Gamma-ray burst distances and the timescape cosmology

Peter R. Smale 0 0 Department of Physics and Astronomy, University of Canterbury , Private Bag 4800, Christchurch 8140 , New Zealand 1 2 of one. For the CDM calibration , we find a A B S T R A C T Gamma-ray bursts can potentially be used as distance indicators, providing the possibility of extending the Hubble diagram to redshifts 7. Here we follow the GRB analysis of Schaefer, with the aim of distinguishing the timescape cosmological model from the cold dark matter (CDM) model by means of the additional leverage provided by Gamma-ray bursts (GRBs) in the range 2 z 7. We find that the timescape model fits the GRB sample slightly better than the CDM model, but that the systematic uncertainties are still too little understood to distinguish the models. 1 I N T R O D U C T I O N The timescape (TS) model is an inhomogeneous cosmological model that explains the apparently accelerated cosmic expansion first observed in the supernova luminosity distances as an artefact of gradients in gravitational energy between gravitationally bound systems and the intervening negatively curved voids. In the dynamical spacetime of general relativity, this leads to a variance in the calibration of the clock rates of ideal observers who fit average smoothed-out geometries to the underlying inhomogeneous matter distribution. The TS model agrees closely with the cold dark matter (CDM) model over the range of scales probed by the supernova data (Leith, Ng & Wiltshire 2008), with certain qualifications: parameter values obtained by minimizing 2 fits to the TS Hubble curve depend significantly on the process used to reduce the SN Ia light curves (Smale & Wiltshire 2011). The current state of knowledge of systematic uncertainties in the SN Ia data precludes discrimination between the TS and CDM models using SNe Ia (Smale & Wiltshire 2011). In fact, the calculation of the effective comoving distance H0D(z) shows that in the redshift range probed by SNe Ia there is little to distinguish between the TS model with the best-fitting value for the present void fraction f v0 = 0.762 from the Gold data set of Riess et al. (2007). Wiltshire (2009) has noted that over different redshift ranges H0D(z) for the TS model closely approximates H0D(z) for spatially flat CDM models with different values of m0 and 0. It is thus seen to interpolate between different CDM models as the redshift is varied (see Fig. 1). Fig. 1 shows that between z 2 and z 6, the TS H0D(z) crosses from coinciding closely with the best-fitting line from the SNe Ia only to that predicted by the best fit to Wilkinson Microwave Anisotropy Probe (WMAP), Baryon Acoustic Oscillation Scale (BAO) and the SNe Ia. In principle, Gamma-ray bursts (GRBs), which probe this redshift range, could distinguish the TS and CDM models in this redshift range, although their use as distance indicators is far from established. This paper will establish that the TS model is also supported by the current GRB data (Schaefer 2007, hereafter S07), but that, as one might expect from the SNe Ia results, the uncertainties in the data are as yet too large to distinguish the models in the redshift range 2 < z < 6. The paper is organized as follows. Section 2 explains the method of standardizing the GRBs for their use as distance indicators, and gives a brief derivation of the TS luminosity distance. Section 3 describes the results, before a discussion and conclusion are presented in Section 4. 2 B AC K G R O U N D 2.1 The timescape model In keeping with current observations that the large-scale cosmic structure consists of voids of average diameter 30 h1 Mpc (Hoyle & Vogeley 2004; Pan et al. 2011) separated and threaded by walls and filaments containing clusters of galaxies, the TS model is based on a differentiation of the Universe into gravitationally bound spatially flat wall regions and negatively curved voids. There is a consequent small backreaction (5 per cent as a normalized energy density) which nevertheless leads to significant cosmological effects over cosmological time-scales (Wiltshire 2007a). At late epochs the construction of a single smoothed-out geometry becomes problematic when the underlying geometry varies. The TS model is based on the assumption that different equivalent descriptions of a smoothedout average geometry can be given, but these descriptions will vary between canonical observers who each assume that the average geometry has the same spatial curvature as the locally determined geometry. Differences in the calibration of rulers and clocks grow cumulatively as the variance in spatial geometry grows, and these must be taken into account when reconstructing the expansion history of the universe from information on null geodesics. As observers in galaxies, our local average geometry, assumed to be spatially flat with scalefactor aw, is given by dsfi2 = d 2 + aw2( )[dw2 + w2d 2]. Finite infinity (Ellis 1984), denoted by fi, demarcates the boundary between gravitationally bou (...truncated)