arXiv subjects

Timothy Clifton

Publications and source records attributed to Timothy Clifton.

At least 55 records · Page 3Linked to original sources

arXiv2016

Cosmology on all scales: a two-parameter perturbation expansion

We propose and construct a two-parameter perturbative expansion around a Friedmann-Lemaître-Robertson-Walker geometry that can be used to model high-order gravitational effects in the presence of non-linear structure. This framework reduces to the weak-field and slow-motion post-Newtonian treatment of gravity in the appropriate limits, but also includes the low-amplitude large-scale fluctuations that are important for cosmological modelling. We derive a set of field equations that can be applied to the late Universe, where non-linear structure exists on supercluster scales, and perform a detailed investigation of the associated gauge problem. This allows us to identify a consistent set of perturbed quantities in both the gravitational and matter sectors, and to construct a set of gauge-invariant quantities that correspond to each of them. The field equations, written in terms of these quantities, take on a relatively simple form, and allow the effects of small-scale structure on the large-scale properties of the Universe to be clearly identified. We find that inhomogeneous structures source the global expansion, that there exist new field equations at new orders, and that there is vector gravitational potential that is a hundred times larger than one might naively expect from cosmological perturbation theory. Finally, we expect our formalism to be of use for calculating relativistic effects in upcoming ultra-large-scale surveys, as the form of the gravitational coupling between small and large scales depends on the non-linearity of Einstein's equations, and occurs at what is normally thought of as first order in cosmological perturbations.

astro-ph.CO↗

arXiv2016

Decay of the Cosmic Vacuum Energy

In his 2005 review, Gravity and the Thermodynamics of Horizons, Paddy suggested that a vacuum in thermal equilibrium with a bath of radiation should have a gradually diminishing energy. We work through the consequences of this scenario, and find that a coupling between the vacuum and a bath of black-body radiation at the temperature of the horizon requires the Hubble rate, $H$, to approach the same type of evolution as in the "intermediate inflation" scenario, with $H\propto t^{-1/3}$, rather than as a constant. We show that such behaviour does not conflict with observations when the vacuum energy is described by a slowly-rolling scalar field, and when the fluctuations in the scalar field are treated as in the "warm inflation" scenario. It does, however, change the asymptotic states of the universe. We find that the existence of the radiation introduces a curvature singularity at early times, where the energy densities in both the radiation and the vacuum diverge. Furthermore, we show that the introduction of an additional non-interacting perfect fluid into the space-time reveals that radiation can dominate over dust at late times, in contrast to what occurs in the standard cosmological model. Such a coupling can also lead to a negative vacuum energy becoming positive.

gr-qc↗

arXiv2016

Post-Newtonian Cosmological Modelling

We develop a new approach to building cosmological models, in which small pieces of perturbed Minkowski space are joined together at reflection-symmetric boundaries in order to form a global, dynamical space-time. Each piece of this patchwork universe is described using post-Newtonian gravitational physics, with the large-scale expansion of the universe being an emergent phenomenon. This approach to cosmology does not require any assumptions about non-local averaging processes. Our framework clarifies the relation between the weak-field limit of general relativity, and the cosmological solutions that result from solving Einstein's equations with a set of symmetry assumptions. It also allows the effects of structure formation on the large-scale expansion of the universe to be investigated in an unambiguous way. As an explicit example, we use this formalism to investigate the cosmological behaviour of a large number of regularly arranged point-like masses. In this case we find that the large-scale expansion is well modelled by a Friedmann-like equation that contains terms that take the form of dust, radiation, and spatial curvature. The radiation term, while small compared to the dust term, is purely a result of the non-linearity of Einstein's equations.

gr-qc↗

arXiv2015

Embedding Non-Linear Structures in f(R) Cosmologies

When using Einstein's equations, there exist a number of techniques for embedding non-linear structures in cosmological backgrounds. These include Swiss cheese models, in which spherically symmetric vacua are patched onto Friedmann solutions, and lattice models, in which weak-field regions are joined together directly. In this talk we will consider how these methods work in f(R) theories of gravity. We will show that their existence places constraints on the large-scale expansion of the universe, and that it may not always be possible to consider the Friedmann solutions and weak-field solutions of a theory independently from each other.

gr-qc↗

arXiv2015

What's the Matter in Cosmology?

