This is the fourth edition of a series of workshops, focused on different aspects of modern theoretical cosmology, the challenge to be consistent with experimental data and the necessary connection of cosmological theories with the quantum nature of the vacuum. A basic question in modern cosmology is why we do not see vacuum fluctuations at cosmological scales? In addition, should the singularities of cosmological theories treated as necessary ingredients of the classical theory or should these be the indicators of an underlying quantum theory yet to be discovered? In this aspect, in this workshop we aim to bring along all the leading scientists working on these problems and present all the up to date results in these strongly interdependent physics areas. Hence the workshop will cover topics related to modified theories of gravities, other theories of Dark Energy and Inflation, the description of the universe’s evolution in these theories and the elegant and compulsory modification of these within the theoretical framework of quantum gravity, with Loop Quantum Cosmology being the most elegant theory providing up to date a singularity free cosmological evolution. The description and understanding of the quantum vacuum is always a challenge to these theories so the understanding of the main manifestation of the quantum vacuum, the Casimir effect, is always a challenge.