Beyond the ACDM model: Addressing observational tensions of cosmology with negative and/or oscillating dark energy density

Abstract

The standard cosmological paradigm, the Lambda Cold Dark Matter ($\Lambda$CDM) model, despite its prominence in explaining the existing cosmological data, encounters challenges due to inconsistencies observed across various cosmological probes over the past decade. While these observational tensions may stem from systematic errors, their increasing statistical significance with improved observations, and their recurrence through the increased diversity of observations, coupled with the inherent ambiguities surrounding dark energy (DE) and cold dark matter (CDM) in the $\Lambda$CDM model, indicate the necessity of looking for more realistic cosmological models to better elucidate current observations and refine our comprehension of the universe. This thesis explores what kind of phenomenology is necessary for an alternative model to resolve the observational tensions and what would that phenomena imply for fundamental physics; particular attention is paid to the proposal of a dynamical DE whose density attains negative values in the past before becoming positive to drive the present-day acceleration of the Universe, and/or the DE density having an oscillatory behaviour. Moreover, alternative models to $\Lambda$CDM are built and observationally analysed utilizing the state of the art statistical methods. The research conducted within the scope of this thesis extensively use analytical arguments to show in which way the features of having negative values and oscillatory behaviors in the DE density allow a better fit to the available cosmological data, and what are the properties of such a DE source. These arguments are used as a motivation to introduce a new cosmological model/paradigm that replaces the usual cosmological constant of the $\Lambda$CDM model with a sign switching one dubbed $\Lambda_{\rm s}$CDM; later this phenomenological model is promoted to a fully predictive one by embedding it in the theoretical framework of a preexisting type-II minimally modified theory of gravity, and this combination is dubbed $\Lambda_{\rm s}$VCDM. The analytical arguments are also used to introduce a new class of rampant DE models incorporating both of the negative and oscillatory features dubbed \textit{omnipotent dark energy}, and the preexisting DMS20 model in the literature that fits this classification is studied. Four cosmological models, namely, $\Lambda_{\rm s}$CDM, DMS20, $\Lambda_{\rm s}$VCDM, and a combination of $\Lambda_{\rm s}$CDM with the preexisting proposal of a time-varying electron mass, are observationally analyzed using a Bayesian approach. Broadly, the methodology used for analyzing the models consist of the following steps: the equations of the model for the relevant cosmological observables are derived, a preliminary analyses is conducted through plotting these equations with rough constraints from observations to understand the potential phenomenology of the model and how it relates to its parameters, meaningful combinations of robust cosmological data are chosen to constrain the parameter space of the model, state of the art cosmological codes are used to sample from the posterior of the parameters of the model, the parameter constraints and visualisations of the posteriors are constructed from the output samples, the results are discussed in light of the observational tensions. A very brief summary of the conclusions derived from the research conducted within the scope of this thesis is as follows. It is proved that a DE density whose density crosses from negative to positive values has a singular equation of state parameter. It is shown that, under reasonable conditions, any deviations from the Hubble radius of the $\Lambda$CDM model should oscillate in the form of an admissible wavelet in order to preserve the excellent fit of the $\Lambda$CDM model to the cosmic microwave background data. A combination of the two features in the DE density, namely, having oscillations and attaining negative values in the past as exhibited by omnipotent dark energy models, is a promising direction of research in alleviation of the cosmological tensions. Both of these features play an important role in relaxing the cosmological tensions within the DMS20 model. The $\Lambda_{\rm s}$CDM model shows remarkable success in alleviation of a multitude of cosmological tensions including the most major ones when the baryon acoustic oscillations data is not present in the constraining data set. Baryon acoustic oscillations data spoils this success by preferring an earlier time for the sign-switch of the cosmological constant contrary to the rest of the data sets. The $\Lambda_{\rm s}$VCDM model promotes the model to a fully predictive and theoretically viable one, and this new model performs even better observationally albeit this is very marginal. Combination of the $\Lambda_{\rm s}$CDM model with a promising early time modification to $\Lambda$CDM based on a time-varying electron mass do not perform better than the individual models contrary to naive expectations.