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.     

A regularized free-form estimator for dark energy

We construct a simple, regularized estimator for the dark energy equation of state by using the recently introduced linear response approximation. We show that even a simple regularization substantially improves the performance of the free-form fitting approach. The use of the linear response approximation allows an analytical construction of the maximum likelihood estimator, in a convenient and easy to use matrix form. We show that, in principle, such regularized free-form fitting can give us an unbiased estimate of the functional form of the equation of state of dark energy. We show the efficacy of this approach on simulated SuperNova Acceleration Probe class data, but it is easy to generalize this method to include other cosmological tests. We provide a possible explanation for the sweet spots seen in other reconstruction methods.     

Constraints on perfect fluid and scalar field dark energy models from future redshift surveys

We discuss the constraints that future photometric and spectroscopic redshift surveys can put on dark energy through the baryon oscillations of the power spectrum. We model the dark energy either with a perfect fluid or a scalar field and take into account the information contained in the linear growth function. We show that the growth function helps to break the degeneracy in the dark energy parameters and reduce the errors on   w ₀, w ₁  roughly by 30 per cent, making more appealing multicolour surveys based on photometric redshifts. We find that a 200-deg² spectroscopic survey reaching   z ≈ 3  can constrain   w ₀, w ₁  to within  Δ w ₀= 0.21, Δ w ₁= 0.26  , to  Δ w ₀= 0.39, Δ w ₁= 0.54  using photometric redshifts with an absolute uncertainty of 0.02, and to  Δ w ₀= 0.43, Δ w ₁= 0.66  with an uncertainty of 0.04. In the scalar field case, we show that the slope n of the inverse power-law potential for dark energy can be constrained to  Δ n = 0.26  (spectroscopic redshifts) or  Δ n = 0.40  (photometric redshifts), i.e. better than with future ground-based supernovae surveys or cosmic microwave background data.     

Formation of voids in the Universe within the Lemaître–Tolman model

We develop models of void formation starting from a small initial fluctuation at recombination and growing to a realistic present-day density profile in agreement with observations of voids. The model construction is an extension of previously developed algorithms for finding a Lemaître–Tolman metric that evolves between two profiles of either density or velocity specified at two times. Of the four profiles of concern (those of density and velocity at recombination and at the present day), two can be specified and the other two follow from the derived model.
We find that, in order to reproduce the present-day void density profiles, the initial velocity profile is more important than the initial density profile.
Extrapolation of current cosmic microwave background (CMB) observations to the scales relevant to protovoids is very uncertain. Even so, we find that it is very difficult to make both the initial density and velocity fluctuation amplitudes small enough and still obtain a realistic void by today.     

Cosmological parameters from velocities, cosmic microwave background and supernovae

We compare and combine likelihood functions of the cosmological parameters Ω_m, h and σ ₈, from peculiar velocities, cosmic microwave background (CMB) and type Ia supernovae. These three data sets directly probe the mass in the Universe, without the need to relate the galaxy distribution to the underlying mass via a 'biasing' relation. We include the recent results from the CMB experiments BOOMERANG and MAXIMA-1. Our analysis assumes a flat Λ cold dark matter (ΛCDM) cosmology with a scale-invariant adiabatic initial power spectrum and baryonic fraction as inferred from big-bang nucleosynthesis. We find that all three data sets agree well, overlapping significantly at the 2 σ level. This therefore justifies a joint analysis, in which we find a joint best-fitting point and 95 per cent confidence limits of     (0.17,0.39),     (0.64,0.86) and     (0.98,1.37). In terms of the natural parameter combinations for these data     (0.40,0.73),     (0.16,0.27). Also for the best-fitting point,     and the age of the Universe is 13.2 Gyr.     

