In this thesis a viable theory of gravity resulting from the spontaneous symmetry breaking of some more fundamental theory is developed. This fundamental theory does not include any notion of a metric or geometry. All the corresponding degrees of freedom are obtained dynamically from the symmetry breaking. The low energy effective theory corresponds to the Einstein-Hilbert theory naturally equipped with a cosmological term. The appearance of such term makes the cosmological constant interpretable as an intrinsic property of space time rather than an effective description valid at cosmological scales. The effect of this cosmological constant different from zero in the propagation of gravitational waves is assessed. In the presence of an cosmological constant gravitational waves propagate in a de Sitter space time and not in a minkoskian at space time. This fact brings about noticeable effects in the propagation of the waves. Finally we study the relevance of such effects due to the cosmological constant in the gravitational waves targeted at the PTA (Pulsar Timing Array) projects. We conclude that the effects can be measured in local systems (low redshits). This could represent an alternative way to set bounds to the value of the cosmological constant and at the same time could even facilitate the first detection of gravitational.
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