Universe

Research

82 pages, 964 KiB

Open AccessFeature PaperArticle

General Relativity and Cosmology: Unsolved Questions and Future Directions

by Ivan Debono^1,*,†

and George F. Smoot^1,2,3,†

¹ Paris Centre for Cosmological Physics, APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/lrfu, Observatoire de Paris, Sorbonne Paris Cité, 10, rue Alice Domon et Léonie Duquet, 75205 Paris CEDEX 13, France

² Physics Department and Lawrence Berkeley National Laboratory, University of California, Berkeley, 94720 CA, USA

³ Helmut and Anna Pao Sohmen Professor-at-Large, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, 999077 Hong Kong, China

Universe 2016, 2(4), 23; https://doi.org/10.3390/universe2040023 - 28 Sep 2016

Cited by 166 | Viewed by 49209

Abstract

For the last 100 years, General Relativity (GR) has taken over the gravitational theory mantle held by Newtonian Gravity for the previous 200 years. This article reviews the status of GR in terms of its self-consistency, completeness, and the evidence provided by observations, [...] Read more.

For the last 100 years, General Relativity (GR) has taken over the gravitational theory mantle held by Newtonian Gravity for the previous 200 years. This article reviews the status of GR in terms of its self-consistency, completeness, and the evidence provided by observations, which have allowed GR to remain the champion of gravitational theories against several other classes of competing theories. We pay particular attention to the role of GR and gravity in cosmology, one of the areas in which one gravity dominates and new phenomena and effects challenge the orthodoxy. We also review other areas where there are likely conflicts pointing to the need to replace or revise GR to represent correctly observations and consistent theoretical framework. Observations have long been key both to the theoretical liveliness and viability of GR. We conclude with a discussion of the likely developments over the next 100 years. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

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34 pages, 683 KiB

Open AccessArticle

Which Quantum Theory Must be Reconciled with Gravity? (And What Does it Mean for Black Holes?)

by Matthew J. Lake^1,2

¹ The Institute for Fundamental Study, “The Tah Poe Academia Institute”, Naresuan University, Phitsanulok 65000, Thailand

² Thailand Center of Excellence in Physics, Ministry of Education, Bangkok 10400, Thailand

Universe 2016, 2(4), 24; https://doi.org/10.3390/universe2040024 - 17 Oct 2016

Cited by 9 | Viewed by 4887

Abstract

We consider the nature of quantum properties in non-relativistic quantum mechanics (QM) and relativistic quantum field theories, and examine the connection between formal quantization schemes and intuitive notions of wave-particle duality. Based on the map between classical Poisson brackets and their associated commutators, [...] Read more.

We consider the nature of quantum properties in non-relativistic quantum mechanics (QM) and relativistic quantum field theories, and examine the connection between formal quantization schemes and intuitive notions of wave-particle duality. Based on the map between classical Poisson brackets and their associated commutators, such schemes give rise to quantum states obeying canonical dispersion relations, obtained by substituting the de Broglie relations into the relevant (classical) energy-momentum relation. In canonical QM, this yields a dispersion relation involving ℏ but not c, whereas the canonical relativistic dispersion relation involves both. Extending this logic to the canonical quantization of the gravitational field gives rise to loop quantum gravity, and a map between classical variables containing G and c, and associated commutators involving ℏ. This naturally defines a “wave-gravity duality”, suggesting that a quantum wave packet describing self-gravitating matter obeys a dispersion relation involving G, c and ℏ. We propose an Ansatz for this relation, which is valid in the semi-Newtonian regime of both QM and general relativity. In this limit, space and time are absolute, but imposing

v_{\max} = c

allows us to recover the standard expressions for the Compton wavelength

λ_{C}

and the Schwarzschild radius

r_{S}

within the same ontological framework. The new dispersion relation is based on “extended” de Broglie relations, which remain valid for slow-moving bodies of any mass m. These reduce to canonical form for

m ≪ m_{P}

, yielding

λ_{C}

from the standard uncertainty principle, whereas, for

m ≫ m_{P}

, we obtain

r_{S}

as the natural radius of a self-gravitating quantum object. Thus, the extended de Broglie theory naturally gives rise to a unified description of black holes and fundamental particles in the semi-Newtonian regime. Full article

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16 pages, 278 KiB

Open AccessArticle

On the Effect of the Cosmological Expansion on the Gravitational Lensing by a Point Mass

by Oliver F. Piattella

Physics Department, Universidade Federal do Espírito Santo, Vitória 29075-910, Brazil

Universe 2016, 2(4), 25; https://doi.org/10.3390/universe2040025 - 18 Oct 2016

Cited by 15 | Viewed by 3967

Abstract

We analyse the effect of the cosmological expansion on the deflection of light caused by a point mass, adopting the McVittie metric as the geometrical description of a point-like lens embedded in an expanding universe. In the case of a generic, non-constant Hubble [...] Read more.

