Jacopo Fumagalli

The motion of the Solar System with respect to the cosmic rest frame induces a kinematic dipole in the stochastic gravitational-wave background (GWB). Detecting this signal with space-based interferometers would provide an independent measurement of our peculiar velocity and a GW probe of cosmic anisotropies. We present a fully analytic derivation of the response of the Laser Interferometer Space Antenna (LISA) to a kinematic dipole, and construct an optimal estimator for its detection. We show that the dipolar response is governed by a single frequency-dependent function fixed by symmetry, and we compute its behaviour across the LISA band. Using Fisher forecasts, we find that for a scale-invariant background detectability requires h ² Ω _GW ≳ 5 × 10 ^-8 for fiducial LISA, and h ² Ω _GW ≳ 5 × 10 ^-10 for a detector with characteristic instrumental-noise amplitudes improved by an order of magnitude. Prospects are more favorable for signals with richer frequency profile. We also explore the potential of the kinematic dipole to break degeneracies, particularly in the presence of strong galactic foregrounds or noise features that closely mimic the primordial signal.

Einstein Telescope (ET) is the European project for a gravitational-wave (GW) observatory of third-generation. In this paper we present a comprehensive discussion of its science objectives, providing state-of-the-art predictions for the capabilities of ET in both geometries currently under consideration, a single-site triangular configuration or two L-shaped detectors. We discuss the impact that ET will have on domains as broad and diverse as fundamental physics, cosmology, early Universe, astrophysics of compact objects, physics of matter in extreme conditions, and dynamics of stellar collapse. We discuss how the study of extreme astrophysical events will be enhanced by multi-messenger observations. We highlight the ET synergies with ground-based and space-borne GW observatories, including multi-band investigations of the same sources, improved parameter estimation, and complementary information on astrophysical or cosmological mechanisms obtained combining observations from different frequency bands. We present advancements in waveform modeling dedicated to third-generation observatories, along with open tools developed within the ET Collaboration for assessing the scientific potentials of different detector configurations. We finally discuss the data analysis challenges posed by third-generation observatories, which will enable access to large populations of sources and provide unprecedented precision.

We present pbhstat, a publicly available Python package designed to compute the mass function and total abundance of primordial black holes (PBHs) from a given primordial power spectrum. The package offers a modular framework using multiple statistical approaches, including Press–Schechter theory, peaks theory, and formalisms based on the non-linear compaction function. Currently, the implementation is limited to scenarios with nearly Gaussian initial conditions.

We present pbhstat, a publicly available Python package designed to compute the mass function and total abundance of primordial black holes (PBHs) from a given primordial power spectrum. The package offers a modular framework using multiple statistical approaches, including Press-Schechter theory, peaks theory, and formalisms based on the non-linear compaction function. Currently, the implementation is limited to scenarios with nearly Gaussian initial conditions.

We question the existence of one-loop corrections to the large-scale power spectrum from small-scale modes in non-slow-roll dynamics which are not volume suppressed by the ratio of the short to long distance scales. One-loop contributions proportional to the long wavelength tree-level power spectrum, and not sharing this suppression, have appeared in studies involving interactions singled out by the non-slow-roll dynamics. In this context, we show the relevance of seemingly irrelevant interactions terms, such as the one provided by total derivative terms (boundary terms), and how they equally lead to non-volume suppressed contributions and exact cancellations.

Many early universe scenarios predict an enhancement of scalar perturbations at scales currently unconstrained by cosmological probes. These perturbations source gravitational waves (GWs) at second order in perturbation theory, leading to a scalar-induced gravitational wave (SIGW) background. The LISA detector, sensitive to mHz GWs, will be able to constrain curvature perturbations in a new window corresponding to scales k ∈ [10¹⁰, 10¹⁴] Mpc^-1, difficult to probe otherwise. In this work, we forecast the capabilities of LISA to constrain the source of SIGWs using different approaches: i) agnostic, where the spectrum of curvature perturbations is binned in frequency space; ii) template-based, modeling the curvature power spectrum based on motivated classes of models; iii) ab initio, starting from first-principles model of inflation featuring an ultra-slow roll phase. We compare the strengths and weaknesses of each approach. We also discuss the impact on the SIGW spectrum of non-standard thermal histories affecting the kernels of SIGW emission and non-Gaussianity in the statistics of the curvature perturbations. Finally, we propose simple tests to assess whether the signal is compatible with the SIGW hypothesis. The pipeline used is built into the SIGWAY code.

A bstract: We prove explicitly the absence of one-loop corrections to large scales from small scales in transient non-slow-roll dynamics. Specifically, we address loop corrections to the primordial power spectrum, relative to tree-level, that are independent of the ratio between the two scales. We review all the necessary components, adapted to our context, to express one-loop diagrams as three-point functions, emphasizing the crucial role played by quartic interactions. Notably, we include the quartic Hamiltonian induced by the cubic Lagrangian and quartic interactions that are ensured by diffeomorphism invariance. We then explicitly prove consistency relations for an arbitrary transient non-slow-roll phase involving operators with (time) derivatives. Finally, we calculate one-loop corrections by including contributions from the relevant cubic and quartic interactions, and express the final result as a total derivative term over comoving momenta, utilizing the consistency relations we established. This leads us to conclude that one-loop corrections to long-wavelength modes are unaffected by the physics of short and enhanced modes in non-slow-roll dynamics.

Various scenarios of cosmic inflation enhance the amplitude of the stochastic gravitational wave background (SGWB) at frequencies detectable by the LISA detector. We develop tools for a template-based analysis of the SGWB and introduce a template databank to describe well-motivated signals from inflation, prototype their template-based searches, and forecast their reconstruction with LISA. Specifically, we classify seven templates based on their signal frequency shape, and we identify representative fundamental physics models leading to them. By running a template-based analysis, we forecast the accuracy with which LISA can reconstruct the template parameters of representative benchmark signals, with and without galactic and extragalactic foregrounds. We identify the parameter regions that can be probed by LISA within each template. Finally, we investigate how our signal reconstructions shed light on fundamental physics models of inflation: we discuss their impact for measurements of e.g., the couplings of inflationary axions to gauge fields; the graviton mass during inflation; the fluctuation seeds of primordial black holes; the consequences of excited states during inflation, and the presence of small-scale spectral features.

We show that, whenever the perturbations of some field are excited during inflation by a physical process on sub-horizon scales, they unavoidably generate, even through gravitational interactions alone, a significant resonant IR cascade of power down to scales that are of the order of the horizon at that time (we denote these scales as near IR). We provide general analytic one-loop results for the enhancement of the IR power of the curvature perturbation generated by this effect, highlighting the role played by the resonance. We then study a number of examples in which the excited state is: (i) an isocurvature field, (ii) the curvature perturbation itself, (iii) a mixture of curvature and isocurvature fluctuations driven to an excited state by their coupled dynamics. In the cases shown, the cascade significantly modifies the near IR part of the power spectrum of the curvature perturbation with respect to the linear theory, indicating that this effect can impact the phenomenology associated with a variety of mechanisms considered in the literature, notably concerning primordial black holes and gravitational waves.