Arman Shafieloo

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 {lambda}. Namely, if the value of Om(z) is the same at different redshifts, then DE{identical_to}{lambda}, exactly. 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). The second diagnostic--acceleration probe q--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 diagnostics to the Union data set of type Ia supernovae combined with recent data from the cosmic microwave background (Wilkinson Microwave Anisotropy Probe 5) and baryon acoustic oscillations.

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 0m is marginalized over. The w-probe can be used to successfully distinguish between A cold dark matter and other models of dark energy to a high degree of accuracy.

Primordial power spectrum from WMAP

Increasingly accurate measurements of the anisotropy in the temperature of the cosmic microwave background ~CMB! has ushered in an era of precision cosmology. A golden decade of CMB anisotropy measurements by numerous experiments was topped by the results from the first year of data obtained by the Wilkinson Microwave Anisotropy Probe ~WMAP !@ 1#. Under simple hypotheses for the spectrum of primordial perturbations, exquisite estimates of the cosmological parameters have been obtained from the angular power spectrum measurement by WMAP combined with other cosmological observations @2#. Although the assumed, scale free ~with mild deviations!, initial power spectra may be a generic prediction of the simplest scenarios of generation of perturbations during inflation, initial spectra with radical deviations are known to arise from very reasonable extensions, or refinements to the simplest scenarios @3‐5#. Consequently, cosmological parameter estimation from the CMB anisotropy and the matter power spectrum obtained from redshift surveys, weak gravitational lensing and Ly-a absorption, depends sensitively on the dimensionality, nature and freedom in the parameter space of initial conditions @6#. The angular power spectrum, Cl , is a convolution of the initial power spectrum P(k) generated in the early universe with a radiative transport kernel, G(l,k), that is determined by the current values of the cosmological parameters. The remarkably precise observations of the angular power spectrum Cl by WMAP, and the concordance of cosmological parameters measured from different cosmological observations opens up the avenue to directly recover the initial power spectrum of the density perturbation from the observations. The Richardson-Lucy ~RL! method deconvolution was shown to be a promising and powerful method to measure the power spectrum of initial perturbations from the CMB angular power spectrum @7#. In this paper, we apply the method to the CMB anisotropy spectrum measured by WMAP. We have also devised and implemented an improvement to the RL scheme, whereby the iterative deconvolution algorithm is designed to converge and match the measurements only within the given error bars.

Estimation of primordial spectrum with post-WMAP 3-year data

In this paper we implement an improved (error-sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from the Wilkinson Microwave Anisotropy Probe (WMAP) 3 year data to determine the primordial power spectrum assuming different points in the cosmological parameter space for a flat {lambda}CDM cosmological model. We also present the preliminary results of the cosmological parameter estimation by assuming a free form of the primordial spectrum, for a reasonably large volume of the parameter space. The recovered spectrum for a considerably large number of the points in the cosmological parameter space has a likelihood far better than a best fit power law spectrum up to {delta}{chi}{sub eff}{sup 2}{approx_equal}-30. We use discrete wavelet transform (DWT) for smoothing the raw recovered spectrum from the binned data. The results obtained here reconfirm and sharpen the conclusion drawn from our previous analysis of the WMAP 1st year data. A sharp cut off around the horizon scale and a bump after the horizon scale seem to be a common feature for all of these reconstructed primordial spectra. We have shown that although the WMAP 3 year data prefers a lower value of matter density for a power law form of the primordial spectrum, formorexa0» a free form of the spectrum, we can get a very good likelihood to the data for higher values of matter density. We have also shown that even a flat cold dark matter model, allowing a free form of the primordial spectrum, can give a very high likelihood fit to the data. Theoretical interpretation of the results is open to the cosmology community. However, this work provides strong evidence that the data retains discriminatory power in the cosmological parameter space even when there is full freedom in choosing the primordial spectrum.«xa0less

Model-independent reconstruction of the expansion history of the Universe and the properties of dark energy

We have improved upon the method of smoothing supernovae data to reconstruct the expansion history of the universe, h(z), using two latest datasets, Gold and SNLS. The reconstruction process does not employ any parameterisation and is independent of any dark energy model. The reconstructed h(z) is used to derive the distance factor A up to redshift 0.35 and the results are compared with the given value of A from detection of baryon acoustic oscillation peak (BAO). We find very good agreement between supernovae observations and the results from BAO for 0m � 0.276±0.023. The estimated values of 0m are completely model-independent and are only based on observational data. The derived values of 0m are then used to reconstruct the equation of state of dark energy, w(z). Using our smoothing method we can demonstrate that

Gaussian process cosmography

Gaussian processes provide a method for extracting cosmological information from observations without assuming a cosmological model. We carry out cosmography -- mapping the time evolution of the cosmic expansion -- in a model-independent manner using kinematic variables and a geometric probe of cosmology. Using the state of the art supernova distance data from the Union2.1 compilation, we constrain, without any assumptions about dark energy parametrization or matter density, the Hubble parameter and deceleration parameter as a function of redshift. Extraction of these relations is tested successfully against models with features on various coherence scales, subject to certain statistical cautions.

