arXiv subjects

John D. Barrow

Publications and source records attributed to John D. Barrow.

At least 37 records · Page 2Linked to original sources

arXiv2020

Non-Euclidean Newtonian Cosmology

We formulate and solve the problem of Newtonian cosmology under the assumption that the absolute space of Newton is non-Euclidean. In particular, we focus on the negatively-curved hyperbolic space, H3. We point out the inequivalence between the curvature term that arises in the Friedmann equation in Newtonian cosmology in Euclidean space and the role of curvature in the H3 space. We find the generalisation of the inverse-square law and the solutions of the Newtonian cosmology that follow from it. We find the generalisations of the Euclidean Michell 'black hole' in H3 and show that it leads to different maximum force and area results to those we have found in general relativity. We show how to add the counterpart of the cosmological constant to the gravitational potential in H3 and explore the solutions and asymptotes of the cosmological models that result. We also discuss the problems of introducing compact topologies in Newtonian cosmologies with non-negative spatial curvature.

gr-qc↗

arXiv2020

Non-linear interactions in cosmologies with energy exchange

We investigate the case of two interacting fluids in homogeneous and isotropic cosmologies with a non-linear interaction term. The interaction term avoids the unrealistic form generally used in the literature, beginning with Tolman, in which the interaction is zero when the Hubble parameter vanishes. A variety of exact solutions for the scale factor are found and describe a range of new behaviors. We also extend the analysis of possible cosmological solutions with interacting fluids when curvature is taken into consideration. We use an example of energy exchange between radiation and scalar field to alleviate the flatness problem.

gr-qc↗

arXiv2020

Sudden Singularities in Brans-Dicke Cosmology and its Generalisations

We show that cosmological sudden singularities that respect the energy conditions can occur at finite times in Brans-Dicke and more general scalar-tensor theories of gravity. We construct these explicitly in the Friedmann universes. Higher-order versions of these singularities are also possible, including those that arise with when scalar fields have a self-interaction potential of power-law form.7 pages, no figures

gr-qc↗

arXiv2020

Finite Action Principle Revisited

We extend the cosmological predictions from assuming the total action of the universe is finite. When initial and final singularities in curvature invariants are avoided, it leads to singularities in the gravitational action of the universe. The following properties are required of a universe with finite action: Compact spatial sections (ie a closed universe) giving a finite total lifetime for the universe. Compactification of flat and open universes is excluded. The universe can contain perfect fluids with -1 2 in a closed, flat or open universe is excluded. Any bouncing model with indefinite past or future evolution is ruled out. Einstein static and steady-state universes are ruled out along with past or future eternal inflating universes. Anisotropies cannot dominate the dynamics at singularities. This excludes density inhomogeneity spectra versus mass, of the form δ\r{ho}/\r{ho}proportional to M^{-q}, with q>2/3.Higher-order lagrangian theories of gravity are constrained. The Gauss-Bonnet combination causes an action singularity even though it does not contribute terms to the field equations. Scalar-tensor theories dominated by the scalar field on approach to singularities have action singularities. Dark energy cannot be a cosmological constant. The dark energy must evolve in a closed universe that collapses to a future singularity that cannot be dominated by the kinetic energy of the scalar field.

gr-qc↗

arXiv2019

Screening $Λ$ in a new modified gravity model

We study a new model of Energy-Momentum Squared Gravity (EMSG), called Energy-Momentum Log Gravity (EMLG), constructed by the addition of the term $f(T_{μν}T^{μν})=α\ln(λ\,T_{μν}T^{μν})$, envisaged as a correction, to the Einstein-Hilbert action with cosmological constant $Λ$. The choice of this modification is made as a specific way of including new terms in the right-hand side of the Einstein field equations, resulting in constant effective inertial mass density and, importantly, leading to an explicit exact solution of the matter energy density in terms of redshift. We look for viable cosmologies, in particular, an extension of the standard $Λ$CDM model. EMLG provides an effective dynamical dark energy passing below zero at large redshifts, accommodating a mechanism for screening $Λ$ in this region, in line with suggestions for alleviating some of the tensions that arise between observational data sets within the standard $Λ$CDM model. We present a detailed theoretical investigation of the model and then constrain the free parameter $α'$, a normalisation of $α$, using the latest observational data. The data does not rule out the $Λ$CDM limit of our model ($α'= 0$), but prefers slightly negative values of the EMLG model parameter ($α'= -0.032\pm 0.043$), which leads to the screening of $Λ$. We also discuss how EMLG relaxes the persistent tension that appears in the measurements of $H_0$ within the standard $Λ$CDM model.

