Abstract: Cosmological phase transitions in the early Universe may produce relics in the form of a network of cosmic defects. Independently of the order of a phase transition, topology of the defects, and their global or gauge nature, the defects are expected to emit gravitational waves (GWs) as the network energy-momentum tensor adapts itself to maintaining scaling. We show that the evolution of any defect network (and for that matter any scaling source) emits a GW background with spectrum Omega(GW) proportional to f(3) for f << f(0), Omega(GW) proportional to 1/f(2) for f(0) less than or similar to f less than or similar to feq, and Omega(GW) proportional to const (i.e., exactly scale invariant) for f >> f(eq), where f(0) and f(eq) denote respectively the frequencies corresponding to the present and matter-radiation equality horizons. This background represents an irreducible emission of GWs from any scaling network of cosmic defects, with its amplitude characterized only by the symmetry-breaking scale and the nature of the defects. Using classical lattice simulations we calculate the GW signal emitted by defects created after the breaking of a global symmetry O(N) -> O(N – 1). We obtain the GW spectrum for N between 2 and 20 with two different techniques: integrating over unequal-time correlators of the energy-momentum tensor, updating our previous work on smaller lattices, and for the first time, comparing the result with the real-time evolution of the tensor perturbations sourced by the same defects. Our results validate the equivalence of the two techniques. Using cosmic microwave background upper bounds on the defects' energy scale, we discuss the difficulty of detecting this GW background in the case of global defects.

Abstract: We study the impact of stochastic noise on the generation of primordial black hole (PBH) seeds in ultra-slow-roll (USR) inflation with numerical simulations. We consider the non-linearity of the system by consistently taking into account the noise dependence on the inflaton perturbations, while evolving the perturbations on the coarse-grained background affected by the noise. We capture in this way the non-Markovian nature of the dynamics, and demonstrate that non-Markovian effects are subleading. Using the Delta N formalism, we find the probability distribution P(R) of the comoving curvature perturbation R. We consider inflationary potentials that fit the CMB and lead to PBH dark matter with i) asteroid, ii) solar, or iii) Planck mass, as well as iv) PBHs that form the seeds of supermassive black holes. We find that stochastic effects enhance the PBH abundance by a factor of O(10)-O(10(8)), depending on the PBH mass. We also show that the usual approximation, where stochastic kicks depend only on the Hubble rate, either underestimates or overestimates the abundance by orders of magnitude, depending on the potential. We evaluate the gauge dependence of the results, discuss the quantum-to-classical transition, and highlight open issues of the application of the stochastic formalism to USR inflation.

Abstract: The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational-wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational-wave observations by LISA to probe the universe.