A new null diagnostic customized for reconstructing the properties of dark energy from BAO data

Baryon Acoustic Oscillations (BAO) provide an important standard ruler which can be used to probe the recent expansion history of our universe. We show how a simple extension of the Om diagnostic, which we call Om3, can combine standard ruler information from BAO with standard candle information from type Ia supernovae (SNIa) to yield a powerful novel null diagnostic of the cosmological constant hypothesis. A unique feature of Om3 is that it requires minimal cosmological assumptions since its determination does not rely upon prior knowledge of either the current value of the matter density and the Hubble constant, or the distance to the last scattering surface. Observational uncertainties in these quantities therefore do not affect the reconstruction of Om3. We reconstruct Om3 using the Union 2.1 SNIa data set and BAO data from SDSS, WiggleZ and 6dFGS. Our results are consistent with dark energy being the cosmological constant. We show how Om and Om3 can be used to obtain accurate model independent constraints on the properties of dark energy from future data sets such as BigBOSS.

Features in the Primordial Spectrum from WMAP: A Wavelet Analysis

Precise measurements of the anisotropies in the cosmic microwave background enable us to do an accurate study on the form of the primordial power spectrum for a given set of cosmological parameters. In a previous paper [A. Shafieloo and T. Souradeep, Phys. Rev. D 70, 043523 (2004).], we implemented an improved (error sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from the first year of WMAP data to determine the primordial power spectrum assuming a concordance cosmological model. This recovered spectrum has a likelihood far better than a scale invariant, or, best fit scale free spectra ({delta}lnL{approx_equal}25 with respect to the Harrison-Zeldovich spectrum, and, {delta}lnL{approx_equal}11 with respect to the power law spectrum with n{sub s}=0.95). In this paper we use the discrete wavelet transform (DWT) to decompose the local features of the recovered spectrum individually to study their effect and significance on the recovered angular power spectrum and hence the likelihood. We show that besides the infrared cutoff at the horizon scale, the associated features of the primordial power spectrum around the horizon have a significant effect on improving the likelihood. The strong features are localized at the horizon scale.

Cosmological parameter estimation with free-form primordial power spectrum

Constraints on the main cosmological parameters using cosmic microwave background (CMB) or large scale structure data are usually based on the power-law assumption of the primordial power spectrum (PPS). However, in the absence of a preferred model for the early Universe, this raises a concern that current cosmological parameter estimates are strongly prejudiced by the assumed power-law form of PPS. In this paper, for the first time, we perform cosmological parameter estimation allowing the free form of the primordial spectrum. This is in fact the most general approach to estimate cosmological parameters without assuming any particular form for the primordial spectrum. We use a direct reconstruction of the PPS for any point in the cosmological parameter space using the recently modified Richardson-Lucy algorithm; however, other alternative reconstruction methods could be used for this purpose as well. We use WMAP 9 year data in our analysis considering the CMB lensing effect, and we report, for the first time, that the flat spatial universe with no cosmological constant is ruled out by more than a 4σ confidence limit without assuming any particular form of the primordial spectrum. This would be probably the most robust indication for dark energy using CMB data alone. Our results on the estimated cosmological parameters show that higher values of the baryonic and matter density and a lower value of the Hubble parameter (in comparison to the estimated values by assuming power-law PPS) is preferred by the data. However, the estimated cosmological parameters by assuming a free form of the PPS have an overlap at 1σ confidence level with the estimated values assuming the power-law form of PPS.

Inflation with whip-shaped suppressed scalar power spectra.

Motivated by the idea that inflation occurs at the GUT symmetry breaking scale, in this paper we construct a new class of large field inflaton potentials where the inflaton starts with a power law potential; after initial period of relative fast roll that lasts until after a few e-folds inside the horizon, it transits to the attractor of the slow roll part of the potential with a lower power. Due to the initial fast roll stages of inflation, we find a suppression in scalar primordial power at large scales and at the same time the choice of the potential can provide us a tensor primordial spectrum with high amplitude. This suppression in scalar power with a large tensor-to-scalar ratio helps us to reconcile the Planck and BICEP2 data in a single framework. We find that a transition from a cubic to quadratic form of inflaton potential generates an appropriate suppression in power of scalar primordial spectrum that provides significant improvement in fit compared to power law model when compared with Planck and BICEP2 data together. We calculate the extent of nonGaussianity, specifically, the bispectrum for the best fit potential and show that it is consistent with Planck bispectrum constraints.