General Relativity and Quantum Cosmology
New submissions
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New submissions for Tue, 2 Dec 08
- [1] arXiv:0812.0012 [ps, pdf, other]
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Title: The n-body problem in General Relativity up to the second post-Newtonian order from perturbative field theoryAuthors: Yi-Zen ChuComments: 39 pages. The Mathematica code used in this paper can be found at this http URLSubjects: General Relativity and Quantum Cosmology (gr-qc)
Motivated by experimental probes of general relativity, we adopt methods from perturbative (quantum) field theory to compute, up to certain integrals, the effective lagrangian for its n-body problem. Perturbation theory is performed about a background Minkowski spacetime to O[(v/c)^4] beyond Newtonian gravity, where v is the typical speed of these n particles in their center of energy frame. For the specific case of the 2 body problem, the major efforts underway to measure gravitational waves produced by in-spiraling compact astrophysical binaries require their gravitational interactions to be computed beyond the currently known O[(v/c)^7]. We argue that such higher order post-Newtonian calculations must be automated for these field theoretic methods to be applied successfully to achieve this goal. In view of this, we outline an algorithm that would in principle generate the relevant Feynman diagrams to an arbitrary order in v/c and take steps to develop the necessary software. The Feynman diagrams contributing to the n-body effective action at O[(v/c)^6] beyond Newton are derived.
- [2] arXiv:0812.0034 [ps, pdf, other]
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Title: Does a tensorial energy-momentum density for gravitation exist?Comments: 11 pages, no figuresSubjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
No tensorial expression for the energy-momentum density of the gravitational field seems to exist in general relativity. Would this be an ineluctable property of nature, or just a limitation of the general-relativistic geometric bias? An analysis of the spin connection shows that the non-tensorial character of the general relativity expressions is due to the fact that they all include the energy-momentum density of the fictitious forces associated to the non-inertiality of the adopted frame--which is non-tensorial by its very nature. Splitting the spin connection in such a way as to separate gravity from inertia, one ends up with teleparallel gravity, where a tensorial expression for the energy-momentum of gravity alone naturally emerges. Like the energy-momentum tensor of any other field in the presence of gravitation, it is conserved only in the covariant sense.
- [3] arXiv:0812.0069 [ps, pdf, other]
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Title: Post-Newtonian corrections to the gravitational-wave memory for quasi-circular, inspiralling compact binariesAuthors: Marc Favata (KITP)Comments: 25 pages, 6 figuresSubjects: General Relativity and Quantum Cosmology (gr-qc)
The Christodoulou memory is a nonlinear contribution to the gravitational-wave field that is sourced by the gravitational-wave stress-energy tensor. For quasi-circular, inspiralling binaries, the Christodoulou memory produces a growing, non-oscillatory change in the gravitational-wave "plus" polarization, resulting in the permanent displacement of a pair of freely-falling test masses after the wave has passed. In addition to its non-oscillatory behavior, the Christodoulou memory is interesting because even though it originates from 2.5 post-Newtonian (PN) order multipole interactions, it affects the waveform at leading-(Newtonian)-order. The memory is also potentially detectable in binary black hole mergers. While the oscillatory pieces of the gravitational-wave polarizations for quasi-circular, inspiralling compact binaries have been computed to 3PN order, the memory contribution to the polarizations has only been calculated to leading-order (the next-to-leading order 0.5PN term has previously been shown to vanish). Here the calculation of the memory for quasi-circular, inspiralling binaries is extended to 3PN order. While the angular dependence of the memory is essentially unchanged, the PN correction terms tend to reduce the memory's magnitude. Explicit expressions are given for the memory contributions to the polarizations and the spin-weighted spherical-harmonic modes of the metric and curvature perturbations. Combined with the results of Blanchet et al. (2008), this completes the waveform to 3PN order. This paper also discusses: (i) difficulties in extracting the memory from numerical simulations, (ii) other non-oscillatory effects that enter the waveform at high PN orders, and (iii) issues concerning the observability of the memory.
