Timelike and null focusing singularities in spherical symmetry: a solution to the cosmological horizon problem and a challenge to the cosmic censorship hypothesis

Extending the study of spherically symmetric metrics satisfying the dominant energy condition and exhibiting singularities of power-law type initiated in SI93, we identify two classes of peculiar interest: focusing timelike singularity solutions with the stress-energy tensor of a radiative perfect fluid (equation of state: $p={1\over 3} \rho$) and a set of null singularity classes verifying identical properties. We consider two important applications of these results: to cosmology, as regards the possibility of solving the horizon problem with no need to resort to any inflationary scenario, and to the Strong Cosmic Censorship Hypothesis to which we propose a class of physically consistent counter-examples.Comment: 26 pages, 2 figures, LaTeX file. Submitted to Phys. Rev.

Redshift drift in axially symmetric quasi-spherical Szekeres models

Models of inhomogeneous universes constructed with exact solutions of Einstein's General Relativity have been proposed in the literature with the aim of reproducing the cosmological data without any need for a dark energy component. Besides large scale inhomogeneity models spherically symmetric around the observer, Swiss-cheese models have also been studied. Among them, Swiss-cheeses where the inhomogeneous patches are modeled by different particular Szekeres solutions have been used for reproducing the apparent dimming of the type Ia supernovae (SNIa). However, the problem of fitting such models to the SNIa data is completely degenerate and we need other constraints to fully characterize them. One of the tests which is known to be able to discriminate between different cosmological models is the redshift-drift. This drift has already been calculated by different authors for Lema\^itre-Tolman-Bondi (LTB) models. We compute it here for one particular axially symmetric quasi-spherical Szekeres (QSS) Swiss-cheese which has previously been shown to reproduce to a good accuracy the SNIa data, and we compare the results to the drift in the $\Lambda$CDM model and in some LTB models that can be found in the literature. We show that it is a good discriminator between them. Then, we discuss our model's remaining degrees of freedom and propose a recipe to fully constrain them.Comment: 15 pages, 7 figures, minor changes in title, text, figures and references; conclusions unchanged, this version matches the published versio

The Pauli equation in scale relativity

In standard quantum mechanics, it is not possible to directly extend the Schrodinger equation to spinors, so the Pauli equation must be derived from the Dirac equation by taking its non-relativistic limit. Hence, it predicts the existence of an intrinsic magnetic moment for the electron and gives its correct value. In the scale relativity framework, the Schrodinger, Klein-Gordon and Dirac equations have been derived from first principles as geodesics equations of a non-differentiable and continuous spacetime. Since such a generalized geometry implies the occurence of new discrete symmetry breakings, this has led us to write Dirac bi-spinors in the form of bi-quaternions (complex quaternions). In the present work, we show that, in scale relativity also, the correct Pauli equation can only be obtained from a non-relativistic limit of the relativistic geodesics equation (which, after integration, becomes the Dirac equation) and not from the non-relativistic formalism (that involves symmetry breakings in a fractal 3-space). The same degeneracy procedure, when it is applied to the bi-quaternionic 4-velocity used to derive the Dirac equation, naturally yields a Pauli-type quaternionic 3-velocity. It therefore corroborates the relevance of the scale relativity approach for the building from first principles of the quantum postulates and of the quantum tools. This also reinforces the relativistic and fundamentally quantum nature of spin, which we attribute in scale relativity to the non-differentiability of the quantum spacetime geometry (and not only of the quantum space). We conclude by performing numerical simulations of spinor geodesics, that allow one to gain a physical geometric picture of the nature of spin.Comment: 22 pages, 2 figures, accepted for publication in J. Phys. A: Math. & Ge

APSIS - an Artificial Planetary System in Space to probe extra-dimensional gravity and MOND

A proposal is made to test Newton's inverse-square law using the perihelion shift of test masses (planets) in free fall within a spacecraft located at the Earth-Sun L2 point. Such an Artificial Planetary System In Space (APSIS) will operate in a drag-free environment with controlled experimental conditions and minimal interference from terrestrial sources of contamination. We demonstrate that such a space experiment can probe the presence of a "hidden" fifth dimension on the scale of a micron, if the perihelion shift of a "planet" can be measured to sub-arc-second accuracy. Some suggestions for spacecraft design are made.Comment: 17 pages, revtex, references added. To appear in Special issue of IJMP