We analyse the effect of the cosmological expansion on the deflection of light caused by a point mass, adopting the McVittie metric as the geometrical description of a point-like lens embedded in an expanding universe. In the case of a generic, non-constant Hubble parameter, H, we derive and approximately solve the null geodesic equations, finding an expression for the bending angle δ, which we expand in powers of the mass-to-closest approach distance ratio and of the impact parameter-to-lens distance ratio. It turns out that the leading order of the aforementioned expansion is the same as the one calculated for the Schwarzschild metric and that cosmological corrections contribute to δ only at sub-dominant orders. We explicitly calculate these cosmological corrections for the case of the H constant and find that they provide a correction of order 10⁻¹¹ on the lens mass estimate. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

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13 pages, 241 KiB

Open AccessFeature PaperArticle

A Solution of the Mitra Paradox

by Øyvind Grøn

Oslo and Akershus University College of Applied Sciences, Faculty of Technology, Art and Sciences, PB 4 St. Olavs. Pl., NO-0130 Oslo, Norway

Universe 2016, 2(4), 26; https://doi.org/10.3390/universe2040026 - 4 Nov 2016

Cited by 1 | Viewed by 4876

Abstract

The “Mitra paradox” refers to the fact that while the de Sitter spacetime appears non-static in a freely falling reference frame, it looks static with reference to a fixed reference frame. The coordinate-independent nature of the paradox may be gauged from the fact [...] Read more.

The “Mitra paradox” refers to the fact that while the de Sitter spacetime appears non-static in a freely falling reference frame, it looks static with reference to a fixed reference frame. The coordinate-independent nature of the paradox may be gauged from the fact that the relevant expansion scalar,

θ = \sqrt{3 Λ}

, is finite if

Λ > 0

. The trivial resolution of the paradox would obviously be to set

Λ = 0

. However, here it is assumed that

Λ > 0

, and the paradox is resolved by invoking the concept of “expansion of space”. This is a reference-dependent concept, and it is pointed out that the solution of the Mitra paradox is obtained by taking into account the properties of the reference frame in which the coordinates are co-moving. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

10 pages, 450 KiB

Open AccessArticle

Strategies to Ascertain the Sign of the Spatial Curvature

by Pedro C. Ferreira¹ and Diego Pavón^2,*

¹ Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte, Natal 59072-970, Rio Grande do Norte, Brazil

² Departamento de Física, Universidad Autónoma de Barcelona, Bellaterra, Barcelona 08193, Spain

Universe 2016, 2(4), 27; https://doi.org/10.3390/universe2040027 - 24 Nov 2016

Cited by 3 | Viewed by 4256

Abstract

The second law of thermodynamics, in the presence of gravity, is known to hold at small scales, as in the case of black holes and self-gravitating radiation spheres. Using the Friedmann–Lemaître–Robertson–Walker metric and the history of the Hubble factor, we argue that this [...] Read more.

The second law of thermodynamics, in the presence of gravity, is known to hold at small scales, as in the case of black holes and self-gravitating radiation spheres. Using the Friedmann–Lemaître–Robertson–Walker metric and the history of the Hubble factor, we argue that this law also holds at cosmological scales. Based on this, we study the connection between the deceleration parameter and the spatial curvature of the metric,

Ω_{k}

, and set limits on the latter, valid for any homogeneous and isotropic cosmological model. Likewise, we devise strategies to determine the sign of the spatial curvature index k. Finally, assuming the lambda cold dark matter model is correct, we find that the acceleration of the cosmic expansion is increasing today. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

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14 pages, 304 KiB

Open AccessArticle

The Problem of Embedded Eigenvalues for the Dirac Equation in the Schwarzschild Black Hole Metric

by Davide Batic^1,*, Marek Nowakowski^2,* and Kirk Morgan^3,*

¹ Department of Mathematics, The Petroleum Institute, P.O. Box 2533 Abu Dhabi, UAE

² Departamento de Fisica, Universidad de los Andes, Cra.1E No.18A-10 Bogota, Colombia

³ Department of Mathematics, University of the West Indies, Kingston 6, Jamaica

Universe 2016, 2(4), 31; https://doi.org/10.3390/universe2040031 - 2 Dec 2016

Cited by 18 | Viewed by 5047

Abstract

We use the Dirac equation in a fixed black hole background and different independent techniques to demonstrate the absence of fermionic bound states around a Schwarzschild black hole. In particular, we show that no embedded eigenvalues exist which has been claimed for the [...] Read more.

