Researchers have developed a novel analytical approach to study multi-component FLRW cosmologies and their perturbations. This framework unifies standard Big Bang cosmologies, cosmic inflation models, and dark energy under a single description. The dynamics are governed by a single scalar field whose potential encodes the energy density and pressure of a multi-component fluid, allowing for a more coherent understanding of the universe's evolution.

The key to this model lies in expressing the scalar potential in terms of the Hubble function, H(φ), which acts as a 'fake superpotential'. This transforms the dynamics into a first-order problem that can be analytically solved in a suitable time coordinate. Within this framework, integrable inflationary models are proposed that exhibit properties similar to those previously analyzed in the literature and are compatible with current cosmological observations.

The study also addresses scalar and tensor cosmological perturbations in each model, integrating the Mukhanov-Sasaki equations using numerical and semi-analytical techniques. This allows for the calculation of the power spectrum, spectral indices, and the tensor-to-scalar ratio beyond the slow-roll approximation. The general results are compared against available observations and theoretical predictions based on the slow-roll approximation, offering validation and an extension of existing models.