We study the cosmological constant (Λ) in the standard ΛCDM model by introducing the graduated dark energy (gDE) characterised by a minimal dynamical deviation from the null inertial mass density of the Λ in the form ρinert ∝ ρ λ < 0 with λ < 1 being a ratio of two odd integers, for which its energy density ρ dynamically takes negative values in the finite past. For large negative values of λ, it creates a phenomenological model described by a smooth function that approximately describes the Λ spontaneously switching sign in the late universe to become positive today. We confront the model with the latest combined observational data sets of PLK+BAO+SN+H. It is striking that the data predict bimodal posterior probability distributions for the parameters of the model along with large negative λ values; the new maximum significantly excludes the Λ, and the old maximum contains the Λ. The improvement in the goodness of the fit for the Λ reaches highly significant levels, ∆χ 2 min = 6.4, for the new maxima, while it remains at insignificant levels, ∆χ 2 min 0.02, for the old maxima. We show that, in contrast to the old maxima, which do not distinguish from the Λ, the new maxima agree with the model-independent H0 measurements, high-precision Ly-α data, and model-independent Omh 2 diagnostic estimates. Our results provide strong hints of a spontaneous sign switch in the cosmological constant and lead us to conjecture that the universe has transitioned from AdS vacua to dS vacua, at a redshift z ≈ 2.32 and triggered the late-time acceleration, and suggests looking for such mechanisms in string theory constructions.

Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In this paper, we review some fundamental concepts to understand Bayesian statistics and then introduce MCMC algorithms and samplers that allow us to perform the parameter inference procedure. We also introduce a general description of the standard cosmological model, known as the ΛCDM model, along with several alternatives, and current datasets coming from astrophysical and cosmological observations. Finally, with the tools acquired, we use an MCMC algorithm implemented in python to test several cosmological models and find out the combination of parameters that best describes the Universe.

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.

The main aim of this paper is to perform a model comparison for non-parametric 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 the 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 to z = 2.8. 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 4σ compared to ΛCDM, 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 observations.