We use the Dirac equation in a fixed black hole background and different independent techniques to demonstrate the absence of fermionic bound states around a Schwarzschild black hole. In particular, we show that no embedded eigenvalues exist which has been claimed for the case when the energy is less than the particle’s mass. We explicitly prove that the claims regarding the embedded eigenvalues can be traced back to an oversimplified approximation in the calculation. We conclude that no bound states exist regardless of the value of the mass. Full article

(This article belongs to the Collection Open Questions in Black Hole Physics)

15 pages, 370 KiB

Open AccessArticle

Baryon Number Transfer Could Delay Quark–Hadron Transition in Cosmology

by Silvio A. Bonometto^1,* and Roberto Mainini²

¹ The National Institute of Astrophysics (INAF)— Astronomical Observatory of Trieste, Departmnet of Physics, University of Trieste, Via Tiepolo 11, Trieste 34143, Italy

² Department of Physics G. Occhialini, Milano-Bicocca University, Piazza della Scienza 3, Milano 20126, Italy

Universe 2016, 2(4), 32; https://doi.org/10.3390/universe2040032 - 13 Dec 2016

Cited by 3 | Viewed by 4020

Abstract

In the early Universe, strongly interacting matter was a quark–gluon plasma. Both lattice computations and heavy ion collision experiments, however, tell us that, in the absence of chemical potentials, no plasma survives at

T < \sim 150

MeV. The cosmological Quark–Hadron transition, however, [...] Read more.

In the early Universe, strongly interacting matter was a quark–gluon plasma. Both lattice computations and heavy ion collision experiments, however, tell us that, in the absence of chemical potentials, no plasma survives at

T < \sim 150

MeV. The cosmological Quark–Hadron transition, however, seems to have been a crossover; cosmological consequences envisaged when it was believed to be a phase transition no longer hold. In this paper, we discuss whether even a crossover transition can leave an imprint that cosmological observations can seek or, vice versa, if there are questions cosmology should address to QCD specialists. In particular, we argue that it is still unclear how baryons (not hadrons) could form at the cosmological transition. A critical role should be played by diquark states, whose abundance in the early plasma needs to be accurately evaluated. We estimate that, if the number of quarks belonging to a diquark state, at the beginning of the cosmological transition, is

< \sim 1 : 10^{6}

, its dynamics could be modified by the process of B-transfer from plasma to hadrons. In turn, by assuming B-transfer to cause just mild perturbations and, in particular, no entropy input, we study the deviations from the tracking regime, in the frame of SCDEW models. We find that, in some cases, residual deviations could propagate down to primeval nuclesynthesis. Full article

(This article belongs to the Special Issue Quark-Gluon Plasma in the Early Universe and in Ultra-Relativistic Heavy-Ion Collisions)

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Review

Jump to: Research, Other

55 pages, 541 KiB

Open AccessReview

World-Line Formalism: Non-Perturbative Applications

by Dmitry Antonov

Erbprinzenstrasse 25, 69126 Heidelberg, Germany

Universe 2016, 2(4), 28; https://doi.org/10.3390/universe2040028 - 28 Nov 2016

Cited by 4 | Viewed by 5328

Abstract

This review addresses the impact on various physical observables which is produced by confinement of virtual quarks and gluons at the level of the one-loop QCD diagrams. These observables include the quark condensate for various heavy flavors, the Yang-Mills running coupling with an [...] Read more.

This review addresses the impact on various physical observables which is produced by confinement of virtual quarks and gluons at the level of the one-loop QCD diagrams. These observables include the quark condensate for various heavy flavors, the Yang-Mills running coupling with an infra-red stable fixed point, and the correlation lengths of the stochastic Yang-Mills fields. Other non-perturbative applications of the world-line formalism presented in the review are devoted to the determination of the electroweak phase-transition critical temperature, to the derivation of a semi-classical analogue of the relation between the chiral and the gluon QCD condensates, and to the calculation of the free energy of the gluon plasma in the high-temperature limit. As a complementary result, we demonstrate Casimir scaling of k-string tensions in the Gaussian ensemble of the stochastic Yang-Mills fields. Full article

(This article belongs to the Special Issue Quark-Gluon Plasma in the Early Universe and in Ultra-Relativistic Heavy-Ion Collisions)

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40 pages, 564 KiB

Open AccessReview

Tests of Lorentz Symmetry in the Gravitational Sector

by Aurélien Hees^1,*, Quentin G. Bailey², Adrien Bourgoin³, Hélène Pihan-Le Bars³, Christine Guerlin^3,4 and Christophe Le Poncin-Lafitte³

¹ Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, USA

² Physics Department, Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA

³ SYRTE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, LNE, 61 avenue de l’Observatoire, 75014 Paris, France

⁴ Laboratoire Kastler Brossel, ENS-PSL Research University, CNRS, UPMC-Sorbonne Universités, Collège de France, 75005 Paris, France

Universe 2016, 2(4), 30; https://doi.org/10.3390/universe2040030 - 1 Dec 2016

Cited by 78 | Viewed by 7282

Abstract

Lorentz symmetry is one of the pillars of both General Relativity and the Standard Model of particle physics. Motivated by ideas about quantum gravity, unification theories and violations of CPT symmetry, a significant effort has been put the last decades into testing Lorentz [...] Read more.