Almost all models of the universe start by assuming that matter fields can be modelled as dust. In the real universe, however, matter is clumped into dense objects that are separated by regions of space that are almost empty. If we are to treat such a distribution of matter as being modelled as a fluid, in some average or coarse-grained sense, then there a number of questions that must be answered. One of the most fundamental of these is whether or not the interaction energy between masses should gravitate. If it does, then a dust-like description may not be sufficient. We would then need to ask how interaction energies should be calculated in cosmology, and how they should appear in the Friedmann-like equations that govern the large-scale behaviour of the universe. I will discuss some recent results that may shed light on these questions.

gr-qc↗

arXiv2015

On the Emergence of Accelerating Cosmic Expansion in f(R) Theories of Gravity

We consider cosmological modelling in $f(R)$ theories of gravity, using both top-down and bottom-up constructions. The top-down models are based on Robertson-Walker geometries, and the bottom-up constructions are built by patching together sub-horizon-sized regions of perturbed Minkowski space. Our results suggest that these theories do not provide a theoretically attractive alternative to the standard general relativistic cosmology. We find that the only $f(R)$ theories that can admit an observationally viable weak-field limit have large-scale expansions that are observationally indistinguishable from the Friedmann solutions of General Relativity with $Λ$. Such theories do not alleviate any of the difficulties associated with $Λ$, and cannot produce any new behaviour in the cosmological expansion without simultaneously destroying the Newtonian approximation to gravity on small scales.

gr-qc↗

arXiv2014

The Method of Images in Cosmology

We apply the method of images to the exact initial data for cosmological models that contain a number of regularly arranged discrete masses. This allows us to join cosmological regions together by throats, and to construct wormholes in the initial data. These wormholes allow for the removal of the asymptotically flat "flange" regions that would otherwise exist on the far side of black holes. The method of images also provides us with a way to investigate the definition of mass is cosmology, and the cosmological consequences of the gravitational interaction energies between massive objects. We find evidence that the interaction energies within clusters of massive objects do indeed appear to contribute to the total energy budget in the cosmological regions of the space-time.

gr-qc↗

arXiv2014

Observational Constraints on the Averaged Universe

Averaging in general relativity is a complicated operation, due to the general covariance of the theory and the non-linearity of Einstein's equations. The latter of these ensures that smoothing spacetime over cosmological scales does not yield the same result as solving Einstein's equations with a smooth matter distribution, and that the smooth models we fit to observations need not be simply related to the actual geometry of spacetime. One specific consequence of this is a decoupling of the geometrical spatial curvature term in the metric from the dynamical spatial curvature in the Friedmann equation. Here we investigate the consequences of this decoupling by fitting to a combination of HST, CMB, SNIa and BAO data sets. We find that only the geometrical spatial curvature is tightly constrained, and that our ability to constrain dark energy dynamics will be severely impaired until we gain a thorough understanding of the averaging problem in cosmology.

astro-ph.CO↗

arXiv2014

Piecewise Silence in Discrete Cosmological Models

We consider a family of cosmological models in which all mass is confined to a regular lattice of identical black holes. By exploiting the reflection symmetry about planes that bisect these lattices into identical halves, we are able to consider the evolution of a number of geometrically distinguished surfaces that exist within each of them. We find that the evolution equations for the reflection symmetric surfaces can be written as a simple set of Friedmann-like equations, with source terms that behave like a set of interacting effective fluids. We then show that gravitational waves are effectively trapped within small chambers for all time, and are not free to propagate throughout the space-time. Each chamber therefore evolves as if it were in isolation from the rest of the universe. We call this phenomenon "piecewise silence".

