ar X iv : g r - qc / 9 80 30 67 v 2 1 9 M ar 1 99 8 A Non - Singular Universe in String Cosmology
چکیده
We consider the low-energy effective string action in four dimensions including the leading order-α ′ terms. An exact homogeneous solution is obtained. It represents a non-singular expanding cosmological model in which the tensor fields tend to vanish as t → ∞. The scale factor a(t) of the very early universe in this model has the time dependence a(t) 2 = a 2 0 + t 2. The violation of the strong energy condition of classical General Relativity to avoid the initial singularity requires that the central charge deficit of the theory be larger than a certain value. The significance of this solution is discussed. The search for cosmological models that do not suffer from the problems inflicting the standard big bang model of cosmology has intensified since the advent of string theory. String theory is particularly relevant to the initial singularity problem whose solution has long been thought to require a quantum theory of gravity, for which string theory seems to be the most promising candidate. The effective action for string theory has been calculated in the α ′-expansion in both the sigma model approach [1-4] in which one looks upon string theory as a two dimensional conformal field theory in background fields and the S-matrix approach [5]. Recently, modifications introduced by string theory, near the Planck scale, to classical general relativity and cosmology have been considered by many physicists [6-28]. Brustein and Veneziano [21] and Kaloper, Madden and Olive [26] showed 1