Higher derivative and mimetic models on non flat FLRW space-times

Understand

An effective Lagrangian approach, partly inspired by Quantum Loop Cosmology (QLC), is presented and formulated in a non flat FLRW space-times, making use of modified gravitational models.

• The models considered are non generic, and their choice is dictated by the necessity to have at least second order differential equations of motion in a non flat FLRW space-time.
• This is accomplished by a class of Lagrangian which are not analytic in the curvature invariants, or making use of a mimetic gravitational scalar field.
• It is shown that, for some effective models, the associated generalized Friedmann equation, in general, may admit non singular metrics as solutions, while the de Sitter space-time is present only for a restricted class, which includes General Relativity and Lovelock gravity.