Cristiano Germani’s research while affiliated with Institut Marqués, Spain, Barcelona and other places

We formulate the statistics of peaks of non-Gaussian random fields and implement it to study the sphericity of peaks. For non-Gaussianity of the local type, we present a general formalism valid regardless of how large the deviation from Gaussian statistics is. For general types of non-Gaussianity, we provide a framework that applies to any system with a given power spectrum and the corresponding bispectrum in the regime in which contributions from higher-order correlators can be neglected. We present an explicit expression for the most probable values of the sphericity parameters, including the effect of non-Gaussianity on the profile. We show that the effects of small perturbative non-Gaussianity on the sphericity parameters are negligible, as they are even smaller than the subleading Gaussian corrections. In contrast, we find that large non-Gaussianity can significantly distort the peak configurations, making them much less spherical.

In a Universe with nearly-Gaussian initial curvature perturbations, the abundance of primordial black holes can be derived from the curvature power spectrum. When the latter is enhanced within a narrow range around a characteristic scale, the resulting mass function has a single distinct peak, corresponding to Schwarzschild radii set by the horizon entry time of that scale. In contrast, we show (both numerically and by providing an analytic estimation) that a broad enhancement - such as a plateau bounded by infrared and ultraviolet scales - produces a bimodal mass function, with a primary peak close to the infrared scale. We find that the typical initial gravitational potential (compaction function), conditioned on meeting the threshold for critical collapse, is generated by a thin spherical shell with infrared radius and a thickness comparable to the ultraviolet scale. This suggests a higher-than-expected abundance of PBH originating from Type II initial fluctuations. Our results significantly impact overproduction bounds on the amplitude of the power spectrum, and tighten the viable mass range for primordial black holes as dark matter.

By introducing the small noise expansion techniques, we show that the fully nonlinear (non-Markovian) stochastic inflationary system, may be re-cast in terms of an infinite set of Wiener processes (stochastic equations with white noises). As a byproduct, we show that the Starobinsky test field approximation might only provide information about the linear regime of cosmological perturbations and scalar-feld non-Gaussianities might only appear at next to leading order in slow-roll parameters.

We review the nonlinear statistics of Primordial Black Holes that form from the collapse of over-densities in a radiation-dominated Universe. We focus on the scenario in which large over-densities are generated by rare and Gaussian curvature perturbations during inflation. As new results, we show that the mass spectrum follows a power law determined by the critical exponent of the self-similar collapse up to a power spectrum dependent cutoff, and that the abundance related to very narrow power spectra is exponentially suppressed. Related to this, we discuss and explicitly show that both the Press–Schechter approximation and the statistics of mean profiles lead to wrong conclusions for the abundance and mass spectrum. Finally, we clarify that the transfer function in the statistics of initial conditions for Primordial Black Holes formation (the abundance) does not play a significant role.

We review the non-linear statistics of Primordial Black Holes that form from the collapse of over-densities in a radiation dominated Universe. We focus on the scenario in which large over-densities are generated by rare and Gaussian curvature perturbations during inflation. As new results, we show that the mass spectrum follows a power law determined by the critical exponent of the self-similar collapse up to a power spectrum dependent cut-off and, that the abundance related to very narrow power spectrums is exponentially suppressed. Related to this, we discuss and explicitly show that the Press-Schechter approximation, as well as the statistics of mean profiles, lead to wrong conclusions for the abundance and mass spectrum. Finally, we clarify that the transfer function in the statistics of initial conditions for primordial black holes formation (the abundance) does not play a significant role.

In this paper, we generalize the Weinberg's procedure to determine the comoving curvature perturbation ℛ to non-attractor inflationary regimes. We show that both modes of ℛ are related to a symmetry of the perturbative equations in the Newtonian gauge. As a byproduct, we clarify that adiabaticity does not generally imply constancy of ℛ, not even in the k ⟶ 0 limit. We then show that there exist non-equivalent definitions of δN that would reproduce ℛ or the uniform density curvature perturbation ζ at linear order. We have then shown that the perturbative δN definition in terms of difference between the number of e-foldings of different gauges, can be extended non-perturbatively at leading order in gradient expansion. Nevertheless, the computer friendly definition in terms of the difference of e-foldings obtained from the evolution of a local FRW Universe, respectively with perturbed and un-perturbed initial conditions, might only give information about the linear order curvature perturbations, contrary to what is stated in the literature.

In this paper, we generalize the Weinberg's procedure to determine the comoving curvature perturbation $\cal R$ to non-attractor inflationary regimes. We show that both modes of $\cal R$ are related to a symmetry of the perturbative equations in the Newtonian gauge. As a byproduct, we clarify that adiabaticity does not generally imply constancy of $\cal R$, not even in the $k\rightarrow 0$ limit. Applying this knowledge to the separate Universe approach, we find that correlators of $\delta N$ {\it do not} generically correspond to comoving curvature perturbations correlators, even at the linear level, but rather to correlators of curvature perturbations at uniform density, at least at linear level. Thus, $\delta N$ formalism does not capture information about decaying (for slow-roll) or growing (beyond slow-roll) modes of $\cal R$. The latter being the only interesting mode for models of inflation related to primordial black holes formation.

One of the most striking evidences of the information loss paradox is that, according to the Hawking’s calculation, the correlation functions of a test scalar field exponentially decay in time. In this paper, I argue that a judicious use of the steepest descent expansion on the classical saddle point (the black hole background) is enough to change this early time decay into a late time growth in agreement with information retrieval. I will explicitly show this in the Jackiw-Teitelboim gravity. There, the so-called “ramp” in the bulk tow-point function is analytically obtained without the need of any other subdominant configurations of the gravity path integral.

One of the most striking evidences of the information loss paradox is that, according to the Hawking's calculation, the correlation functions of a test scalar field exponentially decay in time. In this paper, I argue that a judicious use of the steepest descent expansion on the classical saddle point (the Black Hole background), is enough to change this early time decay into a late time growing, in agreement with information retrieval. I will explicitly show this in the Jackiw-Teitelboim gravity. There, the so-called "ramp" is analytically obtained without the need of any other subdominant configurations of the gravity path integral.

In this paper we develop the formalism for the stochastic approach to inflation at all order in slow-roll parameters. This is done by including the momentum and Hamiltonian constraints into the stochastic equations. We then specialize to the widely used Starobinski approximation where interactions between IR and UV modes are neglected. We show that, whenever this approximation holds, no significant deviations are observed when comparing the two-point correlation functions (power spectrum) calculated with stochastic methods, to the ones calculated with the Quantum Field Theory (QFT) approach to linear theory. As a by-product, we argue that: (i) the approaches based on the Starobinski approximation, generically, do not capture any loop effects of the quantum scalar-gravity system; (ii) correlations functions can only be calculated in the linear theory regimes; thus, no nonperturbative statistics can be extracted within this approximation, as commonly claimed.