The XMM Cluster Survey: forecasting cosmological and cluster scaling-relation parameter constraints

We forecast the constraints on the values of  σ₈, Ω_m  and cluster scaling-relation parameters which we expect to obtain from the XMM Cluster Survey (XCS). We assume a flat Λ cold dark matter Universe and perform a Monte Carlo Markov Chain analysis of the evolution of the number density of galaxy clusters that takes into account a detailed simulated selection function. Comparing our current observed number of clusters shows good agreement with predictions. We determine the expected degradation of the constraints as a result of self-calibrating the luminosity–temperature relation (with scatter), including temperature measurement errors, and relying on photometric methods for the estimation of galaxy cluster redshifts. We examine the effects of systematic errors in scaling relation and measurement error assumptions. Using only  ( T , z )  self-calibration, we expect to measure Ω_m to ±0.03 (and  Ω_Λ  to the same accuracy assuming flatness), and σ₈ to ±0.05, also constraining the normalization and slope of the luminosity–temperature relation to ±6 and ±13 per cent (at 1σ), respectively, in the process. Self-calibration fails to jointly constrain the scatter and redshift evolution of the luminosity–temperature relation significantly. Additional archival and/or follow-up data will improve on this. We do not expect measurement errors or imperfect knowledge of their distribution to degrade constraints significantly. Scaling-relation systematics can easily lead to cosmological constraints 2σ or more away from the fiducial model. Our treatment is the first exact treatment to this level of detail, and introduces a new 'smoothed ML' (Maximum Likelihood) estimate of expected constraints.     

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.     

Primordial non-Gaussianity: local curvature method and statistical significance of constraints on fNL from WMAP data

We test the consistency of estimates of the non-linear coupling constant f _NL using non-Gaussian cosmic microwave background (CMB) maps generated by the method described in the work of Liguori, Matarrese & Moscardini. This procedure to obtain non-Gaussian maps differs significantly from the method used in previous works on the estimation of f _NL. Nevertheless, using spherical wavelets, we find results in very good agreement with Mukherjee & Wang, showing that the two ways of generating primordial non-Gaussian maps give equivalent results. Moreover, we introduce a new method for estimating the non-linear coupling constant from CMB observations by using the local curvature of the temperature fluctuation field. We present both Bayesian credible regions (assuming a flat prior) and proper (frequentist) confidence intervals on f _NL, and discuss the relation between the two approaches. The Bayesian approach tends to yield lower error bars than the frequentist approach, suggesting that a careful analysis of the different interpretations is needed. Using this method, we estimate   f _NL=−10⁺²⁷⁰₋₂₆₀  at the 2σ level (Bayesian) and   f _NL=−10⁺³¹⁰₋₂₇₀  (frequentist). Moreover, we find that the wavelet and the local curvature approaches, which provide similar error bars, yield approximately uncorrelated estimates of f _NL and therefore, as advocated in the work of Cabella et al., the estimates may be combined to reduce the error bars. In this way, we obtain   f _NL=−5 ± 85  and   f _NL=−5 ± 175  at the 1σ and 2σ level respectively using the frequentist approach.     

Lyα damping wing constraints on inhomogeneous reionization

One well-known way to constrain the hydrogen neutral fraction,     , of the high-redshift intergalactic medium (IGM) is through the shape of the red damping wing of the Lyα absorption line. We examine this method's effectiveness in light of recent models showing that the IGM neutral fraction is highly inhomogeneous on large scales during reionization. Using both analytic models and 'seminumeric' simulations, we show that the 'picket-fence' absorption typical in reionization models introduces both scatter and a systematic bias to the measurement of     . In particular, we show that simple fits to the damping wing tend to overestimate the true neutral fraction in a partially ionized universe, with a fractional error of ∼30 per cent near the middle of reionization. This bias is generic to any inhomogeneous model. However, the bias is reduced and can even underestimate     if the observational sample only probes a subset of the entire halo population, such as quasars with large H  ii regions. We also find that the damping wing absorption profile is generally steeper than one would naively expect in a homogeneously ionized universe. The profile steepens and the sightline-to-sightline scatter increases as reionization progresses. Of course, the bias and scatter also depend on     and so can, at least in principle, be used to constrain it. Damping wing constraints must therefore be interpreted by comparison to theoretical models of inhomogeneous reionization.