Measuring dark energy with the shear triplet statistics

The shear triplet statistics is a geometric method to measure cosmological parameters with observations in the weak gravitational lensing regime towards massive haloes. Here, this proposal is considered to probe the dark energy equation of state and its time derivative in view of future wide-field galaxy surveys. A survey with a median redshift of nearly 0.7 and a total area of nearly 10000 square degrees would be pretty effective in determining the dark matter cosmological density and in putting useful constraints on the dark energy properties.Comment: 5 pages, 3 figures, accepted for publication in MNRA

Weak field limit of Reissner-Nordstrom black hole lensing

We study gravitational lensing by a Reissner-Nordstrom (RN) black hole in the weak field limit. We obtain the basic equations for the deflection angle and time delay and find analytical expressions for the positions and amplifications of the primary and secondary images. Due to a net positive charge, the separation between images increases, but no change in the total magnification occurs.Comment: 8 pages, to appear in Phys. Rev.

Kinematic effect in gravitational lensing by clusters of galaxies

Gravitational lensing provides an efficient tool for the investigation of matter structures, independent of the dynamical or hydrostatic equilibrium properties of the deflecting system. However, it depends on the kinematic status. In fact, either a translational motion or a coherent rotation of the mass distribution can affect the lensing properties. Here, light deflection by galaxy clusters in motion is considered. Even if gravitational lensing mass measurements of galaxy clusters are regarded as very reliable estimates, the kinematic effect should be considered. A typical peculiar motion with respect to the Hubble flow brings about a systematic error < 0.3%, independent of the mass of the cluster. On the other hand, the effect of the spin increases with the total mass. For cluster masses ~ 10^{15}M_{sun}, the effect of the gravitomagnetic term is < 0.04% on strong lensing estimates and < 0.5% in the weak lensing analyses. The total kinematic effect on the mass estimate is then < 1%, which is negligible in current statistical studies. In the weak lensing regime, the rotation imprints a typical angular modulation in the tangential shear distortion. This would allow in principle a detection of the gravitomagnetic field and a direct measurement of the angular velocity of the cluster but the required background source densities are well beyond current tecnological capabilities.Comment: 6 pages; accepted for publication in MNRA

Lensing in an interior Kottler solution

We derive the interior Kottler solution of the incompressible fluid and show that the bending of light in this solution does depend on the cosmological constant.Comment: The inner Kottler solution derived and used in this paper is not new. Corresponding references to Stuchlik (2000) and Boehmer (2003) are added. Also added: a numerical example and a figure. This is the version accepted by Gen. Rel. Grav. However it includes a short passage that an anonymous referee had me suppress

Spherical symmetry in a dark energy permeated space-time

The properties of a spherically symmetric static space-time permeated of dark energy are worked out. Dark energy is viewed as the strain energy of an elastically deformable four dimensional manifold. The metric is worked out in the vacuum region around a central spherical mass/defect in the linear approximation. We discuss analogies and differences with the analogue in the de Sitter space time and how these competing scenarios could be differentiated on an observational ground. The comparison with the tests at the solar system scale puts upper limits to the parameters of the theory, consistent with the values obtained applying the classical cosmological tests.Comment: 14 pages, 1 figure, in press on Classical and Quantum Gravit

Cosmological constraints for the Cosmic Defect theory

The Cosmic Defect theory has been confronted with four observational constraints: primordial nuclear species abundances emerging from the big bang nucleosynthesis; large scale structure formation in the universe; cosmic microwave background acoustic scale; luminosity distances of type Ia supernovae. The test has been based on a statistical analysis of the a posteriori probabilities for three parameters of the theory. The result has been quite satisfactory and such that the performance of the theory is not distinguishable from the one of the Lambda-CDM theory. The use of the optimal values of the parameters for the calculation of the Hubble constant and the age of the universe confirms the compatibility of the Cosmic Defect approach with observations.Comment: 13 pages, 1 figure, in press on IJMP

