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Register a new userFables of reconstruction: controlling bias in the dark energy equation of state
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We develop an efficient, non-parametric Bayesian method for reconstructing the time evolution of the dark energy equation of state w(z) from observational data. Of particular importance is the choice of prior, which must be chosen carefully to minimise variance and bias in the reconstruction. Using a principal component analysis, we show how a correlated prior can be used to create a smooth reconstruction and also avoid bias in the mean behaviour of w(z). We test our method using Wiener reconstructions based on Fisher matrix projections, and also against more realistic MCMC analyses of simulated data sets for Planck and a future space-based dark energy mission. While the accuracy of our reconstruction depends on the smoothness of the assumed w(z), the relative error for typical dark energy models is <10% out to redshift z=1.5.
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Non-parametric reconstruction of the dark energy equation of state (EoS) aims to determine the EoS as a function of redshift without invoking any particular dark energy model, so that the resulting EoS can be free of model-induced biases or artifacts. Without proper regularization, however, such reconstruction is often overwhelmed by the noise of poorly constrained modes. An intuitive regularization scheme is to assume a priori the dark energy EoS to evolve at most slowly with time, which may be enforced by a correlation between the EoS at different epochs. Indeed, studies that impose the correlation prior are able to significantly reduce the uncertainties of the reconstructed EoS and even show hints for dynamical dark energy. In this work, we examine the correlation prior using mock datasets of type Ia supernovae (SNe Ia), baryonic acoustic oscillations (BAOs), age-derived Hubble parameter, Hubble constant, and cosmic microwave background. We find that even though the prior is designed to disfavor evolving equations of state, it can still accommodate spurious oscillating features at high significance. Within the 1000 mock datasets of existing observations that are generated for the concordance cosmological model, i.e., the input dark energy EoS $w=-1$, there are 688 (69) cases recovering an EoS that departs from $-1$ by more than $1sigma$ ($2sigma$) in one or more redshift bins. The reconstructed EoS turns up and down markedly in many cases. Moreover, inverting the signs of the randomly assigned errors of the mock data more or less reverses the behavior of the EoS. Spurious results occur even more frequently when idealized SN Ia and BAO data from future surveys are included. Our tests suggest that further studies are needed to ensure accurate reconstruction of the EoS with the correlation prior.
We reconstruct the Equation of State of Dark Energy (EoS) from current data using a non-parametric approach where, rather than assuming a specific time evolution of this function, we bin it in time. We treat the transition between the bins with two different methods, i.e. a smoothed step function and a Gaussian Process reconstruction, investigating whether or not the two approaches lead to compatible results. Additionally, we include in the reconstruction procedure a correlation between the values of the EoS at different times in the form of a theoretical prior that takes into account a set of viability and stability requirements that one can impose on models alternative to $Lambda$CDM. In such case, we necessarily specialize to broad, but specific classes of alternative models, i.e. Quintessence and Horndeski gravity. We use data coming from CMB, Supernovae and BAO surveys. We find an overall agreement between the different reconstruction methods used; with both approaches, we find a time dependence of the mean of the reconstruction, with different trends depending on the class of model studied. The constant EoS predicted by the $Lambda$CDM model falls anyway within the $1sigma$ bounds of our analysis.
We combine recent measurements of Cosmic Microwave Background Anisotropies, Supernovae luminosity distances and Baryonic Acoustic Oscillations to derive constraints on the dark energy equation of state w in the redshift range 0<z<2, using a principal components approach. We find no significant deviations from the expectations of a cosmological constant. However, combining the datasets we find slight indication for w<-1 at low redshift, thus highlighting how these datasets prefer a non-constant w. Nevertheless the cosmological constant is still in agreement with these observations, while we find that some classes of alternative models may be in tension with the inferred w(z) behaviour.
The immediate observational consequence of a non-trivial spatial topology of the Universe is that an observer could potentially detect multiple images of radiating sources. In particular, a non-trivial topology will generate pairs of correlated circles of temperature fluctuations in the anisotropies maps of the cosmic microwave background (CMB), the so-called circles-in-the-sky. In this way, a detectable non-trivial spatial topology may be seen as an observable attribute, which can be probed through the circles-in-the-sky for all locally homogeneous and isotropic universes with no assumptions on the cosmological dark energy (DE) equation of state (EOS) parameters. We show that the knowledge of the spatial topology through the circles-in-the-sky offers an effective way of reducing the degeneracies in the DE EOS parameters. We concretely illustrate the topological role by assuming, as an exanple, a Poincar{e} dodecahedral space topology and reanalyzing the constraints on the parameters of a specific EOS which arise from the supernovae type Ia, baryon acoustic oscillations and the CMB plus the statistical topological contribution.
In this letter we propose a test to detect the linearity of the dark energy equation of state, and apply it to two different Type Ia Supernova (SN Ia) data sets, Union2.1 and SNLS3. We find that: a. current SN Ia data are well described by a dark energy equation of state linear in the cosmic scale factor a, at least up to a redshift z = 1, independent of the pivot points chosen for the linear relation; b. there is no significant evidence of any deviation from linearity. This apparent linearity may reflect the limit of dark energy information extractable from current SN Ia data.
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