Reconstructing the equation of state and density parameter for dark energy from combined analysis of recent SNe Ia, OHD and BAO data

Abstract

Abstract. We reconstruct the dark energy equation of state by analyzing 5 sets of SNe Iadata along with Baryon Acoustic Oscillation (BAO) and Observational Hubble Data (OHD). A closed form parametrization of the luminosity distance in terms of redshift is assumed for the χ 2 analysis of the observational data. A strong dependence of dark energy equation of state on the matter density in the present and earlier epoch is obtained and the lower limit of matter density parameter at an earlier epoch for a flat FRW universe has been predicted. The variation of dark energy density parameter and the matter density parameter are also obtained. IntroductionObservations on type Ia supernovae (SNe Ia) [1,2], Baryon Acoustic Oscillation (BAO) [3], Hubble data based on differential ages of the galaxies (OHD) [4,5] reveal that the universe is undergoing accelerated expansion in the present epoch. This can be explained by invoking the existence of dark energy -a hypothetical energy component with a negative pressure. In this paper we have made an attempt to reconstruct the equation of state of dark energy from the analysis of observational data from SNe Ia, BAO and OHD. Taking a parametric form of the luminosity distance d L (z) in terms of redshift z and considering the matter density at the present epoch (Ω 0 m ) a free parameter, we perform a χ 2 analysis of these combined data sets to obtain the best-fit values and allowed ranges of the parameters -Ω 0 m and those appearing in the parametrization of d L (z) -from the observational data. Assuming present universe to be spatially flat and containing only matter and dark energy, we further estimate the variation of ω X (z) as a function of z for the best-fit values of the parameters and their 1σ limits as well for different data sets considered. The results of the analysis show that knowledge of the matter density of the universe at some earlier epoch is instrumental in providing observational evidences in favour of varying dark energy or cosmological constant solutions. We have also shown the simultaneous variation of matter density parameter Ω m (z) and dark energy density parameter Ω X (z) with z for the best-fit values of the parameters (obtained from χ 2 fitting) and their 1σ range. We also found the epoch at which the dark energy started dominating over the matter component of the universe.

Quintom scalar field : Varying dark energy equation of state obtained from recent SNe Ia, BAO and OHD data

“…The purpose of this work is to show the viability of the present formalism of quintom scalar field model in explaining the dark energy and the variation of its equation of state with z. In order to obtain the dark energy equation of state from observational data, a parametric form for d L (z) [13,14] is first considered whose parameters are fixed by the χ 2 minimization of the combined data (SNe Ia, OHD, BAO). The matter density at the present epoch Ω 0 m is also made a parameter in this χ 2 analyses and its value is obtained from the same χ 2 minimization.…”

“…The parametric form of d L (z) should respect the conditions that d L (z) = 0 at z = 0 and d L (z) ∝ z for large z. SNe Ia data are available for z < ∼ 1.76 from various supernova observations. A parametrised form of d L (z) can be written as [13,14]…”

“…The parameters a, b and Ω 0 m are obtained by minimising a suitably defined χ 2 . In the present case the χ 2 is defined as [14],…”

Direct reconstruction of dynamical dark energy from observational Hubble parameter data

“…To suppress the noise, Shafieloo et al [8] smoothed the SN Ia data by applying a Gaussian kernel over the whole redshift range before performing reconstruction. Majumdar et al [9] expressed the distance modulus in a parametric form, µ = 5 log [z(1 + az)/(1 + bz)] + µ 0 , and used the standard χ 2 minimization to determine the parameters (a, b, µ 0 ).…”

“…With observational data getting richer and more diverse, recently researchers have begun to study dark energy reconstruction with multiple sets of measurements. Holsclaw et al [11] extended their Gaussian process method [5] to include a diverse set of measurements: baryon acoustic oscillations (BAO), cosmic microwave background measurements (CMB), and supernova data (SNe), while observational Hubble parameter H(z) data (OHD) were used by other researchers [9,6,12]. So far, most research has focused on observational data acquired from SNe, CMB, and BAO, especially from SNe, or their hypothetical counterparts.…”