gr-qc↗

arXiv2019

Dynamics of Einstein-Aether Scalar field Cosmology

We study the cosmological evolution of the field equations in the context of Einstein-Aether cosmology by including a scalar field in a spatially flat Friedmann--Lema\^ıtre--Robertson--Walker spacetime. Our analysis is separated into two separate where a pressureless fluid source is included or absent. In particular, we determine the critical points of the field equations and we study the stability of the specific solutions. The limit of general relativity is fully recovered, while the dynamical system admits de Sitter solutions which can describe the past inflationary era and the future late-time attractor. Results for generic scalar field potentials are presented while some numerical behaviours are given for specific potential forms.

gr-qc↗

arXiv2019

Cyclic Szekeres Universes

We consider the Szekeres universe with an inhomogeneous dust fluid and a homogeneous and isotropic ghost matter source with equation of state $p_{g}=\left( γ-1\right) ρ_{g},$ where $γ$ is a constant. The field equations determine two families of spacetimes which describe homogeneous Kantowski-Sachs universes and inhomogeneous Friedmann universe. The ghost field Einstein permits static and cyclic solutions to exist. The stability of the Einstein static and cyclic solutions are studied with a critical point analysis.

gr-qc↗

arXiv2019

Cosmological Models in Energy-Momentum-Squared Gravity

We study the cosmological effects of adding terms of higher-order in the usual energy-momentum tensor to the matter lagrangian of general relativity. This is in contrast to most studies of higher-order gravity which focus on generalising the Einstein-Hilbert curvature contribution to the lagrangian. The resulting cosmological theories include many particular theories, like bulk viscous cosmologies, loop quantum gravity, K-essence, and brane-world cosmologies. We find a range of exact solutions for isotropic universes, discuss their behaviours with reference to the early and late-time evolution, accelerated expansion, and the occurrence or avoidance of singularities. We briefly discuss extensions to anisotropic cosmologies and delineate the situations where the higher-order matter terms will dominate over anisotropies on approach to cosmological singularities.

gr-qc↗

arXiv2019

Two-fluid solutions of particle-creation cosmologies

Cosmological evolution driven incorporating continuous particle creation by the time-varying gravitational field is investigated. We consider a spatially flat, homogeneous and isotropic universe with two matter fluids in the context of general relativity. One fluid is endowed with gravitationally induced `adiabatic' particle creation, while the second fluid simply satisfies the conservation of energy. We show that the dynamics of the two fluids is entirely controlled by a single nonlinear differential equation involving the particle creation rate, $Γ(t)$. We consider a very general particle creation rate, $Γ(t)$, that reduces to several special cases of cosmological interest, including $Γ=$ constant, $% Γ\propto 1/H^{n}$ ($n\in \mathbb{N}$), $Γ\propto \exp (1/H)$. Finally, we present singular algebraic solutions of the gravitational field equations for the two-fluid particle creation models and discuss their stability.

gr-qc↗

arXiv2018

Do we live in an eigenstate of the "fundamental constants" operators?

We propose that the constants of Nature we observe (which appear as parameters in the classical action) are quantum observables in a kinematical Hilbert space. When all of these observables commute, our proposal differs little from the treatment given to classical parameters in quantum information theory, at least if we were to inhabit a constants' eigenstate. Non-commutativity introduces novelties, due to its associated uncertainty and complementarity principles, and it may even preclude hamiltonian evolution. The system typically evolves as a quantum superposition of hamiltonian evolutions resulting from a diagonalization process, and these are usually quite distinct from the original one (defined in terms of the non-commuting constants). We present several examples targeting $G$, $c$ and $Λ$, and the dynamics of homogeneous and isotropic Universes. If we base our construction on the Heisenberg algebra and the quantum harmonic oscillator, the alternative dynamics tends to silence matter (effectively setting $G$ to zero), and make curvature and the cosmological constant act as if their signs are reversed. Thus, the early Universe expands as a quantum superposition of different Milne or de Sitter expansions for all material equations of state, even though matter nominally dominates the density, $ρ$, because of the negligible influence of $Gρ$ on the dynamics. A superposition of Einstein static universes can also be obtained. We also investigate the results of basing our construction on the algebra of $SU(2)$, into which we insert information about the sign of a constant of Nature, or whether its action is switched on or off. In this case we find examples displaying quantum superpositions of bounces at the initial state for the Universe.

