Models Independent Approaches to test Modified Gravity and Dark Energy Models

The cosmological standard model, dubbed ΛCDM, is the minimal model in concordance with current observations. The latter however still allows, though within small margins, a landscape of possible viable theories, such as a different evolution for the dark energy component, or a modification of the general relativity theory, to either mimic the Universe accelerating effect of dark energy or to test whether new theories could better fit the data on the background evolution or the formation of structures level.

However, testing all these models, by stemming them from first principles, has the disadvantage to be, computationally expensive since each model must be separately constrained, and to force us to be limited to pre-existing theoretical frameworks. Hence the need for model-independent approaches and methods in cosmology that do not rely on specific theoretical models or assumptions about the underlying physics but aim to extract information about the large-scale structure and evolution of the cosmos directly from observational data, without being constrained by pre-existing theoretical frameworks. By adopting these approaches, researchers can explore the fundamental properties of the universe and test the validity of different cosmological theories without bias towards any particular model by adopting a more agnostic approach to data analysis, reducing by then the risk of drawing incorrect conclusions or making unwarranted assumptions about the nature of the universe.

Moreover, model-independent approaches can help to identify potential discrepancies or inconsistencies between observational data and existing theoretical frameworks, especially with the advent of the last discrepancies on some of the cosmological parameters, such as the one on the Hubble parameter or the amplitude of matter fluctuations, as well as to mitigate the impact of systematic errors or biases that may arise from relying too heavily on specific theoretical assumptions.

Model-independent approaches could be realized along different ways, among them would be parameterizing a phenomenological model where we encapsulate different extensions and modifications to the standard model of the Universe under parameterized functions tailored to test their phenomenological imprints on the cosmological observables. One of the challenges would then be for example, to keep theoretical consistency with first principles. Another is to avoid degeneracies from redundant parameters. Another approach, more data driven, consists in expressing theoretical pivotal quantities directly from observables. A method employed when the latter have weak cross correlations between them so that they form a base of independent elements from which we construct unambiguously the theoretical function to test, while more mixed observables in terms of information content, could benefit from machine learning technics where algorithms are trained over simulations to recognize and distillate features in order then to estimate hidden models behind the acquired real data.

These approaches are practically often used through and in synergy with each other in order to offer a structured and predictive systematic way to describe and interpret the results of model-independent analyses.

The aim of this topical collection is to gather works focused on the aforementioned approaches in order to offer a set of focused studies that combines the strengths of both model-independent approaches, data driven and general parameterized models, to leverage the flexibility and objectivity of the former with the structure and predictive power of the latter to help deepen our understanding of the universe.

Keywords: model independent approaches, data driven parameterizations, dark energy, modified gravity, observables in the Universe, parameterized phenomenological models