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Register a new userGravitational lensing statistics with extragalactic surveys. I. A lower limit on the cosmological constant
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Ralf Quast
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We reanalyse optical gravitational lens surveys from the literature in order to determine relative probabilities in the $lambda_{0}$-$Omega_{0}$ plane, using a softened singular isothermal sphere lens model. In addition, we examine a portion of the $lambda_{0}$-$Omega_{0}$ plane which includes all viable cosmological models; this is vital for comparison with other cosmological tests. The results are, within the errors, consistent with those of more specialised analyses, such as those concerning upper limits on $lambda_{0}$ in a flat universe. We note that gravitational lensing statistics can provide a quite robust LOWER limit on the cosmological constant as well, which could prove important in confirming current claims of a positive cosmological constant. At 95% confidence, our lower and upper limits on $lambda_{0}-Omega_{0}$, using lens statistics information alone, are respectively -3.17 and 0.3. For a flat universe, these correspond to lower and upper limits on $lambda_{0}$ of respectively -1.09 and 0.65.
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We present constraints on the cosmological constant lambda_0 and the density parameter Omega_0 from joint constraints from the analyses of gravitational lensing statistics of the Jodrell Bank-VLA Astrometric Survey (JVAS), optical gravitational lens surveys from the literature and CMB anisotropies. This is the first time that quantitative joint constraints involving lensing statistics and CMB anisotropies have been presented. Within the assumptions made, we achieve very tight constraints on both lambda_0 and Omega_0. These assumptions are cold dark matter models, no tensor components, no reionisation, CMB temperature T_CMB=2.728, number of neutrinos n_nu=3, helium abundance Y_He=0.246, spectral index n_s=1.0, Hubble constant H_0=68km/s/Mpc, baryonic density Omega_b=0.05. All models were normalised to the COBE data and no closed models (k=+1) were computed. Using the CMB data alone, the best-fit model has lambda_0=0.60 and Omega_0=0.34 and at 99% confidence the lower limit on lambda_0+Omega_0 is 0.8. Including constraints from gravitational lensing statistics doesnt change this significantly, although it does change the allowed region of parameter space. A universe with lambda_0=0 is ruled out for any value of Omega_0 at better than 99% confidence using the CMB alone. Combined with constraints from lensing statistics, lambda_0=0 is also ruled out at better than 99% confidence. As the region of parameter space allowed by the CMB is, within our assumptions, much smaller than that allowed by lensing statistics, the main result of combining the two is to change the range of parameter space allowed by the CMB along its axis of degeneracy.
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.
We consider the effect of a positive cosmological constant on spherical gravitational collapse to a black hole for a few simple, analytic cases. We construct the complete Oppenheimer-Snyder-deSitter (OSdS) spacetime, the generalization of the Oppenheimer-Snyder solution for collapse from rest of a homogeneous dust ball in an exterior vacuum. In OSdS collapse, the cosmological constant may affect the onset of collapse and decelerate the implosion initially, but it plays a diminishing role as the collapse proceeds. We also construct spacetimes in which a collapsing dust ball can bounce, or hover in unstable equilibrium, due to the repulsive force of the cosmological constant. We explore the causal structure of the different spacetimes and identify any cosmological and black hole event horizons which may be present.
Weak lensing peak counts are a powerful statistical tool for constraining cosmological parameters. So far, this method has been applied only to surveys with relatively small areas, up to several hundred square degrees. As future surveys will provide weak lensing datasets with size of thousands of square degrees, the demand on the theoretical prediction of the peak statistics will become heightened. In particular, large simulations of increased cosmological volume are required. In this work, we investigate the possibility of using simulations generated with the fast Comoving-Lagrangian acceleration (COLA) method, coupled to the convergence map generator Ufalcon, for predicting the peak counts. We examine the systematics introduced by the COLA method by comparing it with a full TreePM code. We find that for a 2000 deg$^2$ survey, the systematic error is much smaller than the statistical error. This suggests that the COLA method is able to generate promising theoretical predictions for weak lensing peaks. We also examine the constraining power of various configurations of data vectors, exploring the influence of splitting the sample into tomographic bins and combining different smoothing scales. We find the combination of smoothing scales to have the most constraining power, improving the constraints on the $S_8$ amplitude parameter by at least 40% compared to a single smoothing scale, with tomography brining only limited increase in measurement precision.
In this paper, we analyze in detail with numerical simulations how the mask effect can influence the weak lensing peak statistics reconstructed from the shear measurement of background galaxies. It is found that high peak fractions are systematically enhanced due to masks, the larger the masked area, the higher the enhancement. In the case with about $13%$ of the total masked area, the fraction of peaks with SNR $ uge 3$ is $sim 11%$ in comparison with $sim 7%$ of the mask-free case in our considered cosmological model. This can induce a large bias on cosmological studies with weak lensing peak statistics. Even for a survey area of $9hbox{ deg}^2$, the bias in $(Omega_m, sigma_8)$ is already close to $3sigma$. It is noted that most of the affected peaks are close to the masked regions. Therefore excluding peaks in those regions can reduce the bias but at the expense of loosing usable survey areas. Further investigations find that the enhancement of high peaks number can be largely attributed to higher noise led by the fewer number of galaxies usable in the reconstruction. Based on Fan et al. (2010), we develop a model in which we exclude only those large masks with radius larger than $3arcmin. For the remained part, we treat the areas close to and away from the masked regions separately with different noise levels. It is shown that this two-noise-level model can account for the mask effect on peak statistics very well and the cosmological bias is significantly reduced.
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