Testing gravitational physics on large and small scales

Einstein's theory of General Relativity has long been considered the standard theory of gravity, as it provides us with an extremely good description of how objects interact gravitationally at all scales. The Standard Model of cosmology, based on General Relativity, provides an excellent description of how astrophysical objects and matter interact. However, it requires the addition of two exotic ingredients: cold dark matter and dark energy, in order to correctly account for some observational phenomena, such as the accelerated expansion of the universe and the flat galaxy rotation curves that we observe. This has prompted the exploration of alternative theories of gravity, which can account for these observations without invoking the need for one or both of these exotic types of matter. In this thesis we build different tools for testing such alternatives at large and small scales. The majority of the work focuses on testing beyond General Relativity models on large scales using cosmological probes. We derive theory-informed priors, find suitable forms for the time evolution of the functions parametrising specific sets of extensions to General Relativity, and put constraints on their parameters from cosmological data. In the last chapter we shift the focus to small scales, where we numerically confirm an expression for the drag force on a moving black hole. This result can be used to test a model of dark matter using the gravitational wave signal from a black hole binary merger. With the growing amount of gravitational wave data, testing alternative theories of gravity in this way is becoming an increasingly popular area of research. The future direction of this work is to apply the methods we commonly use for testing gravity on large scales, as described in this work, to test beyond General Relativity theories on small scales using gravitational wave data

The phenomenology of beyond Horndeski gravity

We study the phenomenology of the beyond Horndeski class of scalar-tensor theories of gravity, which on cosmological scales can be characterised in terms of one extra function of time, $\alpha_{\rm H}$, as well as the usual four Horndeski set of free functions. We show that $\alpha_{\rm H}$ can be directly related to the the damping of the matter power spectrum on both large and small scales. We also find that the temperature power spectrum of the cosmic microwave background (CMB) is enhanced at low multipoles and the lensing potential is decreased, as a function of $\alpha_{\rm H}$. We find constraints on $\alpha_{\rm H}$ of order ${\cal O}(1)$ using measurements of the temperature and polarisation of the CMB, as well as the lensing potential derived from it, combined with large scale structure data. We find that redshift space distortion measurements can play a significant role in constraining these theories. Finally, we comment on the recent constraints from the observation of an electromagnetic counterpart to a gravitational wave signal; we find that these constraints reduce the number of free parameters of the model but do not significantly change the constraints on the remaining parameters.Comment: 33 pages; 10 figures; 4 tables; Version as accepted for publication in JCA

Accretion of a Symmetry Breaking Scalar Field by a Schwarzschild Black Hole

We simulate the behaviour of a Higgs-like field in the vicinity of a Schwarzschild black hole using a highly accurate numerical framework. We consider both the limit of the zero-temperature Higgs potential, and a toy model for the time-dependent evolution of the potential when immersed in a slowly cooling radiation bath. Through these numerical investigations, we aim to improve our understanding of the non-equilibrium dynamics of a symmetry breaking field (such as the Higgs) in the vicinity of a compact object such as a black hole. Understanding this dynamics may suggest new approaches for studying properties of scalar fields using black holes as a laboratory.Comment: 16 pages, 5 figure

Theoretical priors in scalar-tensor cosmologies: Shift-symmetric Horndeski models

Attempts at constraining theories of late time accelerated expansion often assume broad priors for the parameters in their phenomenological description. Focusing on shift-symmetric scalar-tensor theories with standard gravitational wave speed, we show how a more careful analysis of their dynamical evolution leads to much narrower priors. In doing so, we propose a simple and accurate parametrisation of these theories, capturing the redshift dependence of the equation of state, $w(z)$, and the kinetic braiding parameter, $\alpha_{\rm B}(z)$, with only two parameters each, and derive their statistical distribution (a.k.a. theoretical priors) that fit the cosmology of the underlying model. We have considered two versions of the shift-symmetric model, one where the energy density of dark energy is given solely by the scalar field, and another where it also has a contribution from the cosmological constant. By including current data, we show how theoretical priors can be used to improve constraints by up to an order of magnitude. Moreover, we show that shift-symmetric theories without a cosmological constant are observationally viable. We work up to quartic order in first derivatives of the scalar in the action and our results suggest this truncation is a good approximation to more general shift-symmetric theories. This work establishes an actionable link between phenomenological parameterisations and Lagrangian-based theories, the two main approaches to test cosmological gravity and cosmic acceleration.Comment: 18 pages, 13 figures; Version as accepted in PRD - minor changes

GRDzhadzha: A code for evolving relativistic matter on analytic metric backgrounds

GRDzhadzha is an open-source code for relativistic simulations of matter fields on curved spacetimes that admit an analytic description (e.g. stationary black holes). It is based on the publicly available 3+1D numerical relativity code GRChombo. Such a description is valid where the density of the matter is small compared to the curvature scale of the spacetime, which is the case for many physical scenarios - for example, dark matter environments. The approach offers significant savings on memory and speed compared to running full numerical relativity simulations, since the metric variables and their derivatives are calculated analytically, and therefore are not evolved or stored on the grid. This brief paper introduces the code and gives details of some applications for which it has already been used.Comment: Submitted for review in the Journal of Open Source Software; Comments welcome; The code can be found at https://github.com/GRChombo/GRDzhadzha.gi

GRChombo: An adaptable numerical relativity code for fundamental physics

GRChombo is an open-source code for performing Numerical Relativity time evolutions, built on top of the publicly available Chombo software for the solution of PDEs. Whilst GRChombo uses standard techniques in NR, it focusses on applications in theoretical physics where adaptability, both in terms of grid structure, and in terms of code modification, are key drivers

Theoretical priors in scalar-tensor cosmologies: Thawing quintessence

International audienceThe late time acceleration of the Universe can be characterized in terms of an extra, time-dependent, component of the Universe—dark energy. The simplest proposal for dark energy is a scalar-tensor theory—quintessence—which consists of a scalar field, ϕ, whose dynamics is solely dictated by its potential, V(ϕ). Such a theory can be uniquely characterized by the equation of state of the scalar field energy momentum-tensor. We find the time dependence of the equation of state for a broad family of potentials and, using this information, we propose an analytic prior distribution for the most commonly used parametrization. We show that this analytic prior can be used to accurately predict the distribution of observables for the next generation of cosmological surveys. Including the theoretical priors in the comparison with observations considerably improves the constraints on the equation of state