# Gravitational lensing statistics with extragalactic surveys. IV. Joint constraints on $\lambda_{0}$ and $\Omega_{0}$ from gravitational lensing statistics and CMB anisotropies

## J. F. Macias-Perez, Phillip Helbig, R. Quast, A. Wilkinson & R. D. Davies

### A&A, 353, 2, 419–426 (January (II) 2000)

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 doesn't 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.

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