arXiv subjects

John D. Barrow

Publications and source records attributed to John D. Barrow.

At least 19 recordsLinked to original sources

arXiv2021

A contextual Planck parameter and the classical limit in quantum cosmology

We propose that whatever quantity controls the Heisenberg uncertainty relations (for a given complementary pair of observables) it should be identified with an effective Planck parameter. With this definition it is not difficult to find examples where the Planck parameter depends on the region under study, varies in time, and even depends on which pair of observables one focuses on. In quantum cosmology the effective Planck parameter depends on the size of the comoving region under study, and so depends on that chosen region and on time. With this criterion, the classical limit is expected, not for regions larger than the Planck length, $l_{P}$, but for those larger than $l_{Q}=(l_{P}^{2}H^{-1})^{1/3}$, where $H$ is the Hubble parameter. In theories where the cosmological constant is dynamical, it is possible for the latter to remain quantum even in contexts where everything else is deemed classical. These results are derived from standard quantization methods, but we also include more speculative cases where ad hoc Planck parameters scale differently with the length scale under observation. Even more speculatively, we examine the possibility that similar complementary concepts affect thermodynamical variables, such as the temperature and the entropy of a black hole.

gr-qc↗

arXiv2020

Screening anisotropy via energy-momentum squared gravity: $Λ$CDM model with hidden anisotropy

We construct a generalization of the standard $Λ$CDM model, wherein we simultaneously replace the spatially flat Robertson-Walker metric with its simplest anisotropic generalization (LRS Bianchi I metric), and couple the cold dark matter to the gravity in accordance with the energy-momentum squared gravity (EMSG) of the form $f(T_{μν}T^{μν})\propto T_{μν}T^{μν}$. These two modifications -- namely, two new stiff fluid-like terms of different nature -- can mutually cancel out, i.e., the shear scalar can be screened completely, and reproduce mathematically exactly the same Friedmann equation of the standard $Λ$CDM model. This evades the BBN limits on the anisotropy, and thereby provides an opportunity to manipulate the cosmic microwave background quadrupole temperature fluctuation at the desired amount. We further discuss the consequences of the model on the very early times and far future of the Universe. This study presents also an example of that the EMSG of the form $f(T_{μν}T^{μν})\propto T_{μν}T^{μν}$, as well as similar type other constructions, is not necessarily relevant only to very early Universe but may even be considered in the context of a major problem of the current cosmology related to the present-day Universe, the so-called $H_0$ problem.

astro-ph.CO↗

arXiv2020

The Generic Sudden Singularity in Brans-Dicke Theory

We construct a formal asymptotic series expansion for a general solution of the Brans-Dicke equations with a fluid source near a sudden singularity. This solution contains eleven independent arbitrary functions of the spatial coordinates as required by the Cauchy problem of the theory. We show that the solution is geodesically complete and has the character of a shock wave in the sudden asymptotic region. This solution is weak in the senses of Tipler and Krolak as in the corresponding case of general relativity.

gr-qc↗

arXiv2020

Big Bang Nucleosynthesis constraints on Barrow entropy

We use Big Bang Nucleosynthesis (BBN) data in order to impose constraints on the exponent of Barrow entropy. The latter is an extended entropy relation arising from the incorporation of quantum-gravitational effects on the black-hole structure, parameterized effectively by the new parameter $Δ$. When considered in a cosmological framework and under the light of the gravity-thermodynamics conjecture, Barrow entropy leads to modified cosmological scenarios whose Friedmann equations contain extra terms. We perform a detailed analysis of the BBN era and we calculate the deviation of the freeze-out temperature comparing to the result of standard cosmology. We use the observationally determined bound on $ |\frac{δ{T}_f}{{T}_f}|$ in order to extract the upper bound on $Δ$. As we find, the Barrow exponent should be inside the bound $Δ\lesssim 1.4\times 10^{-4}$ in order not to spoil the BBN epoch, which shows that the deformation from standard Bekenstein-Hawking expression should be small as expected.

