Time evolution of the matter content of the expanding universe in the framework of Brans-Dicke gravity

A cosmological model has been constructed in the framework of Brans-Dicke(BD) gravity,based on an inter-conversion between matter and dark energy, for a spatially flat universe in the era of pressureless dust. To account for the non-conservation of the matter content, a function of time f(t) has been arbitrarily put into the expression for the density of matter(ρa^3= f(t)ρ_0 a_0~3). By definition, f(t) is proportional to the matter content of the universe. Using suitable ansatzes for the scale factor and scalar field, the functional form of f(t) has been determined from the BD field equations. The scale factor has been so chosen that it would cause a signature flip in the deceleration parameter with time. The function f(t) decreases monotonically with time, indicating a transformation of matter into dark energy. The time dependence of the proportions of matter and dark energy in the universe has been determined. The effect of non-conservation of the matter content upon various cosmological parameters has been explored in the present study. Two models of matter-energy interaction have been proposed and f(t) has been expressed as a function of their interaction term. The dark energy equation-of-state(EoS) parameter has been expressed and analyzed in terms of f(t).     

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.     

On model selection forecasting, dark energy and modified gravity

The Fisher matrix approach allows one to calculate in advance how well a given experiment will be able to estimate model parameters, and has been an invaluable tool in experimental design. In the same spirit, we present here a method to predict how well a given experiment can distinguish between different models, regardless of their parameters. From a Bayesian viewpoint, this involves computation of the Bayesian evidence. In this paper, we generalize the Fisher matrix approach from the context of parameter fitting to that of model testing, and show how the expected evidence can be computed under the same simplifying assumption of a Gaussian likelihood as the Fisher matrix approach for parameter estimation. With this 'Laplace approximation' all that is needed to compute the expected evidence is the Fisher matrix itself. We illustrate the method with a study of how well upcoming and planned experiments should perform at distinguishing between dark energy models and modified gravity theories. In particular, we consider the combination of 3D weak lensing, for which planned and proposed wide-field multiband imaging surveys will provide suitable data, and probes of the expansion history of the Universe, such as proposed supernova and baryonic acoustic oscillations surveys. We find that proposed large-scale weak-lensing surveys from space should be able readily to distinguish General Relativity from modified gravity models.     

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.     

Local Group velocity versus gravity: the coherence function

In maximum-likelihood analyses of the Local Group (LG) acceleration, the object describing non-linear effects is the coherence function (CF), i.e. the cross-correlation coefficient of the Fourier modes of the velocity and gravity fields. We study the CF both analytically, using perturbation theory, and numerically, using a hydrodynamic code. The dependence of the function on Ω_m and the shape of the power spectrum is very weak. The only cosmological parameter that the CF is strongly sensitive to is the normalization σ ₈ of the underlying density field. A perturbative approximation for the function turns out to be accurate as long as σ ₈ is smaller than about 0.3. For higher normalizations we provide an analytical fit for the CF as a function of σ ₈ and the wavevector. The characteristic decoherence scale which our formula predicts is an order of magnitude smaller than that determined by Strauss et al. This implies that present likelihood constraints on cosmological parameters from analyses of the LG acceleration are significantly tighter than hitherto reported.     

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.     

Limitations of Bayesian Evidence applied to cosmology

There has been increasing interest by cosmologists in applying Bayesian techniques, such as Bayesian Evidence, for model selection. A typical example is in assessing whether observational data favour a cosmological constant over evolving dark energy. In this paper, the example of dark energy is used to illustrate limitations in the application of Bayesian Evidence associated with subjective judgements concerning the choice of model and priors. An analysis of recent cosmological data shows a statistically insignificant preference for a cosmological constant over simple dynamical models of dark energy. It is argued that for nested problems, as considered here, Bayesian parameter estimation can be more informative than computing Bayesian Evidence for poorly motivated physical models.     

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.     

The Universe With Bulk Viscosity

Exact solutions for a model with variable G,A and bulk viscosity are obtained,Inflationary solutions with constant(de Sitter-type )and variable energy density are found.An expanding anisotropic universe is found to isotropize during its expansion but a static universe cannot isotropize.The gravitational constant is found to increase with time and the cosmological constant decreases with time as A∝t^-2。