  In this work, we systematically investigate for the first time the nature of
stress correlations in soft colloidal gel materials which support tensile and
compressive forces as well as finite rolling torque, as a function of system
pressure. Similar to previous studies on frictional granular matter with only
compressive forces and without any rolling torque, the full stress
autocorrelation matrix is dictated by the pressure and torque autocorrelations
due to mechanical balance and material isotropy constraints. Surprisingly, it
is observed that the gel materials do not behave as a normal elastic solid
close to the gel point as assumed loosely in the literature because the real
space pressure fluctuations decay slower than the normal. We also demonstrate
that at low pressure the fractal like structural correlation determines the
pressure fluctuations and this is manifested in the real space in terms of
inhomogeneous and anisotropic force networks formed due to large voids. Far
away from the gel point, as the voids collapse under compression, the force
chain network becomes homogeneous and isotropic and the pressure fluctuations
become normal leading to normal elastic decay at long range, behaving similar
to frictionless granular matter and glass. We also observe that the torque
autocorrelation is not hyperuniform in the presence of rolling resistance close
to the gel point. Furthermore, we link the abnormal pressure fluctuations to
the non-hyperuniform behaviour of the system with respect to the local packing
fraction fluctuations, thus relating the deviations from the normal elastic
behaviour across various non-equilibrium systems under a common framework.
