We review analytical solutions of the Einstein equations which are expressed in terms of
elementary functions and describe Friedmann–Lemaître–Robertson–Walker universes …

We emphasize two connections, one well known and another less known, between the
dissipative nonlinear second order differential equations and the Abel equations which in …

A method for generating exact solutions of the equations of the scalar field dynamics in the
case of flat Friedmann-Robertson-Walker space on the basis of form-invariant …

We study the class of integrable self-action potentials satisfying the conditions that (1) they
spontaneously break the symmetry,(2) they describe the inflation phase with a graceful exit …

We propose a new representation of the Schrödinger-like equation for scalar field
Friedmann cosmology where the scalar field is the argument, and the Hubble parameter is …

For nonzero cosmological constant Λ, we show that the barotropic FRW cosmologies as
worked out in the comoving time lead in the radiation-dominated case to scale factors of …

We revisit the relationship between the Einstein-Friedmann and Abel equations to
demonstrate how the latter might be applied to the inflationary analysis in a spatially-flat …

A geometric approach is used to study the Abel first-order differential equation of the first
kind. The approach is based on the recently developed theory of quasi-Lie systems which …

We consider a model of a holographic 2+ 1d CFT interacting with an oscillating background
gauge field. It is solved by an AdS-Vaidya metric describing Ohmic heating of the boundary …

For the convenience of the reader, and with the purpose of establishing the notation, in this
first chapter we review Einstein's theory of general relativity and its description of cosmology …