- [4] arXiv:0812.0110 [ps, pdf, other]
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Title: Carter-like constants of the motion in Newtonian gravity and electrodynamicsAuthors: Clifford M. WillComments: 4 pagesSubjects: General Relativity and Quantum Cosmology (gr-qc)
For a test body orbiting an axisymmetric body in Newtonian gravitational theory with multipole moments Q_L, (and for a charge in a non-relativistic orbit about a charge distribution with the same multipole moments) we show that there exists, in addition to the energy and angular momentum component along the symmetry axis, a conserved quantity analogous to the Carter constant of Kerr spacetimes in general relativity, if the odd-L moments vanish, and the even-L moments satisfy Q_2L = m (Q_2/m)^L. Strangely, this is precisely the relation among mass moments enforced by the no-hair theorems of rotating black holes. By contrast, if Newtonian gravity is supplemented by a multipolar gravitomagnetic field, whose leading term represents frame-dragging (or if the electrostatic field is supplemented by a multipolar magnetic field), we are unable to find an analogous Carter-like constant. This further highlights the very special nature of the Kerr geometry of general relativity.
- [5] arXiv:0812.0167 [pdf]
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Title: A scaling law for the cosmological constant from a stochastic model for cosmic structuresComments: 7 pages, 2 figuresSubjects: General Relativity and Quantum Cosmology (gr-qc)
A set of scaling laws, based on the stochastic motions of the granular components of astronomical systems, is applied to a cosmological model with a positive cosmological constant. It follows that the mass of the dominant particle in the observable universe must be proportional to the sixth root of the cosmological constant and of the order of the nucleon mass, which is consistent with the Zeldovich scaling law. The approach is a natural way to solve the cosmic coincidence problem. On the other hand, the observed value of the cosmological constant emerges as the result of a scaling law induced by the stochastic mechanism which gives rise to the gravitationally bound systems.
- [6] arXiv:0812.0168 [ps, pdf, other]
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Title: Stochastic Background of Gravitational Waves as a Benchmark for Extended Theories of GravityComments: 4 Pages, in "Problems of Modern Cosmology" for the 50th bithday of S.D. OdintsovSubjects: General Relativity and Quantum Cosmology (gr-qc)
The cosmological background of gravitational waves can be tuned by Extended Theories of Gravity. In particular, it can be shown that assuming a generic function f(R) of the Ricci scalar R gives a parametric approach to control the evolution and the production mechanism of gravitational waves in the early Universe.
- [7] arXiv:0812.0170 [ps, pdf, other]
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Title: Dark energy towards observational tests and dataAuthors: S. CapozzielloComments: 12 pages, Vulcano Workshop 2008, "Frontiers objects in Astrophysics and Particle Physics" May 26-31, 2008Subjects: General Relativity and Quantum Cosmology (gr-qc)
A huge amount of good quality data converges towards the picture of a spatially flat universe undergoing the today observed phase of accelerated expansion. This new observational trend is commonly addressed as Precision Cosmology. Despite of the excellent surveys, the nature of dark energy, dominating the matter-energy content of the universe, is still unknown and a lot of different scenarios are viable candidates to explain cosmic acceleration. Methods to test these cosmological models are based on distance measurements and lookback time toward astronomical objects used as standard candles. The related degeneracy problem is the signal that more data at low 0<z<1, medium 1<z<10 and high 10 <z< 1000 redshift are needed to definitively select realistic models.
- [8] arXiv:0812.0173 [ps, pdf, other]
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Title: A Note on Distributional Semi-Riemannian GeometryAuthors: Roland SteinbauerComments: 11 pages, Contribution presented at the 12th Serbian Mathematical Congress, Novi Sad, September 2008Subjects: General Relativity and Quantum Cosmology (gr-qc); Differential Geometry (math.DG)
We discuss some basic concepts of semi-Riemannian geometry in low-regularity situations. In particular, we compare the settings of (linear) distributional geometry in the sense of L. Schwartz and nonlinear distributional geometry in the sense of J.F. Colombeau.
- [9] arXiv:0812.0177 [ps, pdf, other]
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Title: Loop Quantum Cosmology: An OverviewAuthors: Abhay AshtekarComments: To appear in the Proceedings of the Bad Honef Workshop entitled \emph{Quantum Gravity: Challenges and Perspectives}, dedicated to the memory of John A. WheelerSubjects: General Relativity and Quantum Cosmology (gr-qc)
A brief overview of loop quantum cosmology of homogeneous isotropic models is presented with emphasis on the origin of and subtleties associated with the resolution of big bang and big crunch singularities. These results bear out the remarkable intuition that John Wheeler had. Discussion is organized at two levels. The the main text provides a bird's eye view of the subject that should be accessible to non-experts. Appendices address conceptual and technical issues that are often raised by experts in loop quantum gravity and string theory.
