While the current vacuum energy of the Universe is very small, in our standard cosmological picture it has been much larger at earlier epochs. We try to address the question of what are possible ways to try to experimentally verify this. One direction is to look for systems where vacuum energy constitutes a non-negligible fraction of the total energy, and study the properties of those. Another possibility is to focus on the epochs around cosmic phase transitions, when the vacuum energy is of the same order as the total energy. Along these lines we investigate properties of neutron stars and the imprint of phase transitions on primordial gravitational waves.