Dynamical Analysis of Scalar Field Cosmologies with Spatial Curvature

We explore the dynamical behaviour of cosmological models involving a scalar field (with an exponential potential and a canonical kinetic term) and a matter fluid with spatial curvature included in the equations of motion. Using appropriately defined parameters to describe the evolution of the scalar field energy in this situation, we find that there are two extra fixed points that are not present in the case without curvature. We also analyse the evolution of the effective equation-of-state parameter for different initial values of the curvature.Comment: 17 pages, 11 figures. Amended in response to peer review in the Open Journal of Astrophysic

Cosmological dynamics and structure formation

Observational surveys which probe our universe deeper and deeper into the nonlinear regime of structure formation are becoming increasing accurate. This makes numerical simulations an essential tool for theory to be able to predict phenomena at comparable scales. In the first part of this thesis we study the behaviour of cosmological models involving a scalar field. We are particularly interested in the existence of fixed points of the dynamical system and the behaviour of the system in their vicinity. Upon addition of spatial curvature to the single-scalar field model with an exponential potential, canonical kinetic term, and a matter fluid, we demonstrate the existence of two extra fixed points that are not present in the case without curvature. We also analyse the evolution of the equation-of-state parameter. In the second part, we numerically simulate collisionless particles in the weak field approximation to General Relativity, with large gradients of the fields and relativistic velocities allowed. To reduce the complexity of the problem and enable high resolution simulations, we consider the spherically symmetric case. Comparing numerical solutions to the exact Schwarzschild and Lemaître-Tolman-Bondi solutions, we show that the scheme we use is more accurate than a Newtonian scheme, correctly reproducing the leading-order post-Newtonian behaviour. Furthermore, by introducing angular momentum, configurations corresponding to bound objects are found. In the final part, we simulate the conditions under which one would expect to form ultracompact minihalos, dark matter halos with a steep power-law profile. We show that an isolated object exhibits the profile predicted analytically. Embedding this halo in a perturbed environment we show that its profile becomes progressively more similar to the Navarro-Frenk-White profile with increasing amplitude of perturbations. Next, we boost the power spectrum at a very early redshift during radiation domination on a chosen scale and simulate clustering of dark matter particles at this scale until low redshift. In this scenario halos form earlier, have higher central densities, and are more compact

3D simulations with boosted primordial power spectra and ultracompact minihalos

We perform three-dimensional simulations of structure formation in the early Universe, when boosting the primordial power spectrum on ∼kpc scales. We demonstrate that our simulations are capable of producing power-law profiles close to the steep ρ ∝ r−9=4 halo profiles that are commonly assumed to be a good approximation to ultracompact minihalos (UCMHs). However, we show that for more realistic initial conditions in which halos are neither perfectly symmetric nor isolated the steep power-law profile is disrupted, and we find that the Navarro-Frenk-White profile is a better fit to most halos. In the presence of background fluctuations, even extreme, nearly spherical initial conditions do not remain exceptional. Nonetheless, boosting the amplitude of initial fluctuations causes all structures to form earlier and thus at larger densities. With a sufficiently large amplitude of fluctuations, we find that values for the concentration of typical halos in our simulations can become very large. However, despite the signal coming from dark matter annihilation inside the cores of these halos being enhanced, it is still orders of magnitude smaller compared to the usually assumed UCMH profile. The upper bound on the primordial power spectrum from the nonobservation of UCMHs should therefore be reevaluated

WIMPs and stellar-mass primordial black holes are incompatible

We recently showed that postulated ultracompact minihalos with a steep density profile do not form in realistic simulations with enhanced initial perturbations. In this paper we assume that a small fraction of the dark matter consists of primordial black holes (PBHs) and simulate the formation of structures around them. We find that in this scenario halos with steep density profiles do form, consistent with theoretical predictions. If the rest of the dark matter consists of weakly interacting massive particles (WIMPs), we also show that WIMPs in the dense innermost part of halos surrounding the PBH would annihilate and produce a detectable gamma-ray signal. The non-detection of this signal implies that PBHs make up at most one billionth of the dark matter, provided that their mass is greater than one millionth of the mass of the Sun. Similarly, a detection of PBHs would imply that the remaining dark matter could not be WIMPs

