Exponential gravity with logarithmic corrections in the presence of axion dark matter

An exponential modified gravity with additional logarithmic corrections is considered with the presence of an axion-like scalar field in the role of dark matter. Axion fields are thought to become important at late-times when the axion-like scalar field oscillates around its vacuum expectation value, mimicking dark matter behaviour. The model is compared with the usual pressureless fluid description of dark matter. Both models are tested with observational data including some of the latest sources, providing similar fits in comparison with the $\mathrm{\Lambda }$CDM model. Despite results are not statistically relevant to rule out any model, the number of free parameters still favours $\mathrm{\Lambda }$CDM model, as shown by computing the goodness of the fits.