Cosmic backreaction and the mean redshift drift from symbolic regression

The possibility of obtaining symbolic expressions for cosmic backreaction is explored through a case study of so-called 2-region models. By using the publicly available symbolic regression algorithm AI Feynman, it is shown that the kinematical backreaction from a single 2-region model can be well described as a function of the mean redshift (or, equivalently, the volume averaged scale factor). A single expression depending on the redshift/scale factor as well as a model parameter, $f$, that can accurately describe the backreaction for a significant range of models is naturally more complicated but is also achieved with percent-level accuracy. \newline\indent Data sets of redshift drift in the 2-region models are also considered. Again utilizing AI Feynman, expressions for the redshift drift are found. In particular, an expression for the difference between the mean redshift drift and the drift of the mean redshift in terms of the kinematical backreaction is easily obtained for a single 2-region model. An accurate symbolic expression that describes this difference for an array of 2-region models is achieved by using the redshift as a feature instead of the kinematical backreaction.Comment: 20 pages incl. 16 captioned figures. Accepted for publication in PR

Cosmological parameter constraints using phenomenological symbolic expressions: On the significance of symbolic expression complexity and accuracy

Phenomenological models are widely used in cosmology in relation to constraining different cosmological models, with two common examples being cosmographic expansions and modeling the equation-of-state parameter of dark energy. This work presents a study of how using different phenomenological expressions for observables and physical quantities versus using physically motivated, derived expressions affects cosmological parameter constraints. The study includes the redshift-distance relation and Hubble parameter as observables, and the dark energy equation-of-state parameter as a physical quantity, and focuses on constraining the cosmological parameter $\Omega_{\Lambda}$. The observables and equation-of-state parameter are all modeled both using the physical, derived expressions and a variety of phenomenological models with different levels of accuracy and complexity. The results suggest that the complexity of phenomenological expressions only has minor impact on the parameter constraints unless the complexity is very high. The results also indicate that statistically significantly different results can be expected from parameter constraints using different phenomenological models if the models do not have very similar accuracy. This suggests that a good practice is to use multiple phenomenological models when possible, in order to assess the model dependence of results. Straightforward examples of this is that results obtained using cosmographic expansions should always be checked against similar results obtained with expansions of other order, and when using phenomenological models such as for the equation-of-state parameters, robustness of results could be assessed using fitted models from symbolic regression, similar to what is done in this study.Comment: 17 pages, 8 captioned figures. To be published in PR

Machine learning cosmic backreaction and its effects on observations

Symbolic expressions for cosmic backreaction and mean redshift drift in a range of 2-region models in terms of average quantities are presented. The demonstration that these expressions can be obtained constitutes the opening of a new avenue towards understanding the effects of cosmic backreaction in our universe: With a symbolic expression for the redshift drift at hand, the redshift drift can be used to constrain cosmological parameters including the large-scale expansion rate and backreaction. In addition, by introducing symbolic expressions for cosmic backreaction, this quantity can be constrained with observations such as redshift-distance measures.Comment: 6 pages, 3 captioned figures. Accepted for publication in PR