- [10] arXiv:0812.0235 [ps, pdf, other]
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Title: Geodesics and Symmetries of Doubly-Spinning Black RingsAuthors: Mark DurkeeComments: 25 pages, 5 figuresSubjects: General Relativity and Quantum Cosmology (gr-qc)
This paper studies various properties of the Pomeransky-Sen'kov doubly-spinning black ring spacetime. I discuss the structure of the ergoregion, and then go on to demonstrate the separability of the Hamilton-Jacobi equation for null, zero energy geodesics, which exist in the ergoregion. These geodesics are used to construct geometrically motivated coordinates that cover the black hole horizon. Finally, I relate this weak form of separability to the existence of a conformal Killing tensor in a particular 4-dimensional spacetime obtained by Kaluza-Klein reduction, and show that a related conformal Killing-Yano tensor only exists in the singly-spinning case.
- [11] arXiv:0812.0240 [pdf]
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Title: On the Flow of TimeAuthors: George F R EllisComments: 9 pages, 2 figures. Essay for the Fqxi essay contest on THE NATURE OF TIMESubjects: General Relativity and Quantum Cosmology (gr-qc)
Current theoretical physics suggests the flow of time is an illusion: the entire universe just is, with no special meaning attached to the present time. This paper points out that this view, in essence represented by usual space-time diagrams, is based on time-reversible microphysical laws, which fail to capture essential features of the time-irreversible nature of decoherence and the quantum measurement process, as well as macro-physical behaviour and the development of emergent complex systems, including life, which exist in the real universe. When these are taken into account, the unchanging block universe view of spacetime is best replaced by an evolving block universe which extends as time evolves, with the potential of the future continually becoming the certainty of the past; spacetime itself evolves, as do the entities within it. However this time evolution is not related to any preferred surfaces in spacetime; rather it is associated with the evolution of proper time along families of world lines. The default state of fundamental physics should not be taken to be a time irreversible evolution of physical states: it is an ongoing irreversible development of time itself.
- [12] arXiv:0812.0272 [ps, pdf, other]
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Title: On the resolution of the big bang singularity in isotropic Loop Quantum CosmologyAuthors: Madhavan VaradarajanComments: 26 pages, no figuresSubjects: General Relativity and Quantum Cosmology (gr-qc)
In contrast to previous work in the field, we construct the Loop Quantum Cosmology (LQC) of the flat isotropic model with a massless scalar field in the absence of higher order curvature corrections to the gravitational part of the Hamiltonian constraint. The matter part of the constraint contains the inverse triad operator which can be quantized with or without the use of a Thiemann- like procedure. With the latter choice, we show that the LQC quantization is identical to that of the standard Wheeler DeWitt theory (WDW) wherein there is no singularity resolution. We argue that the former choice leads to singularity resolution in the sense of a well defined, regular (backward) evolution through and beyond the epoch where the size of the universe vanishes.
Our work along with that of the seminal work of Ashtekar, Pawlowski and Singh (APS) clarifies the role, in singularity resolution, of the three `exotic' structures in this LQC model, namely: curvature corrections, inverse triad definitions and the `polymer' nature of the kinematic representation. We also critically examine certain technical assumptions made by APS in their analysis of WDW semiclassical states and point out some problems stemming from the infrared behaviour of their wave functions - [13] arXiv:0812.0295 [ps, pdf, other]
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Title: Quantum geometrodynamics: whence, whither?Authors: Claus KieferComments: 25 pages; invited contribution for the Proceedings of the seminar "Quantum Gravity: Challenges and Perspectives", Bad Honnef, Germany, April 2008Subjects: General Relativity and Quantum Cosmology (gr-qc)
Quantum geometrodynamics is canonical quantum gravity with the three-metric as the configuration variable. Its central equation is the Wheeler--DeWitt equation. Here I give an overview of the status of this approach. The issues discussed include the problem of time, the relation to the covariant theory, the semiclassical approximation as well as applications to black holes and cosmology. I conclude that quantum geometrodynamics is still a viable approach and provides insights into both the conceptual and technical aspects of quantum gravity.