gr-qc↗

arXiv2020

Maximum Force in Modified Gravity Theories

We investigate the existence and nature of classical maximum force bound between two black holes with touching horizons. Besides general relativity, the maximum force bound is independent of black hole masses only in Moffat's theory, Brans Dicke theory (which is the same as Einstein's for vacuum) and the higher dimensional generalization of Einstein's theory, pure Lovelock gravity which is characterised by having single $n$th order term in Lovelock polynomial without sum over lower orders in the action. Further if the bound is to exist in higher dimensions and is entirely in terms of the velocity of light and the gravitational constant, it has uniquely to be pure Lovelock gravity. In pure Lovelock gravity, the maximum force bound exists in all $3n$-space dimensions and has the value, $c^4/4G_n$ where $G_n$ is the corresponding gravitational constant. The absence of mass dependence in the maximum force bound may have relevance for the formation of naked singularities.

gr-qc↗

arXiv2020

Inhomogeneous spacetimes in Weyl integrable geometry with matter source

We investigate the existence of inhomogeneous exact solutions in Weyl Integrable theory with a matter source. In particular, we consider the existence of a dust fluid source while for the underlying geometry we assume a line element which belongs to the family of silent universes. We solve explicitly the field equations and we find the Szekeres spacetimes in Weyl Integrable theory. We show that only the isotropic family can describe inhomogeneous solutions where the LTB spacetimes are included. A detailed analysis of the dynamics of the field equations is given where the past and future attractors are determined. It is interesting that the Kasner spacetimes can be seen as past attractors for the gravitation models, while the unique future attractor describes the Milne universe similar with the behaviour of the gravitational model in the case of General Relativity.

gr-qc↗

arXiv2020

Kinematical and dynamical aspects of ghost-matter cosmologies

We consider the kinematical and dynamical evolution of Friedmann universes with a mixture of non-interacting matter and a ghost-like field, in a scenario analogous to that advocated by the Quintom model. Assuming that the conventional matter dominates today, we find that the ghost component can bring the future expansion and the past contraction of the model to a finite halt. Moreover, at the moment the expansion or contraction stops, we find that the tendency of the universe is to bounce back and re-collapse or re-expand. Therefore, the presence of a (never dominant) ghost-field with negative density could, in principle, drive the universe into an eternal cycle of finite expansion, collapse, and re-expansion. Our study outlines the key features of such a scenario and provides a simple condition for it to occur. We also derive an autonomous set of differential equations and then employ dynamical-system techniques to identify two families of fixed points, with and without spatial curvature respectively. The members of the first family correspond to coasting universes and are stable in the Lyapunov sense. Those of the latter family are unstable repellers when their matter satisfies the strong energy condition and Lyapunov stable in the opposite case.

gr-qc↗

arXiv2020

Is the universe ill-posed?

We discuss an unusual consequence of the behaviour of general relativistic cosmological models when they initial value problem is not well-posed because of the lack of the local Lipschitz condition. A new type of 'zero universe' arises with vanishing scale factor, and its first time derivative, at all times. We discuss briefly some of the questions this raises about creation out of nothing.

gr-qc↗

arXiv2020

Multifractality in the general cosmological solution of Einstein's equations

We demonstrate the scale invariance of the vacuum Bianchi type IX equations and use this to argue for the possibility of multifractal turbulence as a realisation of the suggestion by Belinski that there will be a fragmentation of local regions of inhomogeneous Mixmaster chaos on approach to an initial inhomogeneous cosmological singularity. Differences between the gravitational and hydrodynamical situations are outlined. Various potential obstacles to this picture of gravitational turbulence are discussed.