gr-qc↗

arXiv2018

Szekeres Universes with Homogeneous Scalar Fields

We consider the existence of an "inflaton" described by an homogeneous scalar field in the Szekeres cosmological metric. The gravitational field equations are reduced to two families of solutions which describe the homogeneous Kantowski-Sachs spacetime and an inhomogeneous FLRW(-like) spacetime with spatial curvature a constant. The main differences with the original Szekeres spacetimes containing only pressure-free matter are discussed. We investigate the stability of the two families of solution by studying the critical points of the field equations. We find that there exist stable solutions which describe accelerating spatially-flat FLRW geometries.

gr-qc↗

arXiv2018

Inhomogeneous Initial Data and Small-Field Inflation

We consider the robustness of small-field inflation in the presence of scalar field inhomogeneities. Previous numerical work has shown that if the scalar potential is flat only over a narrow interval, such as in commonly considered inflection-point models, even small-amplitude inhomogeneities present at the would-be onset of inflation at $τ= τ_i$ can disrupt the accelerated expansion. In this paper, we parametrise and evolve the inhomogeneities from an earlier time $τ_{IC}$ at which the initial data were imprinted, and show that for a broad range of inflationary and pre-inflationary models, inflection-point inflation withstands initial inhomogeneities. We consider three classes of perturbative pre-inflationary solutions (corresponding to energetic domination by the scalar field kinetic term, a relativistic fluid, and isotropic negative curvature), and two classes of exact solutions to Einstein's equations with large inhomogeneities (corresponding to a stiff fluid with cylindrical symmetry, and anisotropic negative curvature). We derive a stability condition that depends on the Hubble scales $H(τ_ i)$ and $H(τ_{IC})$, and a few properties of the pre-inflationary cosmology. For initial data imprinted at the Planck scale, the absence of an inhomogeneous initial data problem for inflection-point inflation leads to a novel, lower limit on the tensor-to-scalar ratio.

gr-qc↗

arXiv2018

Constraining Density Fluctuations with Big Bang Nucleosynthesis in the Era of Precision Cosmology

We reexamine big bang nucleosynthesis with large-scale baryon density inhomogeneities when the length scale of the density fluctuations exceeds the neutron diffusion length ($\sim 10^7-10^8$ cm at BBN), and the amplitude of the fluctuations is sufficiently small to prevent gravitational collapse. In this limit, the final light element abundances can be determined by simply mixing the abundances from regions with different baryon/photon ratios without interactions. We examine gaussian, lognormal, and gamma distributions for the baryon/photon ratio, $η$. We find that the deuterium and lithium-7 abundances increase with the RMS fluctuation in $η$, while the effect on helium-4 is much smaller. We show that these increases in the deuterium and lithium-7 abundances are a consequence of Jensen's inequality, and we derive analytic approximations for these abundances in the limit of small RMS fluctuations. Observational upper limits on the primordial deuterium abundance constrain the RMS fluctuation in $η$ to be less than $17\%$ of the mean value of $η$. This provides us with a new limit on the graininess of the early universe.

astro-ph.CO↗

arXiv2018

Reconstructions of the dark-energy equation of state and the inflationary potential

We use a mathematical approach based on the constraints systems in order to reconstruct the equation of state and the inflationary potential for the inflaton field from the observed spectral indices for the density perturbations $n_{s}$ and the tensor to scalar ratio $r$. From the astronomical data, we can observe that the measured values of these two indices lie on a two-dimensional surface. We express these indices in terms of the Hubble slow-roll parameters and we assume that $n_{s}-1=h\left( r\right) $. For the function $h\left( r\right) $, we consider three cases, where $h\left( r\right) $ is constant, linear and quadratic, respectively. From this, we derive second-order equations whose solutions provide us with the explicit forms for the expansion scale-factor, the scalar-field potential, and the effective equation of state for the scalar field. Finally, we show that for there exist mappings which transform one cosmological solution to another and allow new solutions to be generated from existing ones.

gr-qc↗

arXiv2018

Constraint on energy-momentum squared gravity from neutron stars and its cosmological implications

