Abstract. The kinematic expansion history of the universe is investigated by using the 307 supernovae type Ia from the Union Compilation set. Three simple model parameterizations for the deceleration parameter (constant, linear and abrupt transition) and two different models that are explicitly parametrized by the cosmic jerk parameter (constant and variable) are considered. Likelihood and Bayesian analyses are employed to find best fit parameters and compare models among themselves and with the flat ΛCDM model. Analytical expressions and estimates for the deceleration and cosmic jerk parameters today (q 0 and j 0 ) and for the transition redshift (z t ) between a past phase of cosmic deceleration to a current phase of acceleration are given. All models characterize an accelerated expansion for the universe today and largely indicate that it was decelerating in the past, having a transition redshift around 0.5. The cosmic jerk is not strongly constrained by the present supernovae data. For the most realistic kinematic models the 1σ confidence limits imply the following ranges of values: q 0 ∈ [−0.96, −0.46], j 0 ∈ [−3.2, −0.3] and z t ∈ [0.36, 0.84], which are compatible with the ΛCDM predictions, q 0 = −0.57 ± 0.04, j 0 = −1 and z t = 0.71 ± 0.08. We find that even very simple kinematic models are equally good to describe the data compared to the concordance ΛCDM model, and that the current observations are not powerful enough to discriminate among all of them.

A possible slowing down of the cosmic expansion is investigated through a cosmographic approach. By expanding the luminosity distance to fourth order and fitting the SN Ia data from the most recent compilations (Union, Constitution and Union 2), the marginal likelihood distributions for the deceleration parameter today suggest a recent reduction of the cosmic acceleration and indicate that there is a considerable probability for q 0 > 0. Also in contrast to the prediction of the ΛCDM model, the cosmographic q(z) reconstruction permits a cosmic expansion history where the cosmic acceleration could already have peaked and be presently slowing down, which would imply that the recent accelerated expansion of the Universe is a transient phenomenon. It is also shown that to describe a transient acceleration the luminosity distance needs to be expanded at least to fourth order. The present cosmographic results depend neither on the validity of general relativity nor on the matter-energy contents of the Universe.

Observational evidence shows that gravitational lensing induces an angular correlation between the distribution of galaxies and much more distant QSOs. We use weak gravitational lensing theory to calculate this angular correlation, updating previous calculations and presenting new results exploring the dependence of the correlation on the large‐scale structure. We study the dependence of the predictions on a variety of cosmological models, such as cold dark matter models, mixed dark matter models and models based on quintessence. We also study the dependence on the assumptions made about the nature of the primordial fluctuation spectrum: adiabatic, isocurvature and power spectra motivated by the cosmic string scenario are investigated. Special attention is paid to the issue of galaxy biasing, which is fully incorporated. We show that different mass power spectra imply distinct predictions for the angular correlation, and therefore the angular correlation provides an extra source of information about cosmological parameters and mechanisms of structure formation. We compare our results with observational data and discuss their potential uses. In particular, it is suggested that the observational determination of the galaxy–QSO correlation may be used to give an independent measurement of the mass power spectrum.

We simulated both the matter and light (galaxy) distributions in a wedge of the universe and calculated the gravitational lensing magnification caused by the mass along the line of sight of galaxies and galaxy groups identified in sky surveys. A large volume redshift cone containing cold dark matter particles mimics the expected cosmological matter distribution in a flat universe with low matter density and a cosmological constant. We generate a mock galaxy catalogue from the matter distribution and identify thousands of galaxy groups in the luminous sky projection. We calculate the expected magnification around galaxies and galaxy groups and then the induced QSO-lens angular correlation due to magnification bias. This correlation is an observable and can be used to estimate the average mass of the lens population and also make cosmological inferences. We also use analytic calculations and various analysis to compare the observational results with theoretical expectations for the cross-correlation between faint QSOs from the 2dF Survey and nearby galaxies and groups from the APM and SDSS EDR. The observed QSO-lens anti-correlations are stronger than the predictions for the cosmological model used. This suggests that there could be unknown systematic errors in the observations and data reduction, or that the model used is not adequate. If the observed signal is assumed to be solely due to gravitational lensing then the lensing is stronger than expected, due to more massive galactic structures or more efficient lensing than simulated.