gr-qc↗

arXiv2020

Inflation Without a Trace of Lambda

We generalise Einstein's formulation of the traceless Einstein equations to $f(R)$ gravity theories. In the case of the vacuum traceless Einstein equations, we show that a non-constant Weyl tensor leads via a conformal transformation to a dimensionally homogeneous (`no-scale') theory in the conformal frame with a scalar field source that has an exponential potential. We then formulate the traceless version of $f(R)$ gravity, and we find that a conformal transformation leads to a no-scale theory conformally equivalent to general relativity and a scalar field $ϕ$ with a potential given by the scale-invariant form: $V(ϕ)=\frac{D-2}{4D}Re^{-ϕ}$, where $ϕ=[2/(D-2)]\ln f^{\prime }(R)$. In this theory, the cosmological constant is a mere integration constant, statistically distributed in a multiverse of independent causal domains, the vacuum energy is another unrelated arbitrary constant, and the same is true of the height of the inflationary plateau present in a huge variety of potentials. Unlike in the conformal equivalent of full general relativity, flat potentials are found to be possible in all spacetime dimensions for polynomial lagrangians of all orders. Hence, we are led to a novel interpretation of the cosmological constant vacuum energy problem and have accelerated inflationary expansion in the very early universe with a very small cosmological constant at late times for a wide range of no-scale theories. Fine-tunings required in traceless general relativity or standard non-traceless $f(R)$ theories of gravity are avoided. We show that the predictions of the scale-invariant conformal potential are completely consistent with microwave background observational data concerning the primordial tilt and the tensor-to-scalar ratio.

gr-qc↗

arXiv2020

Einstein-aether theory in Weyl integrable geometry

We study the Einstein-aether theory in Weyl integrable geometry. The scalar field which defines the Weyl affine connection is introduced in the gravitational field equation. We end up with an Einstein-aether scalar field model where the interaction between the scalar field and the aether field has a geometric origin. The scalar field plays a significant role in the evolution of the gravitational field equations. We focus our study on the case of homogeneous and isotropic background spacetimes and study their dynamical evolution for various cosmological models.

gr-qc↗

arXiv2020

The Area of a Rough Black Hole

We investigate the consequences for the black hole area of introducing fractal structure for the horizon geometry. We create a three-dimensional spherical analogue of a 'Koch Snowflake' using a infinite diminishing hierarchy of touching spheres around the Schwarzschild event horizon. We can create a fractal structure for the horizon with finite volume and infinite (or finite) area. This is a toy model for the possible effects of quantum gravitational spacetime foam, with significant implications for assessments of the entropy of black holes and the universe, which is generally larger than in standard picture of black hole structure and thermodynamics, potentially by very considerable factors. The entropy of the observable universe today becomes log(S) is approximately 120(1+D/2) with D = 0 for a smooth spacetime structure and D = 1 for the most intricate. The Hawking lifetime of black holes is also reduced.

gr-qc↗

arXiv2020

Perturbations and Linearization Stability of Closed Friedmann Universes

We consider perturbations of closed Friedmann universes. Perturbation modes of two lowest wavenumbers ($L=0$ and $1$) are generally known to be fictitious, but here we show that both are physical. The issue is more subtle in Einstein static universes where closed background space has a time-like Killing vector with the consequent occurrence of linearization instability. Proper solutions of the linearized equation need to satisfy the Taub constraint on a quadratic combination of first-order variables. We evaluate the Taub constraint in the two available fundamental gauge conditions, and show that in both gauges the $L\geq 1$ modes should accompany the $L=0$ (homogeneous) mode for vanishing sound speed, $c_{s}$. For $c_{s}^{2}>1/5$ (a scalar field supported Einstein static model belongs to this case with $c_s^2 = 1$), the $L\geq 2$ modes are known to be stable. In order to have a stable Einstein static evolutionary stage in the early universe, before inflation and without singularity, although the Taub constraint does not forbid it, we need to find a mechanism to suppress the unstable $L=0$ and $L=1$ modes.

gr-qc↗

arXiv2020

New Anisotropic Sudden Singularities and Dimensional Reduction

We demonstrate the existence of sudden, finite-time, singularities, with constant scale factor, expansion rate and density, in expanding Bianchi type IX universes with free anisotropic pressures. A new type of non-simultaneous anisotropic sudden singularity arises because of the divergences of the pressures, which may be of barrel or pancake type. The effect of one or more directions of expansion hitting a sudden singularity is tantamount to dimensional reductions as the non-singular directions continue expanding and can see the sudden singularity in their past.

