Speaker
Description
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 ΛCDM model.
The evolution of linear perturbations of a flat ΛCDM 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 N = 2 supersymmetric gauge theories and has proven to be very
effective in the analysis of Black-Hole, fuzzball and ECO perturbations.
