Anne M. Green

Stochastic inflation is a powerful technique for calculating the probability distribution function (PDF) of large inflationary perturbations, which may collapse to form Primordial Black Holes. The PDF, P(𝒩), of the stochastic number of e-folds, 𝒩, satisfies an adjoint Fokker-Planck Equation. We develop a new self-contained eigenvalue technique which can be used to determine P(𝒩). First we apply this method to the simple case of quantum diffusion along a flat potential without any classical drift. We recover the expression for the PDF that has previously been found using characteristic functions, with an exponential tail, and a power-law behaviour, P(𝒩) ∝𝒩 ^-3/2 , in the intermediate regime between the peak and the tail of the PDF. Finally we apply the method to constant drift inflation, in the narrow- and broad-well limits. In the narrow-well limit, there is an analytic solution and the PDF is similar to the drift-free case, with a mildly suppressed tail. In the broad-well limit, determining the full set of eigenvalues and eigenfunctions requires a piecewise construction of the spectrum, and the broad-well PDF is qualitatively different, with an enhanced peak and a strongly suppressed tail.

We present a numerically efficient and accurate implementation of the Passaglia-Hu effective fluid approximation for ultralight axions within the Boltzmann code . This method is specifically designed to evolve the axion field accurately across cosmological timescales, mitigating the challenges associated with its rapid oscillations. Our implementation is based on the latest version of , ensuring compatibility with other cosmological codes., e.g., for calculating cosmological parameter constraints. Compared to exact solutions of the Klein-Gordon equation, our method achieves subpercent accuracy in the cosmic microwave background power spectrum across a broad range of axion masses, from 10 − 28 eV to 10 − 24 eV . We perform Markov chain Monte Carlo analyses incorporating our implementation, and find improved constraints on the axion mass and abundance compared to previous, simpler fluid-based approximations. For example, using Public Release 4 and Dark Energy Spectroscopic Instrument baryon acoustic oscillation data, we find 2 σ upper limits on the axion fraction f ax < 0.0082 and physical density Ω ax h 2 < 0.0010 for m = 10 − 28 eV . Published by the American Physical Society 2025

Microlensing surveys of stars in the Large Magellanic Cloud constrain the fraction of the Milky Way halo in Primordial Black Holes (PBHs) with mass 10^-9 ≲ M/M _⊙ ≲ 10⁴. Various studies have reached different conclusions on the uncertainties in these constraints due to uncertainties in the Dark Matter (DM) distribution. We therefore revisit the dependence of the microlensing differential event rate, and hence exclusion limits, on the DM density and velocity distributions. The constraints on the abundance of low- and high-mass PBHs depend, respectively, on the long- and short-duration tails of the differential event rate distribution. Long-duration events are due to PBHs moving close to the line of sight and their rate (and hence the constraints on low-mass PBHs) has a fairly weak (∼ 10%) dependence on the DM density and velocity distributions. Short-duration events are due to PBHs close to the observer and their rate (and hence the constraints on moderate- and high-mass PBHs) depends much more strongly on the DM velocity distribution. An accurate calculation of the local DM velocity distribution is therefore crucial for accurately calculating PBH stellar microlensing constraints.

Primordial black holes (PBHs) can make up all of the dark matter (DM) if their mass, m m , is in the so-called “asteroid-mass window”, 10^{17} g ≲ m ≲ 10^{22} g 10 17 g ≲ m ≲ 10 22 g . Observational constraints on the abundance of PBHs are usually calculated assuming they all have the same mass, however this is unlikely to be a good approximation. PBHs formed from the collapse of large density perturbations during radiation domination are expected to have an extended mass function (MF), due to the effects of critical collapse. The PBH MF is often assumed to be lognormal, however it has recently been shown that other functions are a better fit to numerically calculated MFs. We recalculate both current and potential future constraints for these improved fitting functions. We find that for current constraints the asteroid-mass window narrows, but remains open (i.e. all of the DM can be in the form of PBHs) unless the PBH MF is wider than expected. Future evaporation and microlensing constraints may together exclude all of the DM being in PBHs, depending on the width of the PBH MF and also the shape of its low and high mass tails.

Historically the most popular dark matter candidates have been new elementary particles, such as Weakly Interacting Massive Particles and axions. However Primordial Black Holes (PBHs), black holes formed from overdensities in the early Universe, are another possibility. The discovery of gravitational waves from mergers of tens of Solar mass black hole binaries by LIGO-Virgo has generated a surge in interest in PBH dark matter. We overview the formation of PBHs, observational probes of their abundance, and some of the key open questions in the field.

Primordial Black Holes (PBHs) may form in the early Universe, from the gravitational collapse of large density perturbations, generated by large quantum fluctuations during inflation. Since PBHs form from rare over-densities, their abundance is sensitive to the tail of the primordial probability distribution function (PDF) of the perturbations. It is therefore important to calculate the full PDF of the perturbations, which can be done non-perturbatively using the `stochastic inflation' framework. In single field inflation models generating large enough perturbations to produce an interesting abundance of PBHs requires violation of slow roll. It is therefore necessary to extend the stochastic inflation formalism beyond slow roll. A crucial ingredient for this are the stochastic noise matrix elements of the inflaton potential. We carry out analytical and numerical calculations of these matrix elements for a potential with a feature which violates slow roll and produces large, potentially PBH generating, perturbations. We find that the transition to an ultra slow-roll phase results in the momentum induced noise terms becoming larger than the field noise whilst each of them falls exponentially for a few e-folds. The noise terms then start rising with their original order restored, before approaching constant values which depend on the nature of the slow roll parameters in the post transition epoch. This will significantly impact the quantum diffusion of the coarse-grained inflaton field, and hence the PDF of the perturbations and the PBH mass fraction.