We consider primordial black hole (PBH) production in inflationary α-attractors. We discuss two classes of models, namely models with a minimal polynomial superpotential as well as modulated chaotic ones that admit PBHs. We find that a significant amplification of the curvature power spectrum P R can be realized in this class of models with a moderate tuning of the potential parameters. We consistently examine the PBH formation during radiation and additionally during reheating eras where the background pressure is negligible. It is shown that basic features of the curvature power spectrum are explicitly related with the postinflationary cosmic evolution and that the PBH mass and abundance expressions are accordingly modified. PBHs in the mass range 10 −16 − 10 −14 M can form with a cosmologically relevant abundance for a power spectrum peak P R ∼ 10 −2 and large reheating temperature and, furthermore, for a moderate peak P R ∼ 10 −5 and reheating temperature T rh ∼ 10 7 GeV, characteristic of the position of the power spectrum peak. Regarding the CMB observables, the α-attractor models utilized here to generate PBH in the low-mass region predict in general a smaller n s and larger r and α s parameter values compared to the conventional inflationary α-attractor models.

We discuss flux compactifications of IIA string theory on G2 holonomy spaces with O2/O6-planes to three dimensions and find two classes of solutions: (1) No-scale Minkowski vacua from NSNS 3-form fluxes and RR 4-form fluxes. (2) By adding Romans mass we find AdS$$_3$$ 3 vacua for which the AdS scale can be decoupled completely from the KK scale while the solution is at tunable weak coupling and large volume. For the AdS$$_3$$ 3 vacuum we only have a proper 3D description (i.e. smeared orientifold description) of the solution like the 4D analogue of IIA moduli stabilization from fluxes and O6-planes. This 3D description reveals that moduli with non-compact moduli spaces can be stabilized at the classical level. For both types of vacua we can have supersymmetry or not.

We investigate the cosmology of mini Primordial Black Holes (PBHs) produced by large density perturbations. The mini PBHs evaporate promptly in the early universe and we assume that a stable remnant is left behind. The PBHs remnants can constitute the entire dark matter of the universe for a wide range of remnant masses. We build inflationary models, in the framework of αattractors utilizing exponential functions, in which the PBHs are produced during matter, radiation and kination domination eras. The advantage of these inflationary models is that the spectral index takes values favorable by the Planck 2018 data. The PBH production from runaway inflaton models has the unique and very attractive feature to automatically reheat the universe. In these models the PBHs are produced during the kination stage and their prompt evaporation efficiently produces the required entropy. Such runaway models are remarkably economic having interesting implications for the early universe cosmology, possibly giving rise to a wCDM late time cosmology as well.

We continue the study of compactifications of massive IIA supergravity on G2 orientifolds and demonstrate that breaking supersymmetry with anti-D2 and anti-D6 sources leads to 3d theories for which the typical tachyons haunting classical dS solutions can be absent. However for a concrete torus example the meta-stable dS window disappears after a quantization of fluxes and charges. We discuss the prospects of more general G2 compactifications and argue that they could potentially alleviate the tachyon problem by introducing larger tadpole numbers and warped throats. However, exactly those ingredients then seem to push the vacuum towards the brink of perturbative brane–flux decay in the open string sector. This is either a remarkable illustration of the no-dS swampland conjecture or such vacua live in very difficult to control regions of parameter space.

We derive the 3D N = 1 superpotential for the closed string sector of type IIB supergravity on toroidal O5 orientifolds with co-calibrated G2 structure and RR background flux. We find that such compactifications can provide full closed string moduli stabilization on supersymmetric $$\hbox {AdS}_3$$ AdS 3 vacua, and once we include brane-supersymmetry-breaking we also find indication for the existence of classical 3D de Sitter solutions. The latter however are rather difficult to reconcile with the “shape” moduli stabilization and flux quantization. We also discuss the possibility of achieving scale separation in $$\hbox {AdS}_3$$ AdS 3 and $$\hbox {dS}_3$$ dS 3 vacua, but such effects seem to be hindered by the geometric flux quantization.