Cosmography with strong lensing of LISA gravitational wave sources

LISA might detect gravitational waves from mergers of massive black hole binaries strongly lensed by intervening galaxies (Sereno et al. 2010). The detection of multiple gravitational lensing events would provide a new tool for cosmography. Constraints on cosmological parameters could be placed by exploiting either lensing statistics of strongly lensed sources or time delay measurements of lensed gravitational wave signals. These lensing methods do not need the measurement of the redshifts of the sources and the identification of their electromagnetic counterparts. They would extend cosmological probes to redshift z <= 10 and are then complementary to other lower or higher redshift tests, such as type Ia supernovae or cosmic microwave background. The accuracy of lensing tests strongly depends on the formation history of the merging binaries, and the related number of total detectable multiple images. Lensing amplification might also help to find the host galaxies. Any measurement of the source redshifts would allow to exploit the distance-redshift test in combination with lensing methods. Time-delay analyses might measure the Hubble parameter H_0 with accuracy of >= 10 km s^{-1}Mpc^{-1}. With prior knowledge of H_0, lensing statistics and time delays might constrain the dark matter density (delta Omega_M >= 0.08, due to parameter degeneracy). Inclusion of our methods with other available orthogonal techniques might significantly reduce the uncertainty contours for Omega_M and the dark energy equation of state.Comment: 10 pages, 10 figures, in press on MNRA

Dark matter vs. modifications of the gravitational inverse-square law. Results from planetary motion in the solar system

Dark matter or modifications of the Newtonian inverse-square law in the solar-system are studied with accurate planetary astrometric data. From extra-perihelion precession and possible changes in the third Kepler's law, we get an upper limit on the local dark matter density, rho_{DM} < 3*10^{-16} kg/m^3 at the 2-sigma confidence level. Variations in the 1/r^2 behavior are considered in the form of either a possible Yukawa-like interaction or a modification of gravity of MOND type. Up to scales of 10^{11} m, scale-dependent deviations in the gravitational acceleration are really small. We examined the MOND interpolating function mu in the regime of strong gravity. Gradually varying mu suggested by fits of rotation curves are excluded, whereas the standard form mu(x)= x/(1+x^2)^{1/2} is still compatible with data. In combination with constraints from galactic rotation curves and theoretical considerations on the external field effect, the absence of any significant deviation from inverse square attraction in the solar system makes the range of acceptable interpolating functions significantly narrow. Future radio ranging observations of outer planets with an accuracy of few tenths of a meter could either give positive evidence of dark matter or disprove modifications of gravity.Comment: 7 pages, 4 figures, accepted for publication in MNRA

Measuring dark energy with the shear triplet statistics

The shear triplet statistics is a geometric method to measure cosmological parameters with observations in the weak gravitational lensing regime towards massive haloes. Here, this proposal is considered to probe the dark energy equation of state and its time derivative in view of future wide-field galaxy surveys. A survey with a median redshift of ∼0.7 and a total area of ∼10 000 deg2 would be pretty effective in determining the dark matter cosmological density and in putting useful constraints on the dark energy propertie

Imprints of deviations from the gravitational inverse-square law on the power spectrum of mass fluctuations

Deviations from the gravitational inverse-square law would imprint scale-dependent features on the power spectrum of mass density fluctuations. We model such deviations as a Yukawa-like contribution to the gravitational potential and discuss the growth function in a mixed dark matter model with adiabatic initial conditions. Evolution of perturbations is considered in general non-flat cosmological models with a cosmological constant, and an analytical approximation for the growth function is provided. The coupling between baryons and cold dark matter across recombination is negligibly affected by modified gravity physics if the proper cutoff length of the long-range Yukawa-like force is > 10 h^{-1} Mpc. Enhancement of gravity affects the subsequent evolution, boosting large-scale power in a way that resembles the effect of a lower matter density. This phenomenon is almost perfectly degenerate in power-spectrum shape with the effect of a background of massive neutrinos. Back-reaction on density growth from a modified cosmic expansion rate should however also affect the normalization of the power spectrum, with a shape distortion similar to the case of a non-modified background.Comment: 8 pages, 7 figures; submitted to MNRA