The Amplitude of Mass Fluctuations and Mass Density of the Universe Constrained by Strong Gravitational Lensing

We investigate the linear amplitude of mass fluctuations in the universe, σ8, and the present mass density parameter of the Universe, Ωm, from statistical strong gravitational lensing. We use the two population model of lens halos with fixed cooling mass scale Mc = 3×1013h-1M⊙ to match the observed lensing probabilities, and leave σ8 orΩm as a free parameter to be constrained by the data. Another varying parameter, the equation of state of dark energy ω, and its typical values of -1, -2/3, -1/2 and -1/3 are investigated. We find that σ8 is degenerate with Ωm in a way similar to that suggested by present day cluster abundance as well as cosmic shear lensing measurements: σ8Ω0.6m≈0.33. However, both σ8≤0.7 and Ωm≤0.2 can be safely ruled out, the best fit is when σ8 = 1.0, Ωm = 0.3 and ω= - 1. This result is different from that obtained by Bahcall & Bode, who gave σ8 = 0.98±0.1 and Ωm = 0.17 ±0.05. For σ8 = 1.0, the higher value ofΩm = 0.35 requires ω = -2/3 and Ωm = 0.40 require     

Smoothing supernova data to reconstruct the expansion history of the Universe and its age

We propose a non-parametric method of smoothing supernova data over redshift using a Gaussian kernel in order to reconstruct important cosmological quantities including   H ( z )  and   w ( z )  in a model-independent manner. This method is shown to be successful in discriminating between different models of dark energy when the quality of data is commensurate with that expected from the future Supernova Acceleration Probe ( SNAP ). We find that the Hubble parameter is especially well determined and useful for this purpose. The look-back time of the Universe may also be determined to a very high degree of accuracy (≲0.2 per cent) using this method. By refining the method, it is also possible to obtain reasonable bounds on the equation of state of dark energy. We explore a new diagnostic of dark energy – the ' w -probe'– which can be calculated from the first derivative of the data. We find that this diagnostic is reconstructed extremely accurately for different reconstruction methods even if Ω_{0 m} is marginalized over. The w -probe can be used to successfully distinguish between Λ cold dark matter and other models of dark energy to a high degree of accuracy.     

Testing anthropic predictions for Λ and the cosmic microwave background temperature

It has been claimed that the observed magnitude of the vacuum energy density is consistent with the distribution predicted in anthropic models, in which an ensemble of universes is assumed. This calculation is revisited, without making the assumption that the cosmic microwave background (CMB) temperature is known, and considering in detail the possibility of a recollapsing universe. New accurate approximations for the growth of perturbations and the mass function of dark haloes are presented. Structure forms readily in the recollapsing phase of a model with negative Λ, so collapse fraction alone cannot forbid Λ from being large and negative. A negative Λ is disfavoured only if we assume that formation of observers can be neglected once the recollapsing universe has heated to   T ≳ 8   K  . For the case of positive Λ, however, the current universe does occupy an extremely typical position compared to the predicted distribution on the Λ− T plane. Contrasting conclusions can be reached if anthropic arguments are applied to the curvature of the universe, and we discuss the falsifiability of this mode of anthropic reasoning.     

Cosmic acceleration and extra dimensions: constraints on modifications of the Friedmann equation

An alternative to dark energy as an explanation for the present phase of accelerated expansion of the Universe is that the Friedmann equation is modified, e.g. by extra dimensional gravity, on large scales. We explore a natural parametrization of a general modified Friedmann equation, and find that the present supernova Type Ia and cosmic microwave background data prefer a correction of the form 1/ H to the Friedmann equation over a cosmological constant.     

Spatial variations of fundamental constants

We show how observational limits on possible time variations of fundamental constants of nature are influenced by spatial variations in the density and gravitational potential. Bekenstein's generalization of Maxwell's equations, incorporating variations of the fine structure 'constant', is used as a simple example. These features are expected to be present in a wide class of theories with varying 'constants' and will affect attempts to coordinate cosmological and geophysical bounds on allowed time variations.     

The time evolution of cosmological redshift as a test of dark energy

The variation of the expansion rate of the Universe with time produces an evolution in the cosmological redshift of distant sources (e.g. quasar Lyman α absorption lines) that might be directly observed by future ultrastable, high-resolution spectrographs (such as the COsmic Dynamics Experiment) coupled to extremely large telescopes (such as the European Southern Observatory's Extremely Large Telescope). This would open a new window to explore the physical mechanism responsible for the current acceleration of the Universe. We investigate the evolution of cosmological redshift from a variety of dark energy models, and compare it with simulated data. We perform a Fisher matrix analysis and discuss the prospects for constraining the parameters of these models and for discriminating among competing candidates. We find that, because of parameter degeneracies, and the inherent technical difficulties involved in this kind of observations, the uncertainties on parameter reconstruction can be rather large unless strong external priors are assumed. However, the method could be a valuable complementary cosmological tool, and give important insights on the dynamics of dark energy, not obtainable using other probes.     

The peculiar velocity field in a quintessence model

We investigate the evolution of matter density perturbations and some properties of the peculiar velocity field for a special class of exponential potentials in a scalar field model for quintessence, for which a general exact solution is known. The data from the 2-degree Field Galaxy Redshift Survey (2dFGRS) suggest a value of the present-day pressureless matter density  Ω_M0= 0.18 ± 0.05  .