ON THE CREATION OF DENSITY FLUCTUATIONS FROM THE HETEROTIC COSMIC SUPERSTRING

Abstract

It has been proved by Witten that the heterotic superstring theory appears phenomeno-logically as a closed, superconducting, axionic cosmic string attached to one axion domain wall. After reduction from ten dimensions to four dimensions, the effective mass per unit length of the string is [Formula: see text], where α′ = 1/2πμ is the Regge slope parameter and bc is the compactification length. The string-wall system is present ab initio in the expanding Friedmann universe, and is dominated energetically by the string. Consequently, a scale-free spectrum of density (metric) fluctuations is impressed upon the space-time at its classical inception, whose magnitude, according to Zel'dovich, is ξ ≡ δρ/ρ ≈ 4πGμc ≈ 4 × 10−2g2, where [Formula: see text] is the Newton gravitational constant, M P is the Planck mass and g is the string gauge coupling parameter. The string disappears via gravitational or electromagnetic radiation on the time scale τ ≲ 2M P /μc, thus removing all conflict with the non-observation of timing residuals in the millisecond pulsars. The value of ξ should be commensurate with that previously obtained from the effective action, illustrating the notion of reciprocity between the two-dimensional, world-sheet and four-dimensional, space-time formulations of the theory. It therefore suggests that bc ≈ b H ≡ 1/2πT H , where [Formula: see text] is the Hagedorn temperature, since the two-loop calculation of the free energy by Hellmund and Kripfganz indicates that g2 → 0 as T → T H .