arXiv subjects

Katy Clough

Publications and source records attributed to Katy Clough.

60 records · Page 4Linked to original sources

arXiv2018

On the difficulty of generating gravitational wave turbulence in the early universe

A recent article by Galtier and Nazarenko [1] proposed that weakly nonlinear gravitational waves could result in a turbulent cascade, with energy flowing from high to low frequency modes or vice versa. This is an interesting proposition for early universe cosmology because it could suggest some "natural" initial conditions for the gravitational background. In this paper we use the ADM formalism to show that, given some simple and, arguably, natural assumptions, such initial conditions lead to expansion (or collapse) of the spacetime on a timescale much faster than that of the turbulent cascade, meaning that the cascade is unlikely to have sufficient time to develop under general conditions. We suggest possible ways in which the expansion could be mitigated to give the cascade time to develop.

gr-qc↗

arXiv2017

Robustness of Inflation to Inhomogeneous Initial Conditions

We consider the effects of inhomogeneous initial conditions in both the scalar field profile and the extrinsic curvature on different inflationary models. In particular, we compare the robustness of small field inflation to that of large field inflation, using numerical simulations with Einstein gravity in 3+1 dimensions. We find that small field inflation can fail in the presence of subdominant gradient energies, suggesting that it is much less robust to inhomogeneities than large field inflation, which withstands dominant gradient energies. However, we also show that small field inflation can be successful even if some regions of spacetime start out in the region of the potential that does not support inflation. In the large field case, we confirm previous results that inflation is robust if the inflaton occupies the inflationary part of the potential. Furthermore, we show that increasing initial scalar gradients will not form sufficiently massive inflation-ending black holes if the initial hypersurface is approximately flat. Finally, we consider the large field case with a varying extrinsic curvature K, such that some regions are initially collapsing. We find that this may again lead to local black holes, but overall the spacetime remains inflationary if the spacetime is open, which confirms previous theoretical studies.

hep-th↗

arXiv2017

Scalar Fields in Numerical General Relativity

Einstein's field equation of General Relativity (GR) has been known for over 100 years, yet it remains challenging to solve analytically in strongly relativistic regimes, particularly where there is a lack of a priori symmetry. Numerical Relativity (NR) - the evolution of the Einstein Equations using a computer - is now a relatively mature tool which enables such cases to be explored. In this thesis, a description is given of the development and application of a new Numerical Relativity code, GRChombo. GRChombo uses the standard BSSN formalism, incorporating full adaptive mesh refinement (AMR) and massive parallelism via the Message Passing Interface (MPI). The AMR capability permits the study of physics which has previously been computationally infeasible in a full 3+1 setting. The functionality of the code is described, its performance characteristics are demonstrated, and it is shown that it can stably and accurately evolve standard spacetimes such as black hole mergers. We use GRChombo to study the effects of inhomogeneous initial conditions on the robustness of small and large field inflationary models. and investigate the critical behaviour which occurs in the collapse of both spherically symmetric and asymmetric scalar field bubbles.

gr-qc↗

arXiv2017

Black hole formation from axion stars

The classical equations of motion for an axion with potential $V(ϕ)=m_a^2f_a^2 [1-\cos (ϕ/f_a)]$ possess quasi-stable, localized, oscillating solutions, which we refer to as "axion stars". We study, for the first time, collapse of axion stars numerically using the full non-linear Einstein equations of general relativity and the full non-perturbative cosine potential. We map regions on an "axion star stability diagram", parameterized by the initial ADM mass, $M_{\rm ADM}$, and axion decay constant, $f_a$. We identify three regions of the parameter space: i) long-lived oscillating axion star solutions, with a base frequency, $m_a$, modulated by self-interactions, ii) collapse to a BH and iii) complete dispersal due to gravitational cooling and interactions. We locate the boundaries of these three regions and an approximate "triple point" $(M_{\rm TP},f_{\rm TP})\sim (2.4 M_{pl}^2/m_a,0.3 M_{pl})$. For $f_a$ below the triple point BH formation proceeds during winding (in the complex $U(1)$ picture) of the axion field near the dispersal phase. This could prevent astrophysical BH formation from axion stars with $f_a\ll M_{pl}$. For larger $f_a\gtrsim f_{\rm TP}$, BH formation occurs through the stable branch and we estimate the mass ratio of the BH to the stable state at the phase boundary to be $\mathcal{O}(1)$ within numerical uncertainty. We discuss the observational relevance of our findings for axion stars as BH seeds, which are supermassive in the case of ultralight axions. For the QCD axion, the typical BH mass formed from axion star collapse is $M_{\rm BH}\sim 3.4 (f_a/0.6 M_{pl})^{1.2} M_\odot$.

astro-ph.CO↗

arXiv2016

Critical Phenomena in Non-spherically Symmetric Scalar Bubble Collapse

We investigate numerically the critical behaviour which occurs in the collapse of both spherically symmetric and asymmetric scalar field bubbles with full general relativity. We use a minimally coupled scalar field subject to a "double well" interaction potential, with the bubble wall spanning the barrier between two degenerate minima. We find that the spherically symmetric case exhibits Type 2 critical behaviour with the critical index consistent with a value of gamma = 0.37 as expected. In the asymmetric case, we find that again our results are consistent with a value of gamma = 0.37 for the dominant unstable mode. We do not see strong evidence of echoing in the solutions, which could be due to the fact that the coordinates are not well adapted to the echoing behaviour, or due to being still too far from the critical point to properly observe the critical solution.

gr-qc↗

arXiv2016

GRChombo : Numerical Relativity with Adaptive Mesh Refinement

In this work, we introduce GRChombo: a new numerical relativity code which incorporates full adaptive mesh refinement (AMR) using block structured Berger-Rigoutsos grid generation. The code supports non-trivial "many-boxes-in-many-boxes" mesh hierarchies and massive parallelism through the Message Passing Interface (MPI). GRChombo evolves the Einstein equation using the standard BSSN formalism, with an option to turn on CCZ4 constraint damping if required. The AMR capability permits the study of a range of new physics which has previously been computationally infeasible in a full 3+1 setting, whilst also significantly simplifying the process of setting up the mesh for these problems. We show that GRChombo can stably and accurately evolve standard spacetimes such as binary black hole mergers and scalar collapses into black holes, demonstrate the performance characteristics of our code, and discuss various physics problems which stand to benefit from the AMR technique.

gr-qc↗