Reconstructing Cosmological Matter Perturbations using Standard Candles and Rulers

For a large class of dark energy (DE) models, for which the effective gravitational constant is a constant and there is no direct exchange of energy between DE and dark matter (DM), knowledge of the expansion history suffices to reconstruct the growth factor of linearized density perturbations in the non-relativistic matter component on scales much smaller than the Hubble distance. In this paper we develop a non-parametric method for extracting information about the perturbative growth factor from data pertaining to the luminosity or angular size distances. A comparison of the reconstructed density contrast with observations of large scale structure and gravitational lensing can help distinguish DE models such as the cosmological constant and quintessence from models based on modified gravity theories as well as models in which DE and DM are either unified, or interact directly. We show that for current SNe data, the linear growth factor at z = 0.3 can be constrained to 5%, and the linear growth rate to 6%. With future SNe data, such as expected from the JDEM mission, we may be able to constrain the growth factor to 2-3% and the growth rate to 3-4% at z = 0.3 with this unbiased, model-independent reconstruction method. For future BAO data which would deliver measurements of both the angular diameter distance and Hubble parameter, it should be possible to constrain the growth factor at z = 2.5 to 9%. These constraints grow tighter with the errors on the datasets. With a large quantity of data expected in the next few years, this method can emerge as a competitive tool for distinguishing between different models of dark energy.

Two new diagnostics of dark energy

We introduce two new diagnostics of dark energy (DE). The first, Om, is a combination of the Hubble parameter and the cosmological redshift and provides a null test of dark energy being a cosmological constant. Namely, if the value of Om(z) is the same at different redshifts, then DE is exactly cosmological constant. The slope of Om(z) can differentiate between different models of dark energy even if the value of the matter density is not accurately known. For DE with an unevolving equation of state, a positive slope of Om(z) is suggestive of Phantom (w < -1) while a negative slope indicates Quintessence (w > -1). The second diagnostic, acceleration probe(q-probe), is the mean value of the deceleration parameter over a small redshift range. It can be used to determine the cosmological redshift at which the universe began to accelerate, again without reference to the current value of the matter density. We apply the Om and q-probe diagnostics to the Union data set of type Ia supernovae combined with recent data from the cosmic microwave background (WMAP5) and baryon acoustic oscillations.

New Universal Local Feature in the Inflationary Perturbation Spectrum

A model is developed in which the inflaton potential experiences a sudden small change in its second derivative (the effective mass of the inflaton). An exact treatment demonstrates that the resulting density perturbation has a quasi-flat power spectrum with a break in its slope (a step in n_s). The step in the spectral index is modulated by characteristic oscillations and results in large running of the spectral index localised over a few e-folds of scales. A field-theoretic model giving rise to such behaviour of the inflationary potential is based on a fast phase transition experienced by a second scalar field weakly coupled to the inflaton. Such a transition is similar to that which terminates inflation in the hybrid inflationary scenario. This scenario suggests that the observed running of the spectral index in the WMAP data may be caused by a fast second order phase transition which occurred during inflation.