Generalized quantum potentials in scale relativity

We first recall that the system of fluid mechanics equations (Euler and continuity) that describes a fluid in irrotational motion subjected to a generalized quantum potential (in which the constant is no longer reduced to the standard quantum constant hbar) is equivalent to a generalized Schrodinger equation. Then we show that, even in the case of the presence of vorticity, it is also possible to obtain, for a large class of systems, a Schrodinger-like equation of the vectorial field type from the continuity and Euler equations including a quantum potential. The same kind of transformation also applies to a classical charged fluid subjected to an electromagnetic field and to an additional potential having the form of a quantum potential. Such a fluid can therefore be described by an equation of the Ginzburg-Landau type, and is expected to show some superconducting-like properties. Moreover, a Schrodinger form can be obtained for the fluctuating rotational motion of a solid. In this case the mass is replaced by the tensor of inertia, and a generalized form of the quantum potential is derived. We finally reconsider the case of a standard diffusion process, and we show that, after a change of variable, the diffusion equation can also be given the form of a continuity and Euler system including an additional potential energy. Since this potential is exactly the opposite of a quantum potential, the quantum behavior may be considered, in this context, as an anti-diffusion.Comment: 33 pages, submitted for publicatio

Tidal Dynamics in Cosmological Spacetimes

We study the relative motion of nearby free test particles in cosmological spacetimes, such as the FLRW and LTB models. In particular, the influence of spatial inhomogeneities on local tidal accelerations is investigated. The implications of our results for the dynamics of the solar system are briefly discussed. That is, on the basis of the models studied in this paper, we estimate the tidal influence of the cosmic gravitational field on the orbit of the Earth around the Sun and show that the corresponding temporal rate of variation of the astronomical unit is negligibly small.Comment: 12 pages, no figures, REVTeX 4.0; appendix added, new references, and minor changes throughout; to appear in Classical and Quantum Gravity; v4: error in (A24) of Appendix A corrected, results and conclusions unchanged. We thank L. Iorio for pointing out the erro

Model- and calibration-independent test of cosmic acceleration

We present a calibration-independent test of the accelerated expansion of the universe using supernova type Ia data. The test is also model-independent in the sense that no assumptions about the content of the universe or about the parameterization of the deceleration parameter are made and that it does not assume any dynamical equations of motion. Yet, the test assumes the universe and the distribution of supernovae to be statistically homogeneous and isotropic. A significant reduction of systematic effects, as compared to our previous, calibration-dependent test, is achieved. Accelerated expansion is detected at significant level (4.3 sigma in the 2007 Gold sample, 7.2 sigma in the 2008 Union sample) if the universe is spatially flat. This result depends, however, crucially on supernovae with a redshift smaller than 0.1, for which the assumption of statistical isotropy and homogeneity is less well established.Comment: 13 pages, 2 figures, major change

Systematic corrections to the measured cosmological constant as a result of local inhomogeneity

We calculate the systematic inhomogeneity-induced correction to the cosmological constant that one would infer from an analysis of the luminosities and redshifts of Type Ia supernovae, assuming a homogeneous universe. The calculation entails a post-Newtonian expansion within the framework of second order perturbation theory, wherein we consider the effects of subhorizon density perturbations in a flat, dust dominated universe. Within this formalism, we calculate luminosity distances and redshifts along the past light cone of an observer. The resulting luminosity distance-redshift relation is fit to that of a homogeneous model in order to deduce the best-fit cosmological constant density Omega_Lambda. We find that the luminosity distance-redshift relation is indeed modified, by a small fraction of order 10^{-5}. When fitting this perturbed relation to that of a homogeneous universe, we find that the inferred cosmological constant can be surprisingly large, depending on the range of redshifts sampled. For a sample of supernovae extending from z=0.02 out to z=0.15, we find that Omega_Lambda=0.004. The value of Omega_Lambda has a large variance, and its magnitude tends to get larger for smaller redshifts, implying that precision measurements from nearby supernova data will require taking this effect into account. However, we find that this effect is likely too small to explain the observed value of Omega_Lambda=0.7. There have been previous claims of much larger backreaction effects. By contrast to those calculations, our work is directly related to how observers deduce cosmological parameters from astronomical data.Comment: 28 pages, 3 figures, revtex4; v2: corrected comments and the section on previous work; v3: clarified wording. References adde

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.Comment: 19 pages, 10 figures. Several references added or amended, some minor clarifications made in the tex