Lorentz symmetry is one of the pillars of both General Relativity and the Standard Model of particle physics. Motivated by ideas about quantum gravity, unification theories and violations of CPT symmetry, a significant effort has been put the last decades into testing Lorentz symmetry. This review focuses on Lorentz symmetry tests performed in the gravitational sector. We briefly review the basics of the pure gravitational sector of the Standard-Model Extension (SME) framework, a formalism developed in order to systematically parametrize hypothetical violations of the Lorentz invariance. Furthermore, we discuss the latest constraints obtained within this formalism including analyses of the following measurements: atomic gravimetry, Lunar Laser Ranging, Very Long Baseline Interferometry, planetary ephemerides, Gravity Probe B, binary pulsars, high energy cosmic rays, … In addition, we propose a combined analysis of all these results. We also discuss possible improvements on current analyses and present some sensitivity analyses for future observations. Full article

(This article belongs to the Special Issue 100 Years of Chronogeometrodynamics: the Status of the Einstein's Theory of Gravitation in Its Centennial Year)

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Other

Jump to: Research, Review

5 pages, 342 KiB

Open AccessConference Report

Experimental Studies on the Lorentz Symmetry in Post-Newtonian Gravity with Pulsars

by Lijing Shao

Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, D-14476 Potsdam-Golm, Germany

Universe 2016, 2(4), 29; https://doi.org/10.3390/universe2040029 - 1 Dec 2016

Cited by 3 | Viewed by 3696

Abstract

Local Lorentz invariance (LLI) is one of the most important fundamental symmetries in modern physics. While the possibility of LLI violation (LLIv) was studied extensively in flat spacetime, its counterpart in gravitational interaction also deserves significant examination from experiments. In this contribution, I [...] Read more.

Local Lorentz invariance (LLI) is one of the most important fundamental symmetries in modern physics. While the possibility of LLI violation (LLIv) was studied extensively in flat spacetime, its counterpart in gravitational interaction also deserves significant examination from experiments. In this contribution, I review several recent studies of LLI in post-Newtonian gravity, using powerful tools of pulsar timing. It shows that precision pulsar timing experiments hold a unique position to probe LLIv in post-Newtonian gravity. Full article

(This article belongs to the Special Issue Varying Constants and Fundamental Cosmology)

8 pages, 671 KiB

Open AccessConference Report

New Constraints on Spatial Variations of the Fine Structure Constant from Clusters of Galaxies

by Ivan De Martino^1,*

, Carlos J. A. P. Martins^2,3, Harald Ebeling⁴ and Dale Kocevski⁵

¹ Faculty of Science and Technology, Department of Theoretical Physics and History of Science, University of the Basque Country (UPV/EHU), Barrio Sarriena s/n, 48940 Leioa, Spain

² Centro de Astrofisica da Universidade do Porto, Rua das Estrelas s/n, 4150-762 Porto, Portugal

³ Instituto de Astrofísica e Ciências do Espaço, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal

⁴ Institute for Astronomy, University of Hawaii, Honolulu, HI 96822, USA

⁵ Department of Physics and Astronomy, Colby College, Waterville, ME 04901, USA

Universe 2016, 2(4), 34; https://doi.org/10.3390/universe2040034 - 21 Dec 2016

Cited by 13 | Viewed by 4315

Abstract

We have constrained the spatial variation of the fine structure constant using multi-frequency measurements of the thermal Sunyaev-Zeldovich effect of 618 X-ray selected clusters. Although our results are not competitive with the ones from quasar absorption lines, we improved by a factor 10 [...] Read more.

We have constrained the spatial variation of the fine structure constant using multi-frequency measurements of the thermal Sunyaev-Zeldovich effect of 618 X-ray selected clusters. Although our results are not competitive with the ones from quasar absorption lines, we improved by a factor 10 and ∼2.5 previous results from Cosmic Microwave Background power spectrum and from galaxy clusters, respectively. Full article

(This article belongs to the Special Issue Varying Constants and Fundamental Cosmology)

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