No Arabic abstract
Verlinde (2016) proposed that the observed excess gravity in galaxies and clusters is the consequence of Emergent Gravity (EG). In this theory the standard gravitational laws are modified on galactic and larger scales due to the displacement of dark energy by baryonic matter. EG gives an estimate of the excess gravity (described as an apparent dark matter density) in terms of the baryonic mass distribution and the Hubble parameter. In this work we present the first test of EG using weak gravitational lensing, within the regime of validity of the current model. Although there is no direct description of lensing and cosmology in EG yet, we can make a reasonable estimate of the expected lensing signal of low redshift galaxies by assuming a background LambdaCDM cosmology. We measure the (apparent) average surface mass density profiles of 33,613 isolated central galaxies, and compare them to those predicted by EG based on the galaxies baryonic masses. To this end we employ the ~180 square degrees overlap of the Kilo-Degree Survey (KiDS) with the spectroscopic Galaxy And Mass Assembly (GAMA) survey. We find that the prediction from EG, despite requiring no free parameters, is in good agreement with the observed galaxy-galaxy lensing profiles in four different stellar mass bins. Although this performance is remarkable, this study is only a first step. Further advancements on both the theoretical framework and observational tests of EG are needed before it can be considered a fully developed and solidly tested theory.
We propose gravitational microlensing as a way of testing the emergent gravity theory recently proposed by Eric Verlinde~cite{Verlinde:2016toy}. We consider two limiting cases: the dark mass of maximally anisotropic pressures (Case I) and of isotropic pressures (Case II). Our analysis of perihelion advancement of a planet shows that only Case I yields a viable theory. In this case the metric outside a star of mass $M_*$ can be modeled by that of a point-like global monopole whose mass is $M_*$ and a deficit angle $Delta = sqrt{(2GH_0M_*)/(3c^3)}$, where $H_0$ is the Hubble rate and $G$ the Newton constant. This deficit angle can be used to test the theory since light exhibits additional bending around stars given by, $alpha_Dapprox -piDelta/2$. This angle is independent on the distance from the star and it affects equally light and massive particles. The effect is too small to be measurable today, but should be within reach of the next generation of high resolution telescopes. Finally we note that the advancement of periastron of a planet orbiting around a star or black hole, which equals $piDelta$ per period, can be also used to test the theory.
In a recent paper, Erik Verlinde has developed the interesting possibility that spacetime and gravity may emerge from the entangled structure of an underlying microscopic theory. In this picture, dark matter arises as a response to the standard model of particle physics from the delocalized degrees of freedom that build up the dark energy component of the Universe. Dark matter physics is then regulated by a characteristic acceleration scale $a_0$, identified with the radius of the (quasi)-de Sitter universe we inhabit. For a point particle matter source, or outside an extended spherically symmetric object, MONDs empirical fitting formula is recovered. However, Verlindes theory critically departs from MOND when considering the inner structure of galaxies, differing by a factor of 2 at the centre of a regular massive body. For illustration, we use the eight classical dwarf spheroidal satellites of the Milky Way. These objects are perfect testbeds for the model given their approximate spherical symmetry, measured kinematics, and identified missing mass. We show that, without the assumption of a maximal deformation, Verlindes theory can fit the velocity dispersion profile in dwarf spheroidals with no further need of an extra dark particle component. If a maximal deformation is considered, the theory leads to mass-to-light ratios that are marginally larger than expected from stellar population and formation history studies. We also compare our results with the recent phenomenological interpolating MOND function of McGaugh {it et al}, and find a departure that, for these galaxies, is consistent with the scatter in current observations.
We test the predictions of Emergent Gravity using matter densities of relaxed, massive clusters of galaxies using observations from optical and X-ray wavebands. We improve upon previous work in this area by including the baryon mass contribution of the brightest cluster galaxy in each system, in addition to total mass profiles from gravitational lensing and mass profiles of the X-ray emitting gas from Chandra. We use this data in the context of Emergent Gravity to predict the apparent dark matter distribution from the observed baryon distribution, and vice-versa. We find that although the inclusion of the brightest cluster galaxy in the analysis improves the agreement with observations in the inner regions of the clusters ($r lesssim 10-30$ kpc), at larger radii ($r sim 100-200$ kpc) the Emergent Gravity predictions for mass profiles and baryon mass fractions are discrepant with observations by a factor of up to $sim2-6$, though the agreement improves at radii near $r_{500}$. At least in its current form, Emergent Gravity does not appear to reproduce the observed characteristics of relaxed galaxy clusters as well as cold dark matter models.
We present weak lensing shear catalogues from the fourth data release of the Kilo-Degree Survey, KiDS-1000, spanning 1006 square degrees of deep and high-resolution imaging. Our `gold-sample of galaxies, with well-calibrated photometric redshift distributions, consists of 21 million galaxies with an effective number density of $6.17$ galaxies per square arcminute. We quantify the accuracy of the spatial, temporal, and flux-dependent point-spread function (PSF) model, verifying that the model meets our requirements to induce less than a $0.1sigma$ change in the inferred cosmic shear constraints on the clustering cosmological parameter $S_8 = sigma_8sqrt{Omega_{rm m}/0.3}$. Through a series of two-point null-tests, we validate the shear estimates, finding no evidence for significant non-lensing B-mode distortions in the data. The PSF residuals are detected in the highest-redshift bins, originating from object selection and/or weight bias. The amplitude is, however, shown to be sufficiently low and within our stringent requirements. With a shear-ratio null-test, we verify the expected redshift scaling of the galaxy-galaxy lensing signal around luminous red galaxies. We conclude that the joint KiDS-1000 shear and photometric redshift calibration is sufficiently robust for combined-probe gravitational lensing and spectroscopic clustering analyses.
We present an analysis of galaxy-galaxy weak gravitational lensing (GGL) in chameleon $f(R)$ gravity - a leading candidate of non-standard gravity models. For the analysis we have created mock galaxy catalogues based on dark matter haloes from two sets of numerical simulations, using a halo occupation distribution (HOD) prescription which allows a redshift dependence of galaxy number density. To make a fairer comparison between the $f(R)$ and $Lambda$CDM models, their HOD parameters are tuned so that the galaxy two-point correlation functions in real space (and therefore the projected two-point correlation functions) match. While the $f(R)$ model predicts an enhancement of the convergence power spectrum by up to $sim30%$ compared to the standard $Lambda$CDM model with the same parameters, the maximum enhancement of GGL is only half as large and less than 5% on separations above $sim1$-$2h^{-1}$Mpc, because the latter is a cross correlation of shear (or matter, which is more strongly affected by modified gravity) and galaxy (which is weakly affected given the good match between galaxy auto correlations in the two models) fields. We also study the possibility of reconstructing the matter power spectrum by combination of GGL and galaxy clustering in $f(R)$ gravity. We find that the galaxy-matter cross correlation coefficient remains at unity down to $sim2$-$3h^{-1}$Mpc at relevant redshifts even in $f(R)$ gravity, indicating joint analysis of GGL and galaxy clustering can be a powerful probe of matter density fluctuations in chameleon gravity. The scale dependence of the model differences in their predictions of GGL can potentially allow to break the degeneracy between $f(R)$ gravity and other cosmological parameters such as $Omega_m$ and $sigma_8$.