  The Cosmic Defect theory (CD), which is presented elsewhere in this
conference, introduces in the standard Einstein-Hilbert Lagrangian an elastic
term accounting for the strain of space-time viewed as a four-dimensional
physical continuum. In this framework the Ricci scalar acts as the kinetical
term of the strain field whose potential is represented by the additional
terms. Here we are presenting the linearised version of the theory in order to
analyze its implications in the weak field limit. First we discuss the recovery
of the Newtonian limit. We find that the typical static weak field limit
imposes a constraint on the values of the two parameters (Lame coefficients) of
the theory. Once the constraint has been implemented, the typical gravitational
potential turns out to be Yukawa-like. The value for the Yukawa parameter is
consistent with the constraints coming from the experimental data at the Solar
system and galactic scales. We then come to the propagating solutions of the
linearised Einstein equations in vacuo, i.e. to gravitational waves. Here,
analogously with other alternative or extended theories of gravity, the
presence of the strain field produces massive waves, where massive (in this
completely classical context) means subluminal. Furthermore longitudinal
polarization modes are allowed too, thus lending, in principle, a way for
discriminating these waves from the plane GR ones.
