 Geometrothermodynamics, GTH, is a formalism that combines contact geometry and Riemannian geometry to study thermodynamic systems. It allows for the invariance of classical thermodynamics under Legendre transformations, meaning that the properties of the system are independent of the choice of thermodynamic potential. GTH also provides a variational principle that generates fundamental equations, which can be applied to cosmological models. In particular, one such equation relating entropy, internal energy, and volume of the universe was constructed and used to fix parameters to match the inflationary era and the standard cosmological paradigm. This article was authored by Orlando Luongo and Hernando Cuavado.