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Register a new userRevisiting Metastable Dark Energy and Tensions in the Estimation of Cosmological Parameters
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We investigate constraints on some key cosmological parameters by confronting metastable dark energy models with different combinations of the most recent cosmological observations. Along with the standard $Lambda$CDM model, two phenomenological metastable dark energy models are considered: (romannumeral1) DE decays exponentially, (romannumeral2) DE decays into dark matter. We find that: (1) when considering the most recent supernovae and BAO data, and assuming a fiducial $Lambda$CDM model, the inconsistency in the estimated value of the $Omega_{rm{m,0}}h^2$ parameter obtained by either including or excluding Planck CMB data becomes very much substantial and points to a clear tension~citep{sahni2014model,zhao2017dynamical}; (2) although the two metastable dark energy models that we study provide greater flexibility in fitting the data, and they indeed fit the SNe Ia+BAO data substantially better than $Lambda$CDM, they are not able to alleviate this tension significantly when CMB data are included; (3) while local measurements of the Hubble constant are significantly higher relative to the estimated value of $H_0$ in our models (obtained by fitting to SNe Ia and BAO data), the situation seems to be rather complicated with hints of inconsistency among different observational data sets (CMB, SNe Ia+BAO and local $H_0$ measurements). Our results indicate that we might not be able to remove the current tensions among different cosmological observations by considering simple modifications of the standard model or by introducing minimal dark energy models. A complicated form of expansion history, different systematics in different data and/or a non-conventional model of the early Universe might be responsible for these tensions.
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The Phenomenologically Emergent Dark Energy model, a dark energy model with the same number of free parameters as the flat $Lambda$CDM, has been proposed as a working example of a minimal model which can avoid the current cosmological tensions. A straightforward question is whether or not the inclusion of massive neutrinos and extra relativistic species may spoil such an appealing phenomenological alternative. We present the bounds on $M_{ u}$ and $N_{rm eff}$ and comment on the long standing $H_0$ and $sigma_8$ tensions within this cosmological framework with a wealth of cosmological observations. Interestingly, we find, at $95%$ confidence level, and with the most complete set of cosmological observations, $M_{ u}sim 0.21^{+0.15}_{-0.14}$ eV and $N_{rm eff}= 3.03pm 0.32$ i.e. an indication for a non-zero neutrino mass with a significance above $2sigma$. The well known Hubble constant tension is considerably easened, with a significance always below the $2sigma$ level.
We discuss how to efficiently and reliably estimate the level of agreement and disagreement on parameter determinations from different experiments, fully taking into account non-Gaussianities in the parameter posteriors. We develop two families of scalable algorithms that allow us to perform this type of calculations in increasing number of dimensions and for different levels of tensions. One family of algorithms rely on kernel density estimates of posterior distributions while the other relies on machine learning modeling of the posterior distribution with normalizing flows. We showcase their effectiveness and accuracy with a set of benchmark examples and find both methods agree with each other and the true tension within $0.5sigma$ in difficult cases and generally to $0.2sigma$ or better. This allows us to study the level of internal agreement between different measurements of the clustering of cosmological structures from the Dark Energy Survey and their agreement with measurements of the Cosmic Microwave Background from the Planck satellite.
We provide a new interpretation for the Bayes factor combination used in the Dark Energy Survey (DES) first year analysis to quantify the tension between the DES and Planck datasets. The ratio quantifies a Bayesian confidence in our ability to combine the datasets. This interpretation is prior-dependent, with wider prior widths boosting the confidence. We therefore propose that if there are any reasonable priors which reduce the confidence to below unity, then we cannot assert that the datasets are compatible. Computing the evidence ratios for the DES first year analysis and Planck, given that narrower priors drop the confidence to below unity, we conclude that DES and Planck are, in a Bayesian sense, incompatible under LCDM. Additionally we compute ratios which confirm the consensus that measurements of the acoustic scale by the Baryon Oscillation Spectroscopic Survey (SDSS) are compatible with Planck, whilst direct measurements of the acceleration rate of the Universe by the SHOES collaboration are not. We propose a modification to the Bayes ratio which removes the prior dependency using Kullback-Leibler divergences, and using this statistical test find Planck in strong tension with SHOES, in moderate tension with DES, and in no tension with SDSS. We propose this statistic as the optimal way to compare datasets, ahead of the next DES data releases, as well as future surveys. Finally, as an element of these calculations, we introduce in a cosmological setting the Bayesian model dimensionality, which is a parameterisation-independent measure of the number of parameters that a given dataset constrains.
A large number of cosmological parameters have been suggested for obtaining information on the nature of dark energy. In this work, we study the efficacy of these different parameters in discriminating theoretical models of dark energy, using both currently available supernova (SNe) data, and simulations of future observations. We find that the current data does not put strong constraints on the nature of dark energy, irrespective of the cosmological parameter used. For future data, we find that the although deceleration parameter can accurately reconstruct some dark energy models, it is unable to discriminate between different models of dark energy, therefore limiting its usefulness. Physical parameters such as the equation of state of dark energy, or the dark energy density do a good job of both reconstruction and discrimination if the matter density is known to high accuracy. However, uncertainty in matter density reduces the efficacy of these parameters. A recently proposed parameter, Om(z), constructed from the first derivative of the SNe data, works very well in discriminating different theoretical models of dark energy, and has the added advantage of not being dependent on the value of matter density. Thus we find that a cosmological parameter constructed from the first derivative of the data, for which the theoretical models of dark energy are sufficiently distant from each other, and which is independent of the matter density, performs the best in reconstructing dark energy from SNe data.
By focusing on the simple $w eq-1$ extension to $Lambda$CDM, we assess which epoch(s) possibly source the $H_0$-tension. We consider Cosmic Microwave Background (CMB) data in three possible ways: $i)$ complete CMB data; $ii)$ excluding the $l<30$ temperature and polarization likelihoods; $iii)$ imposing early universe priors, that disentangle early and late time physics. Through a joint analysis with low-redshift supernovae type-Ia and gravitationally lensed time delay datasets, {and neglecting galaxy clustering Baryonic Acoustic Oscillation (BAO) data}, we find that the inclusion of early universe CMB priors is consistent with the local estimate of $H_0$ while excluding the low-$l$+lowE likelihoods mildly relaxes the tension. This is in contrast to joint analyses with the complete CMB data. Our simple implementation of contrasting the effect of different CMB priors on the $H_0$ estimate shows that the early universe information from the CMB data when decoupled from late-times physics could be in agreement with a higher value of $H_0$. {We also find no evidence for the early dark energy model using only the early universe physics within the CMB data. Finally using the BAO data in different redshift ranges to perform inverse distance ladder analysis, we find that the early universe modifications, while being perfectly capable of alleviating the $H_0$-tension when including the BAO galaxy clustering data, would be at odds with the Ly-$alpha$ BAO data due to the difference in $r_{rm d}, vs., H_0$ correlation between the two BAO datasets.} We therefore infer and speculate that source for the $H_0$-tension between CMB and local estimates could possibly originate in the modeling of late-time physics within the CMB analysis. This in turn recasts the $H_0$-tension as an effect of late-time physics in CMB, instead of the current early-time CMB vs. local late-time physics perspective.
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