  We reconsider linear perturbations around general Friedmann - Lemaitre -
Robertson - Walker (FLRW) cosmological backgrounds. Exploiting gauge freedom
involving only time reparametrizations, we write down classical background
solutions analytically, for an arbitrary number of fluid components. We then
show that the time evolution of scalar and tensor adiabatic perturbations are
governed by Schr\"odinger-like differential equations of generalized Heun type.
After recovering known analytic results for a single-component fluid, we
discuss more general situations with two and three different fluid components,
with special attention to the combination of radiation, matter and vacuum
energy, which is supposed to describe the $\Lambda$CDM model. The evolution of
linear perturbations of a flat $\Lambda$CDM universe is described by a
two-transient model, where the transitions from radiation to matter and matter
to vacuum energy are governed by a Heun equation and a Hypergeometric equation,
respectively. We discuss an analytic approach to the study of the general case,
involving generalized Heun equations, that makes use of (quantum)
Seiberg-Witten curves for ${\cal N}=2$ supersymmetric gauge theories and has
proven to be very effective in the analysis of Black-Hole, fuzzball and ECO
perturbations.