Deviations from the predictions of general relativity due to energy-momentum squared gravity (EMSG) are expected to become pronounced in the high density cores of neutron stars. We derive the hydrostatic equilibrium equations in EMSG and solve them numerically to obtain the neutron star mass-radius relations for four different realistic equations of state. We use the existing observational measurements of the masses and radii of neutron stars to constrain the free parameter, $α,$ that characterizes the coupling between matter and spacetime in EMSG. We show that $-10^{-38}\,\mathrm{cm^{3}/erg}<α<+10^{-37}\,\mathrm{cm^{3}/erg}$. Under this constraint, we discuss what contributions EMSG can provide to the physics of neutron stars, in particular, their relevance to the so called \textit{hyperon puzzle} in neutron stars. We also discuss how EMSG alters the dynamics of the early universe from the predictions of the standard cosmological model. We show that EMSG leaves the standard cosmology safely unaltered back to $t\sim 10^{-4}$ seconds at which the energy density of the universe is $\sim 10^{34}\,\mathrm{erg\,cm^{-3}}$.

gr-qc↗

arXiv2018

Relativistic magnetised perturbations: magnetic pressure vs magnetic tension

We study the linear evolution of magnetised cosmological perturbations in the post-recombination epoch. Using full general relativity and adopting the ideal magnetohydrodynamic approximation, we refine and extend the previous treatments. More specifically, this is the first relativistic study that accounts for the effects of the magnetic tension, in addition to those of the field's pressure. Our solutions show that on sufficiently large scales, larger than the (purely magnetic) Jeans length, the perturbations evolve essentially unaffected by the magnetic presence. The magnetic pressure dominates on small scales, where it forces the perturbations to oscillate and decay. Close to the Jeans length, however, the field's tension takes over and leads to a weak growth of the inhomogeneities. These solutions clearly demonstrate the opposing action of the aforementioned two magnetic agents, namely of the field's pressure and tension, on the linear evolution of cosmological density perturbations.

astro-ph.CO↗

arXiv2018

Large-scale Stability and Astronomical Constraints for Coupled Dark-Energy Models

We study large-scale inhomogeneous perturbations and instabilities of interacting dark energy (IDE) models. Past analysis of large-scale perturbative instabilities, has shown that we can only test IDE models with observational data when its parameter ranges are either $w_{x}\geq -1$ and $ξ\geq 0,$ or $w_{x}\leq -1~$ and $~ξ\leq 0$, where $w_{x}$ is the dark energy equation of state (EoS), and $ξ$ is a coupling parameter governing the strength and direction of the energy transfer. We show that by adding a factor $(1+w_{x})$ to the background energy transfer, the whole parameter space can be tested against all the data and thus, the instabilities in such interaction models can be removed. We test three classes of interaction model using the latest astronomical data from different sources. Precise constraints are found. Our analysis shows that a very small but non-zero deviation from pure $Λ$-cosmology is suggested by the observational data while the no-interaction scenario can be recovered at the 68.3% confidence-level. In particular, for three IDE models, identified as IDE 1, IDE 2, and IDE 3, the 68.3% CL constraints on the interaction coupling strengths are, $ξ= 0.0360_{-0.0360}^{+0.0091}$ (IDE 1), $ξ= 0.0433_{-0.0433}^{+0.0062}$ (IDE 2), $ξ= 0.1064_{-0.1064}^{+0.0437}$ (IDE 3). In addition, we find that the dark energy EoS tends towards the phantom region taking the 68.3% CL constraints, $w_x= -1.0230_{-0.0257}^{+0.0329}$ (IDE 1), $w_x= -1.0247_{-0.0302}^{+0.0289}$ (IDE 2), and $w_x= -1.0275_{-0.0318}^{+0.0228}$ (IDE 3). However, the possibility of $w_{x}>-1$ is also not rejected by the astronomical data used here. Moreover, we find in all IDE models that, as the value of Hubble constant decreases, the behavior of the dark energy EoS shifts from phantom to quintessence type with its EoS very close to that a simple cosmological constant at the present time.

astro-ph.CO↗

arXiv2018

Stability of the Kasner Universe in f(T) Gravity

$f(T)$ gravity offers an alternative context in which to consider gravitational interactions where torsion, rather than curvature, is the mechanism by which gravitation is communicated. We investigate the stability of the Kasner solution with several forms of the arbitrary lagrangian function examined within the $f(T)$ context. This is a Bianchi type--I vacuum solution with anisotropic expansion factors. In the $f(T)$ gravity setting, the solution must conform to a set of conditions in order to continue to be a vacuum solution of the generalized field equations. With this solution in hand, the perturbed field equations are determined for power-law and exponential forms of the $f(T)$ function. We find that the point which describes the Kasner solution is a saddle point which means that the singular solution is unstable. However, we find the de Sitter universe is a late-time attractor. In general relativity, the cosmological constant drives the the isotropization of the spacetime while in this setting the extra $f(T)$ contributions now provide this impetus.

gr-qc↗