gr-qc↗

arXiv2013

Exact Evolution of Discrete Relativistic Cosmological Models

We study the effects of inhomogeneities on the evolution of the Universe, by considering a range of cosmological models with discretized matter content. This is done using exact and fully relativistic methods that exploit the symmetries in and about submanifolds of spacetimes that themselves possess no continuous global symmetries. These methods allow us to follow the evolution of our models throughout their entire history, far beyond what has previously been possible. We find that while some space-like curves collapse to anisotropic singularities in finite time, others remain non-singular forever. The resulting picture is of a cosmological spacetime in which some behaviour remains close to Friedmann-like, while other behaviours deviate radically. In particular, we find that large-scale acceleration is possible without any violation of the energy conditions.

gr-qc↗

arXiv2013

An exact quantification of backreaction in relativistic cosmology

An important open question in cosmology is the degree to which the Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions of Einstein's equations are able to model the large-scale behaviour of the locally inhomogeneous observable universe. We investigate this problem by considering a range of exact n-body solutions of Einstein's constraint equations. These solutions contain discrete masses, and so allow arbitrarily large density contrasts to be modelled. We restrict our study to regularly arranged distributions of masses in topological 3-spheres. This has the benefit of allowing straightforward comparisons to be made with FLRW solutions, as both spacetimes admit a discrete group of symmetries. It also provides a time-symmetric hypersurface at the moment of maximum expansion that allows the constraint equations to be solved exactly. We find that when all the mass in the universe is condensed into a small number of objects (<10) then the amount of backreaction in dust models can be large, with O(1) deviations from the predictions of the corresponding FLRW solutions. When the number of masses is large (>100), however, then our measures of backreaction become small (<1%). This result does not rely on any averaging procedures, which are notoriously hard to define uniquely in general relativity, and so provides (to the best of our knowledge) the first exact and unambiguous demonstration of backreaction in general relativistic cosmological modelling. Discrete models such as these can therefore be used as laboratories to test ideas about backreaction that could be applied in more complicated and realistic settings.

gr-qc↗

arXiv2013

A Gravitational Entropy Proposal

We propose a thermodynamically motivated measure of gravitational entropy based on the Bel-Robinson tensor, which has a natural interpretation as the effective super-energy-momentum tensor of free gravitational fields. The specific form of this measure differs depending on whether the gravitational field is Coulomb-like or wave-like, and reduces to the Bekenstein-Hawking value when integrated over the interior of a Schwarzschild black hole. For scalar perturbations of a Robertson-Walker geometry we find that the entropy goes like the Hubble weighted anisotropy of the gravitational field, and therefore increases as structure formation occurs. This is in keeping with our expectations for the behaviour of gravitational entropy in cosmology, and provides a thermodynamically motivated arrow of time for cosmological solutions of Einstein's field equations. It is also in keeping with Penrose's Weyl curvature hypothesis.

gr-qc↗

arXiv2013

On the absence of the usual weak-field limit, and the impossibility of embedding some known solutions for isolated masses in cosmologies with f(R) dark energy

The problem of matching different regions of spacetime in order to construct inhomogeneous cosmological models is investigated in the context of Lagrangian theories of gravity constructed from general analytic functions f(R), and from non-analytic theories with f(R)=R^n. In all of the cases studied, we find that it is impossible to satisfy the required junction conditions without the large-scale behaviour reducing to that expected from Einstein's equations with a cosmological constant. For theories with analytic f(R) this suggests that the usual treatment of weak-field systems as perturbations about Minkowski space may not be compatible with late-time acceleration driven by anything other than a constant term of the form f(0), which acts like a cosmological constant. In the absence of Minkowski space as a suitable background for weak-field systems, one must then choose and justify some other solution to perform perturbative analyses around. For theories with f(R)=R^n we find that no known spherically symmetric vacuum solutions can be matched to an expanding FLRW background. This includes the absence of any Einstein-Straus-like embeddings of the Schwarzschild exterior solution in FLRW spacetimes.

