Model selection applied to reconstructions of the Dark Energy

Abstract

The main aim of this paper is to perform a model comparison for some reconstructions of the key properties that describe the dark energy of the Universe i.e. energy density and the equation of state (EoS). We carry out this process by using a binning and a linear interpolation methodologies, and on top of that, we incorporate a correlation function mechanism. An extension of the two of them was also introduced, where internal amplitudes are allowed to vary in height as well as in position. The reconstructions were made with data from the Hubble parameter, Supernovae Type Ia and Baryon Acoustic Oscillations (H+SN+BAO), all of which span a range from $$z=0.01$$ z = 0.01 to $$z=2.34$$ z = 2.34 . First we perform the parameter estimation for each of the reconstructions to then provide a model selection through the Bayesian Evidence. Throughout our process we found a better fit to the data, up to $$4\sigma $$ 4 σ compared to $$\Lambda $$ Λ CDM, and the presence of some interesting features, i.e. an oscillatory behaviour at late times, a decrease in the dark energy density component at early times and a transition to the phantom divide-line in the EoS. To discern these features from noisy contributions, we include a principal component analysis and found that some of these characteristics should be taken into account to satisfy current observations.

Model-independent reconstruction of the interacting dark energy kernel: Binned and Gaussian process

“…[60,[62][63][64]66] considering models that suggest such a transition at z ∼ 2 from their observational analysis and references therein for further reading. This type of DE behavior was also predicted in a model-independent manner in a recent study [119] that directly reconstructed the DE density. Our findings here present a noteworthy distinction with this recent study, as in the current study we achieved a similar behavior by incorporating an interacting dark sector (dark matter+dark energy) instead of employing a direct reconstruction of the DE interacting only gravitationally.…”

“…A primary characteristic of the effective EoS parameter is exhibiting a pole (viz., lim z→z ± † w DE (z) = ±∞ with z † being the singular point). As studied in previous works [62,72,119,155] this is nec- essary when a transition to a negative energy density is present, and this can also be easily verifiable by looking at the DE density, ρ DE /ρ c,0 , which allows a transition to negative values at about z ∼ 2.3. As a consequence of the interacting mechanism, the DM effective EoS parameter also shows some oscillations, although statistically in agreement with w DM = 0.…”

“…The parameter w 0 is only present in two of the reconstructions and it is correlated with Π DE,1 when using a GP to perform the ting of specific characteristics and underfitting of others. To counterbalance this trade-off, we may need to incorporate a correlation function into the binning method [119,157], but the consideration of this is beyond the scope of the present work although it might be a promising direction for future investigations. It seems reasonable to conclude from this discussion that some of the observed features may be influenced by the chosen reconstruction method, but certain general characteristics persist regardless of the approach.…”

“…The sound horizon is calibrated by using BBN [148]. For a more detailed description of the datasets refer to [119]. We will call this dataset BAO.…”

“…Another limitation was demonstrated in [107]; expansions in small parameters are more influenced by higher redshift data, whereas data from lower redshifts carry less weight in the analysis. A possible way to avoid these issues it to perform reconstructions by extracting information directly from the data, using model-independent techniques or non-parametric ones, such as Artificial Neural Networks [108][109][110], Gaussian Process [110][111][112][113][114][115][116][117][118] or, recently, we can see applications of binning, linear interpolations and the incorporation of a correlation function in [119]. The Gaussian process (GP), specifically for the IDE models, has become a regular choice for a non-parametric approach [120][121][122][123][124][125].…”