameters in the tachyon potential. Simplifying assumptions made in common practice do not rely on observations, but are rather chosen for technical convenience. Besides, one cosmological observations are model dependent and not devoid of errors. Thus, making assumptions based on observations results in better but not perfect modelling. As put forward many years ago by Andronov and Pontryagin