Cross-lists for Tue, 2 Dec 08
- [14] arXiv:0811.3934 (cross-list from astro-ph) [ps, pdf, other]
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Title: Inflationary trispectrum from graviton exchangeComments: 23 pages, 2 figures. Uses iopart.sty and feynmp.sty. v2: Bibliography updated, no change to textSubjects: Astrophysics (astro-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
We compute the connected four-point correlation function of the primordial curvature perturbation generated during inflation with standard kinetic terms, where the correlation is established via exchange of a graviton between two pairs of scalar fluctuations. Any such correlation yields a contribution to the scalar trispectrum of the order of the tensor to scalar ratio r. This contribution is numerically one order of magnitude larger than the one previously calculated on the basis of scalar perturbations interacting at a point and satisfies a simple relation in the limit where the momentum of the graviton which is exchanged becomes much smaller than the external momenta. We conclude that the total non-linearity parameter generated by single-field models of slow-roll inflation is at maximum tauNL ~ r.
- [15] arXiv:0811.4607 (cross-list from hep-th) [ps, pdf, other]
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Title: Tachyon-Dilaton-induced Inflation as an alpha'-resummed String BackgroundComments: 35 pages Latex, three eps figures incorporatedSubjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph)
Within the framework of a novel functional method on the world-sheet of the string, we discuss simple but re-summed (in the Regge slope) inflationary scenarios in the context of closed Bosonic strings, living in four target-space dimensions, in the presence of non-trivial tachyon, dilaton and graviton cosmological backgrounds. The inflationary solutions are argued to guarantee the vanishing of the corresponding Weyl anomaly coefficients in a given world-sheet renormalization scheme, thereby ensuring conformal invariance of the corresponding sigma-model to all orders in the Regge slope. The key property is the requirement of "homogeneity" of the corresponding Weyl anomaly coefficients. Inflation entails appropriate relations between the dilaton and tachyon field configurations, whose form can lead to either a de Sitter vacuum, incompatible though (due to the cosmic horizons) with the perturbative string scattering amplitudes, or to cosmic space-times involving brief inflationary periods, interpolating smoothly between power-law and/or Minkowski Universes. The latter situation is characterized by well-defined scattering amplitudes, and is thus compatible with a perturbative string framework. It is this scenario that we consider a self-consistent ground state in our framework, which is based on local field redefinitions of background fields.
- [16] arXiv:0811.4629 (cross-list from astro-ph) [ps, pdf, other]
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Title: Braneworlds with timelike extra-dimensionComments: 7 pages, 8 figuresSubjects: Astrophysics (astro-ph); General Relativity and Quantum Cosmology (gr-qc)
In this work, we consider a braneworld model with a timelike extra-dimension. There are strong constraints to the parameter values of such a model resulting from the claim that there must be a physical solution to the Friedmann equation at least between now and the time of recombination. We fitted the model to supernova type Ia data and checked the consistency of the result with other observations. For parameter values that are consistent with observations, the braneworld model is indistinguishable from a LambdaCDM universe as far as the considered cosmological tests are concerned.
- [17] arXiv:0812.0243 (cross-list from math.DG) [ps, pdf, other]
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Title: Causal boundaries and holography on wave type spacetimesAuthors: Miguel SánchezComments: Submitted to the proceedings of WCNA (Orlando '08). 34 pages, including 10 figures and one table; LatexSubjects: Differential Geometry (math.DG); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
The notion of causal boundary of a spacetime has been a controversial topic during the last three decades. Moreover, recently the role of the boundary in the AdS/CFT correspondence for plane waves, have stimulated its redefinition with some possible alternatives.
