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Register a new userCosmological Applications of Gravitational Lensing
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Y. Mellier
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This course presents some applications of gravitational lensing to the measurement of masses of galaxies (galaxy-galaxy lensing, Eintein rings, perturbations of giant arcs) and cluster of galaxies (strong and weak lensing). This complements the F. Bernardeaus course dedicated to some theoretical aspects and weak lensing by large scale structures. In the first section, I describe the most important lensing quantities and lensing properties useful for astrophycal applications. Then I briefly present some academic exemples. Section three is devoted to exemples of mass reconstruction and the study of mass distribution in clusters of galaxies and galaxies.
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We investigate the feasibility of measuring weak gravitational lensing using 21cm intensity mapping with special emphasis on the performance of the planned Square Kilometre Array (SKA). We find that the current design for SKA-Mid should be able to measure the evolution of the lensing power spectrum at z~2-3 using this technique. This will be a probe of the expansion history of the universe and gravity at a unique range in redshift. The signal-to-noise is found to be highly dependent on evolution of the neutral hydrogen fraction in the universe with a higher HI density resulting in stronger signal. With realistic models for this, SKA Phase 1 should be capable of measuring the lensing power spectrum and its evolution. The signal-to-noises dependence on the area and diameter of the telescope array is quantified. We further demonstrate the applications of this technique by applying it to two specific coupled dark energy models that would be difficult to observationally distinguish without information from this range of redshift. We also investigate measuring the lensing signal with 21cm emission from the Epoch of Reionization (EoR) using SKA-Low and find that it is unlikely to constrain cosmological parameters because of the small survey size, but could provide a map of the dark matter within a small region of the sky.
The case for a flat Cold Dark Matter model with a positive cosmological constant $Lambda$ has been recently strongly advocated by some theoreticians. In this paper we give the observers point of view to the light of the most recent observations with a special emphasis on lensing tests. We confirm the apparent cosmic concordance for a flat Universe with $Omega_{Lambda}$ close to 0.6 but we note that a low mass density open universe with no cosmological constant is still quite acceptable for most of the reliable observational tests, including lensing tests as well.
In this article, we develop a formalism which is different from the standard lensing scenario and is necessary for understanding lensing by gravitational fields which arise as solutions of the effective Einstein equations on the brane. We obtain general expressions for measurable quantities such as time delay, deflection angle, Einstein ring and magnification. Subsequently, we estimate the deviations (relative to the standard lensing scenario) in the abovementioned quantities by considering the line elements for clusters and spiral galaxies obtained by solving the effective Einstein equations on the brane. Our analysis reveals that gravitational lensing can be a useful tool for testing braneworld gravity as well as the existence of extra dimensions.
Strong gravitational lensing along with the distance sum rule method can constrain both cosmological parameters as well as density profiles of galaxies without assuming any fiducial cosmological model. To constrain galaxy parameters and cosmic curvature $(Omega_{k0})$, we use the distance ratio data from a recently compiled database of $161$ galactic scale strong lensing systems. We use databases of supernovae type-Ia (Pantheon) and Gamma Ray Bursts (GRBs) for calculating the luminosity distance. To study the model of the lens galaxy, we consider a general lens model namely, the Extended Power-Law model. Further, we take into account two different parametrisations of the mass density power-law index $(gamma)$ to study the dependence of $gamma$ on redshift. The best value of $Omega_{k0}$ suggests a closed universe, though a flat universe is accommodated at $68%$ confidence level. We find that parametrisations of $gamma$ have a negligible impact on the best fit value of the cosmic curvature parameter. Furthermore, measurement of time delay can be a promising cosmographic probe via time delay distance that includes the ratio of distances between the observer, the lens and the source. We again use the distance sum rule method with time-delay distance dataset of H0LiCOW to put constraints on the Cosmic Distance Duality Relation (CDDR) and the cosmic curvature parameter $(Omega_{k0})$. For this we consider two different redshift-dependent parametrisations of the distance duality parameter $(eta)$. The best fit value of $Omega_{k0}$ clearly indicates an open universe. However, a flat universe can be accommodated at $95%$ confidence level. Further, at $95%$ confidence level, no violation of CDDR is observed. We believe that a larger sample of strong gravitational lensing systems is needed in order to improve the constraints on the cosmic curvature and distance duality parameter.
We present cosmological parameter constraints from a tomographic weak gravitational lensing analysis of ~450deg$^2$ of imaging data from the Kilo Degree Survey (KiDS). For a flat $Lambda$CDM cosmology with a prior on $H_0$ that encompasses the most recent direct measurements, we find $S_8equivsigma_8sqrt{Omega_{rm m}/0.3}=0.745pm0.039$. This result is in good agreement with other low redshift probes of large scale structure, including recent cosmic shear results, along with pre-Planck cosmic microwave background constraints. A $2.3$-$sigma$ tension in $S_8$ and `substantial discordance in the full parameter space is found with respect to the Planck 2015 results. We use shear measurements for nearly 15 million galaxies, determined with a new improved `self-calibrating version of $lens$fit validated using an extensive suite of image simulations. Four-band $ugri$ photometric redshifts are calibrated directly with deep spectroscopic surveys. The redshift calibration is confirmed using two independent techniques based on angular cross-correlations and the properties of the photometric redshift probability distributions. Our covariance matrix is determined using an analytical approach, verified numerically with large mock galaxy catalogues. We account for uncertainties in the modelling of intrinsic galaxy alignments and the impact of baryon feedback on the shape of the non-linear matter power spectrum, in addition to the small residual uncertainties in the shear and redshift calibration. The cosmology analysis was performed blind. Our high-level data products, including shear correlation functions, covariance matrices, redshift distributions, and Monte Carlo Markov Chains are available at http://kids.strw.leidenuniv.nl.
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