Cosmological perturbations, originating in the quantum fluctuations of the fields that drive inflation, are observed to be nearly scale invariant at the largest scales. At smaller scales, however, perturbations are not severely constrained and might be of particular importance if their amplitude is large. They can trigger the creation of primordial black holes (PBHs) or stochastic gravitational waves (GWs). Small-scale perturbations are generated during the later stages of inflation, when possible strong features in the inflaton potential can break scale invariance and leave characteristic imprints on the spectrum. We focus on and review three types of features: inflection points and steep steps in the potential, as well as sharp turns in the inflationary trajectory in field space. We show that such features induce a strong enhancement of the curvature spectrum within a certain wavenumber range. In particular cases, they also generate characteristic oscillatory patterns that are transferred in the spectrum of secondary GWs, which are potentially observable by operating or designed experiments. We demonstrate these effects through the calculation of the primordial power spectrum and the PBH abundance in the context of α-attractors and supergravity (SUGRA) models of inflation.

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We study a model including a real scalar field $$\phi $$ϕ non-minimally coupled to $$F(\mathcal{R})$$F(R) gravity, which is conformally equivalent to an Einstein–Hilbert theory, involving two real scalar fields. We consider three special cases of the potential of the field $$\phi $$ϕ in the $$F(\mathcal{R})$$F(R)-frame: a vanishing potential, a mass term and a Higgs potential. All these lead to non-trivial two-field potentials in the Einstein-frame which in particular directions resemble the well-known Starobinsky model. We find, that all these cases can yield viable inflationary models in complete agreement with current observational data.

We demonstrate how to systematically design wave scattering systems with simultaneous coherent perfect absorbing and lasing operation at multiple and prescribed frequencies. The approach is based on the recursive assembly of non-Hermitian emitter and absorber units into self-dual emitter-absorber trimers at different composition levels, exploiting the simple structure of the corresponding transfer matrices. In particular, lifting the restriction to parity-time-symmetric setups enables the realization of emitter and absorber action at distinct frequencies and provides flexibility with respect to the choice of realistic parameters. We further show how the same assembled scatterers can be rearranged to produce unidirectional and bidirectional transparency at the selected frequencies. With the design procedure being generically applicable to wave scattering in single-channel settings, we demonstrate it with concrete examples of photonic multilayer setups.

We investigate the cosmology of mini Primordial Black Holes (PBHs) produced by large density perturbations that collapse during a stiff fluid domination phase. Such a phase can be realized by a runaway-inflaton model that crosses an inflection point or a sharp feature at the last stage of inflation. Mini PBHs evaporate promptly and reheat the early universe. In addition, we examine two notable implications of this scenario: the possible presence of PBH evaporation remnants in galaxies and a non-zero residual potential energy density for the runaway inflaton that might play the role of the dark energy. We specify the parameter space that this scenario can be realized and we find that a transit PBH domination phase is necessary due to gravitational wave (GW) constraints. A distinct prediction of the scenario is a compound GW signal that might be probed by current and future experiments. We also demonstrate our results employing an explicit inflation model.