gr-qc↗

arXiv2020

A conjecture about the general cosmological solution of Einstein's equations

We introduce consideration of a new factor, synchronisation of spacetime Mixmaster oscillations, that may play a simplifying role in understanding the nature of the general inhomogeneous cosmological solution to Einstein's equations. We conjecture that, on approach to a singularity, the interaction of spacetime Mixmaster oscillations in different regions of an inhomogeneous universe can produce a synchronisation of these oscillations through a coupling to their mean field in the way first demonstrated by the Kuramoto coupled oscillator model.

gr-qc↗

arXiv2020

Maximum Force and Naked Singularities in Higher Dimensions

We discuss the existence of maximum forces in 3+1 dimensional spacetimes and show that the existence of a mass-independent maximum force does not occur in general relativity in spaces of more than three dimensions. Instead, the maximum force increases with the masses, M, of merging objects as M to the power (N-3)/(N-2) and allows unbounded gravitational forces to occur. This suggests that naked singularities can arise in more than three dimensions because they are unprotected by a maximum force at the horizon surface. This creates a new perspective on the expectation of naked singularities in higher dimensions.

gr-qc↗

arXiv2020

Four direct measurements of the fine-structure constant 13 billion years ago

Observations of the redshift z=7.085 quasar J1120+0641 have been used to search for variations of the fine structure constant, alpha, over the redshift range 5.5 to 7.1. Observations at z=7.1 probe the physics of the universe when it was only 0.8 billion years old. These are the most distant direct measurements of alpha to date and the first measurements made with a near-IR spectrograph. A new AI analysis method has been employed. Four measurements from the X-SHOOTER spectrograph on the European Southern Observatory's Very Large Telescope (VLT) directly constrain any changes in alpha relative to the value measured on Earth (alpha_0). The weighted mean strength of the electromagnetic force over this redshift range in this location in the universe is da/a = (alpha_z - alpha_0)/alpha_0 = (-2.18 +/- 7.27) X 10^{-5}, i.e. we find no evidence for a temporal change from the 4 new very high redshift measurements. When the 4 new measurements are combined with a large existing sample of lower redshift measurements, a new limit on possible spatial variation of da/a is marginally preferred over a no-variation model at the 3.7 sigma level.

astro-ph.CO↗

arXiv2020

Graduated dark energy: Observational hints of a spontaneous sign switch in the cosmological constant

We study the cosmological constant ($Λ$) in the standard $Λ$CDM model by introducing the \textit{graduated dark energy} (gDE) characterised by a minimal dynamical deviation from the null inertial mass density of the $Λ$ in the form $ρ_{\rm inert}\propto ρ^λ<0$ with $λ<1$ being a ratio of two odd integers, for which its energy density $ρ$ dynamically takes negative values in the finite past. For large negative values of $λ$, it creates a phenomenological model described by a smooth function that approximately describes the $Λ$ spontaneously switching sign in the late universe to become positive today. We confront the model with the latest combined observational data sets of PLK+BAO+SN+$H$. It is striking that the data predict bimodal posterior probability distributions for the parameters of the model along with large negative $λ$ values; the new maximum significantly excludes the $Λ$, and the old maximum contains the $Λ$. The improvement in the goodness of fit for the $Λ$ reaches highly significant levels, $Δχ_{\rm min}^2=6.4$ for the new maxima, while it remains at insignificant levels, $Δχ_{\rm min}^2\lesssim0.02$, for the old maxima. We show that, in contrast to the old maxima, which do not distinguish from the $Λ$, the new maxima agree with the model-independent $H_0$ measurements, high-precision Ly-$α$ data, and model-independent $Omh^2$ diagnostic estimates. Our results provide strong hints of a spontaneous sign switch in the cosmological constant and lead us to conjecture that the universe has transitioned from AdS vacua to dS vacua, at a redshift $z\approx 2.32$ and triggered the late-time acceleration, and suggests looking for such mechanisms in string theory constructions.

astro-ph.CO↗