Our aim is threefold. First, to review the different classical approaches to boundaries of spacetimes, emphasizing their drawbacks and the progressive redefinitions of the c-boundary. Second, to explain how plane waves and AdS/CFT correspondence come into play, stressing the role of the c-boundary as the holographic boundary in this correspondence. And, third, to discuss the present-day status of the c-boundary, making clear the arguments of a definitive proposal. - [18] arXiv:0812.0345 (cross-list from physics.ins-det) [ps, pdf, other]
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Title: Probing For New Physics and Detecting non linear vacuum QED effects using gravitational wave interferometer antennasSubjects: Instrumentation and Detectors (physics.ins-det); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Experiment (hep-ex); High Energy Physics - Phenomenology (hep-ph)
Low energy non linear QED effects in vacuum have been predicted since 1936 and have been subject of research for many decades. Two main schemes have been proposed for such a 'first' detection: measurements of ellipticity acquired by a linearly polarized beam of light passing through a magnetic field and direct light-light scattering. The study of the propagation of light through an external field can also be used to probe for new physics such as the existence of axion-like particles and millicharged particles. Their existence in nature would cause the index of refraction of vacuum to be different from unity in the presence of an external field and dependent of the polarization direction of the light propagating. The major achievement of reaching the project sensitivities in gravitational wave interferometers such as LIGO an VIRGO has opened the possibility of using such instruments for the detection of QED corrections in electrodynamics and for probing new physics at very low energies. In this paper we discuss the difference between direct birefringence measurements and index of refraction measurements. We propose an almost parasitic implementation of an external magnetic field along the arms of the VIRGO interferometer and discuss the advantage of this choice in comparison to a previously proposed configuration based on shorter prototype interferometers which we believe is inadequate. Considering the design sensitivity in the strain, for the near future VIRGO+ interferometer, of $h<2\cdot10^{-23} \frac{1}{\sqrt{\rm Hz}}$ in the range 40 Hz $- 400$ Hz leads to a variable dipole magnet configuration at a frequency above 20 Hz such that $B^{2}D \ge 13000$ T$^{2}$m/$\sqrt{\rm Hz}$ for a `first' vacuum non linear QED detection.
Replacements for Tue, 2 Dec 08
- [19] arXiv:0711.2319 (replaced) [ps, pdf, other]
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Title: Statefinder diagnostic for Yang-Mills dark energy modelAuthors: Wen ZhaoComments: 13 pages, 3figures, minor typos correctedJournal-ref: Int.J.Mod.Phys.D17:1245-1254,2008Subjects: General Relativity and Quantum Cosmology (gr-qc)
- [20] arXiv:0801.0482 (replaced) [ps, pdf, other]
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Title: Geometrical properties of the trans-spherical solutions in higher dimensionsComments: 14 pages, 2 figures, Title changedSubjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
- [21] arXiv:0808.0190 (replaced) [ps, pdf, other]
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Title: Singularities in loop quantum cosmologyComments: 5 pages, 3 figures. v2: Comments and references added. v3: Minor additions, version to appear in PRLSubjects: General Relativity and Quantum Cosmology (gr-qc); Astrophysics (astro-ph); High Energy Physics - Theory (hep-th)
- [22] arXiv:0808.0949 (replaced) [pdf, other]
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Title: Critical behaviour in quantum gravitational collapseAuthors: Viqar HusainComments: 8 pages, 3 figures. Typos corrected -- version to appear in a special issue of Adv. Science Lett. (Ed. M. Bojowald)Subjects: General Relativity and Quantum Cosmology (gr-qc)
- [23] arXiv:0809.4122 (replaced) [ps, pdf, other]
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Title: Perturbation theory of N point-mass gravitational lens systems without symmetry: small mass-ratio approximationAuthors: Hideki AsadaComments: 14 pages, 8 figures, 3 tables; abstract and text improved; accepted for publication in MNRASSubjects: Astrophysics (astro-ph); General Relativity and Quantum Cosmology (gr-qc)
- [24] arXiv:0809.4441 (replaced) [ps, pdf, other]
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Title: Hilltop QuintessenceComments: 7 pages, 9 figures, references and discussion addedSubjects: Astrophysics (astro-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
- [25] arXiv:0810.0072 (replaced) [ps, pdf, other]
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Title: Rigid motion revisited: rigid quasilocal framesComments: 10 pages (two column), 24 pages (preprint), 1 figureSubjects: General Relativity and Quantum Cosmology (gr-qc)
- [26] arXiv:0811.4347 (replaced) [ps, pdf, other]
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Title: Gluonic vacuum, q-theory, and the cosmological constantComments: 14 pages; v2: some remarks and references addedSubjects: General Relativity and Quantum Cosmology (gr-qc)
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