Assisting pre-big bang phenomenology through short-lived axions

We present the results of a detailed study of how isocurvature axion fluctuations are converted into adiabatic metric perturbations through axion decay, and discuss the constraints on the parameters of pre-big bang cosmology needed for consistency with present CMB-anisotropy data. The large-scale normalization of temperature fluctuations has a non-trivial dependence both on the mass and on the initial value of the axion. In the simplest, minimal models of pre-big bang inflation consistency with the COBE normalization requires a slightly tilted (blue) spectrum, while a strictly scale-invariant spectrum requires mild modifications of the minimal backgrounds at large curvature and/or string coupling. It is well known that, in the framework of pre-big bang cosmology (see [1, 2] for recent reviews), the primordial spectrum of scalar (and tensor) metric perturbations is characterized by a steep positive slope [3]. Since the high-frequency normalization of the spectrum is fixed by the ratio of the string to the Planck mass, the amplitude of metric fluctuations turns out to be strongly suppressed at large scales, and thus unable to account for the CMB anisotropies observed by COBE [4] and by other satellite experiments [5] (unless one accepts rather drastic modifications of pre-big bang kinematics, as recently suggested in [6]). A possible solution of this problem could be provided, a priori, by the fluctuations of another background field of string theory, in particular of the so-called Kalb-Ramond axion σ (the dual of the NS-NS two-form appearing in the dimensionally reduced string effective action [7]). As first pointed out in [8], axionic quantum fluctuations of the vacuum are amplified by pre-big bang inflation yielding a final spectrum whose index nσ can vary, depending on the evolution of extra dimensions. The scale-invariant value of nσ = 1 is attained, amusingly enough, for particularly symmetric evolutions of the nine spatial dimensions in which critical superstrings consistently propagate. Indeed, even if no axion potential is present in the post-big bang era, a (generally nonGaussian) spectrum of temperature anisotropies can be induced by the fluctuations of the massless [9, 10] axion field, at second order, through the so-called “seed” mechanism [11]. The same is true for a massive light axion that has not decayed yet [12]. Unfortunately, while the model is capable of reproducing the low-multipole COBE data [4], it clearly appears [13] to be disfavoured with respect to standard inflationary models when it comes to fitting data in the acoustic-peaks region [5]. An interesting alternative possibility, first suggested in [1], and recently discussed in detail (and not exclusively within a string cosmology framework) in [14, 15, 16, 17], uses a general mechanism originally pointed out in [18]. It is based on two basic assumptions: i) the constant value of the axion background after the pre-big bang phase is displaced from the minimum (conventionally defined as σ = 0) of the non-perturbative potential V (σ) generated in the post-big bang epoch ; ii) the axion potential is strong enough to induce a phase of axion dominance before its decay into radiation. Under these two (rather plausible) assumptions, the initially amplified isocurvature axion fluctuations can be converted, without appreciable change of the spectrum, into adiabatic (and Gaussian) scalar curvature perturbations until the time of horizon re-entry: these can then possibly produce the observed CMB anisotropies. Various aspects of this new mechanism have been already discussed in [14] for the string theory axion, and in [15, 16, 17] (mostly in the context of conventional inflationary models) for the case of a generic scalar field (dubbed the “curvaton” in [15]). Here, after providing an explicit derivation and computation of the conversion of axion fluctuations into scalar curvature perturbations, we shall discuss the constraints imposed by the CMB data, and its possible consistency with the small-scale normalization and tilts typical of pre-big bang