Multifield Ultralight Dark Matter

Ultralight dark matter (ULDM) is usually taken to be a single scalar field. Here we explore the possibility that ULDM consists of $N$ light scalar fields with only gravitational interactions. This configuration is more consistent with the underlying particle physics motivations for these scenarios than a single ultralight field. ULDM halos have a characteristic granular structure that increases stellar velocity dispersion and can be used as observational constraints on ULDM models. In multifield simulations, we find that inside a halo the amplitude of the total density fluctuations decreases as $1/\sqrt{N}$ and that the fields do not become significantly correlated over cosmological timescales. Smoother halos heat stellar orbits less efficiently, reducing the velocity dispersion relative to the single field case and thus weakening the observational constraints on the field mass. Analytically, we show that for $N$ equal-mass fields with mass $m$ the ULDM contribution to the stellar velocity dispersion scales as $1/(N m^3)$. Lighter fields heat the most efficiently and if the smallest mass $m_L$ is significantly below the other field masses the dispersion scales as $1/(N^2 m_L^3)$.Comment: 11 pages, 7 figures, to be submitted to PR

Commuter Count: Inferring Travel Patterns from Location Data

In this Working Paper we analyse computational strategies for using aggregated spatio-temporal population data acquired from telecommunications networks to infer travel and movement patterns between geographical regions. Specifically, we focus on hour-by-hour cellphone counts for the SA-2 geographical regions covering the whole of New Zealand. This Working Paper describes the implementation of the inference algorithms, their ability to produce models of travel patterns during the day, and lays out opportunities for future development.Comment: Submitted to Covid-19 Modelling Aotearo

Constraining the WMAP9 bispectrum and trispectrum with needlets

We develop a needlet approach to estimate the amplitude of general (including non-separable) bispectra and trispectra in the cosmic microwave background, and apply this to the WMAP 9-year data. We obtain estimates for the `orthogonal' bispectrum mode, yielding results which are consistent with the WMAP 7-year data. We do not observe the frequency-dependence suggested by the WMAP team's analysis of the 9-year data. We present 1-$\sigma$ constraints on the `local' trispectrum shape \gnl/10^5= -4.1\pm 2.3, the `$c1$' equilateral model \gnl^{c_1}/10^6= -0.8\pm 2.9, and the constant model \gnl^{\rm{const}}/10^6= -0.2\pm 1.8, together with a $95\%$ confidence-level upper bound on the multifield local parameter \taunl<22000. We estimate the bias on these parameters produced by point sources. The techniques developed in this paper should prove useful for other datasets such as Planck.Comment: 21 pages - matches published versio

Semiclassical path to cosmic large-scale structure

International audienceWe chart a path toward solving for the nonlinear gravitational dynamics of cold dark matter by relying on a semiclassical description using the propagator. The evolution of the propagator is given by a Schrödinger equation, where the small parameter ℏ acts as a softening scale that regulates singularities at shell-crossing. The leading-order propagator, called free propagator, is the semiclassical equivalent of the Zel’dovich approximation, that describes inertial particle motion along straight trajectories. At next-to-leading order, we solve for the propagator perturbatively and obtain, in the classical limit the displacement field from second-order Lagrangian perturbation theory (LPT). The associated velocity naturally includes an additional term that would be considered as third order in LPT. We show that this term is actually needed to preserve the underlying Hamiltonian structure, and ignoring it could lead to the spurious excitation of vorticity in certain implementations of second-order LPT. We show that for sufficiently small ℏ the corresponding propagator solutions closely resemble LPT, with the additions that spurious vorticity is avoided and the dynamics at shell-crossing is regularized. Our analytical results possess a symplectic structure that allows us to advance numerical schemes for the large-scale structure. For times shortly after shell-crossing, we explore the generation of vorticity, which in our method does not involve any explicit multistream averaging, but instead arises naturally as a conserved topological charge