gr-qc↗

arXiv2013

Back-Reaction in Relativistic Cosmology

We introduce the concept of back-reaction in relativistic cosmological modeling. Roughly speaking, this can be thought of as the difference between the large-scale behaviour of an inhomogeneous cosmological solution of Einstein's equations, and a homogeneous and isotropic solution that is a best-fit to either the average of observables or dynamics in the inhomogeneous solution. This is sometimes paraphrased as `the effect that structure has of the large-scale evolution of the universe'. Various different approaches have been taken in the literature in order to try and understand back-reaction in cosmology. We provide a brief and critical summary of some of them, highlighting recent progress that has been made in each case.

gr-qc↗

arXiv2012

Observational Cosmology in Macroscopic Gravity

We discuss the construction of cosmological models within the framework of Macroscopic Gravity (MG), which is a theory that models the effects of averaging the geometry of space-time on large scales. We find new exact spatially homogeneous and isotropic FLRW solutions to the MG field equations, and investigate large-scale perturbations around them. We find that any inhomogeneous perturbations to the averaged geometry are severely restricted, but that possible anisotropies in the correlation tensor can have dramatic consequences for the measurement of distances. These calculations are a first step within the MG approach toward developing averaged cosmological models to a point where they can be used to interpret real cosmological data, and hence to provide a working alternative to the "concordance" LCDM model.

astro-ph.CO↗

arXiv2012

The isotropic blackbody CMB as evidence for a homogeneous universe

The question of whether the Universe is spatially homogeneous and isotropic on the largest scales is of fundamental importance to cosmology, but has not yet been answered decisively. Surprisingly, neither an isotropic primary CMB nor combined observations of luminosity distances and galaxy number counts are sufficient to establish such a result. The inclusion of the Sunyaev-Zel'dovich effect in CMB observations, however, dramatically improves this situation. We show that even a solitary observer who sees an isotropic blackbody CMB can conclude that the universe is homogeneous and isotropic in their causal past when the Sunyaev-Zel'dovich effect is present. Critically, however, the CMB must either be viewed for an extended period of time, or CMB photons that have scattered more than once must be detected. This result provides a theoretical underpinning for testing the Cosmological Principle with observations of the CMB alone.

gr-qc↗

arXiv2012

Local and non-local measures of acceleration in cosmology

Current cosmological observations, when interpreted within the framework of a homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) model, strongly suggest that the Universe is entering a period of accelerating expansion. This is often taken to mean that the expansion of space itself is accelerating. In a general spacetime, however, this is not necessarily true. We attempt to clarify this point by considering a handful of local and non-local measures of acceleration in a variety of inhomogeneous cosmological models. Each of the chosen measures corresponds to a theoretical or observational procedure that has previously been used to study acceleration in cosmology, and all measures reduce to the same quantity in the limit of exact spatial homogeneity and isotropy. In statistically homogeneous and isotropic spacetimes, we find that the acceleration inferred from observations of the distance-redshift relation is closely related to the acceleration of the spatially averaged universe, but does not necessarily bear any resemblance to the average of the local acceleration of spacetime itself. For inhomogeneous spacetimes that do not display statistical homogeneity and isotropy, however, we find little correlation between acceleration inferred from observations and the acceleration of the averaged spacetime. This shows that observations made in an inhomogeneous universe can imply acceleration without the existence of dark energy.

astro-ph.CO↗

arXiv2012

Modified Gravity and Cosmology

In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, Scalar-Tensor, Einstein-Aether, and Bimetric theories, as well as TeVeS, f(R), general higher-order theories, Horava-Lifschitz gravity, Galileons, Ghost Condensates, and models of extra dimensions including Kaluza-Klein, Randall-Sundrum, DGP, and higher co-dimension braneworlds. We also review attempts to construct a Parameterised Post-Friedmannian formalism, that can be used to constrain deviations from General Relativity in cosmology, and that is suitable for comparison with data on the largest scales. These subjects have been intensively studied over the past decade, largely motivated by rapid progress in the field of observational cosmology that now allows, for the first time, precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole.

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