Alessandro Tronconi

The generation of large curvature perturbations associated with the production of primordial black holes is studied in the context of a Higgs inflaton. To enable this amplification, we consider an inflationary model in which the tree-level action for gravity and the Standard Model Higgs is modified by quantum corrections, described by a series of higher-dimension operators. Finally within a minimal EFT framework, we present two viable models in which the spectrum of curvature perturbations generated by the Higgs field is consistent with CMB observations and can lead to the formation of primordial black holes in the asteroid mass range, potentially accounting for the entirety of dark matter.

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015–2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14 000 deg² of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance.

We analyze the consequences of different evolutions of the Hubble parameter on the spectrum of scalar inflationary perturbations. The analysis is restricted to inflationary phases described by a transient evolution, when uncommon features arise in the inflationary spectra that may lead to an amplitude enhancement. We then discuss how the spectrum is, respectively, amplified or blue-tilted in the presence or absence of a growing solution of the Mukhanov-Sasaki equation. The cases of general relativity with a minimally coupled inflaton and that of induced gravity are considered explicitly. Finally, some remarks on constant roll inflation are discussed.

We analyze the consequences of different evolutions of the Hubble parameter on the spectrum of scalar inflationary perturbations. The analysis is restricted to inflationary phases described by a transient evolution, when uncommon features arise in the inflationary spectra that may lead to an amplitude enhancement. We then discuss how the spectrum is, respectively, amplified or blue-tilted in the presence or absence of a growing solution of the Mukhanov-Sasaki equation. The cases of general relativity with a minimally coupled inflaton and that of induced gravity are considered explicitly. Finally, some remarks on constant roll inflation are discussed.

In the context of canonical quantum gravity, we consider the effects of a non-standard expression for the gravitational wave function on the evolution of inflationary perturbations. Such an expression and its effects may be generated by a sudden variation in the (nearly constant) inflaton potential. The resulting primordial spectra, up to the leading order, are affected in the short and in the long wavelength regime, where an oscillatory behavior with a non-negligible amplitude is superimposed on the standard semiclassical result. Moreover, a novel, non-perturbative, approach is used to study the evolution. Finally, a simplified application is fully illustrated and commented.

We consider a procedure of elimination of cosmological singularities similar to that suggested in the recent paper by Simpson and Visser for the construction of regular black holes. It is shown that by imposing a non-singular cosmological evolution with a bounce in a flat Friedmann universe filled with a minimally coupled scalar field, we obtain a transition between the standard scalar field and its phantom counterpart. In this case, the potential of the scalar field has a non-analyticity of the cusp type. This result is also readily reproduced in the case of an anisotropic Bianchi I universe. We have also found a spherically symmetric static solution of the Einstein equations, free of singularities and sustained by a scalar field.

We consider a procedure of elimination of cosmological singularities similar to that suggested in the recent paper by Simpson and Visser for the construction of regular black holes. It is shown that by imposing a nonsingular cosmological evolution with a bounce in a flat Friedmann universe filled with a minimally coupled scalar field, we obtain a transition between the standard scalar field and its phantom counterpart. In this case, the potential of the scalar field has a nonanalyticity of the cusp type. This result is also readily reproduced in the case of an anisotropic Bianchi I universe. We have also found a spherically symmetric static solution of the Einstein equations, free of singularities and sustained by a scalar field.