The computation of PBH (primordial black hole) production from primordial perturbations has recently been improved by considering a more accurate relation between the primordial power spectrum and the PBH mass variance. We present here exact expressions which are valid for primordial spectra of arbitrary shape and which allow accurate numerical calculations. We then consider the possibility to have a significant part of dark matter in the form of PBHs produced by a primordial spectrum of inflationary origin possessing a characteristic scale. We show that in this model the relevant PBH mass is constrained to lie in the range 5 × 10 15 g M 10 21 g. This is much less than the mass range coming from the QCD phase transition, allowing the two mechanisms to be easily distinguished.

We perform an accurate computation of the production rate for primordial black holes (PBHs). The reason is that the underlying mass variance had been overestimated systematically, as was shown recently. For scale-free powerlaw primordial spectra, and for a Universe with critical density, the mass variance is less than 34% of its value thought earlier for the spectral index in the range 1 ≤ n ≤ 1.3. We then extend our study to spectra with a characteristic scale and find the accurate shape of the corresponding mass variance. For a pure step in the primordial spectrum, the step in the variance is smoothed around the characteristic scale ks. For a spectrum with large oscillations near ks, we find a pronounced bump in the variance. This could yield a significant part of the cold dark matter in the form of PBHs with mass M in the range 5 × 10 15 g M 10 21 g.

We consider Double Quintessence models for which the Dark Energy sector consists of two coupled scalar fields. We study, in particular, the possibility to have a transient acceleration in these models. In both Double Quintessence models studied here, it is shown that, if acceleration occurs, it is necessarily transient. We consider also the possibility to have transient acceleration in two one-field models, the Albrecht-Skordis model and the pure exponential. Using separate conservative constraints (marginalizing over the other parameters) on the effective equation of state w eff , the relative density of the Dark Energy Q;0 and the present age of the Universe, we construct scenarios with a transient acceleration that has already ended at the present time, and even with no acceleration at all, but a less conservative analysis using the cosmic microwave background data rules out the last possibility. The scenario with a transient acceleration ended by today can be implemented for the range of cosmological parameters m;0 * 0:35 and h & 0:68.