Exceptional sensitivity to spacetime torsion can be achieved by searching for its couplings to fermions. Recent experimental searches for Lorentz violation are exploited to extract new constraints involving 19 of the 24 independent torsion components down to levels of order 10^{-31} GeV.
In this proceedings, similarities between the structure of theories with Lorentz violation and theories with constant torsion in flat spacetime are exploited to place bounds on torsion components. An example is given showing the analysis leading to b
ounds on the axial-vector and mixed-symmetry components of torsion, based on a dual-maser experiment.
Spacetime nonmetricity can be studied experimentally through its couplings to fermions and photons. We use recent high-precision searches for Lorentz violation to deduce first constraints involving the 40 independent nonmetricity components down to levels of order $10^{-43}$ GeV.
Using a deformed dispersion relation for gravitational waves, Advanced LIGO and Advanced Virgo have been able to place constraints on violations of local Lorentz invariance as well as the mass of the graviton. We summarise the method to obtain the cu
rrent bounds from the 10 significant binary black hole detections made during the first and second observing runs of the above detectors.
We present constraints on violations of Lorentz Invariance based on Lunar Laser Ranging (LLR) data. LLR measures the Earth-Moon separation by timing the round-trip travel of light between the two bodies, and is currently accurate to a few centimeters
(parts in $10^{11}$ of the total distance). By analyzing archival LLR data under the Standard-Model Extension (SME) framework, we derived six observational constraints on dimensionless SME parameters that describe potential Lorentz-violation. We found no evidence for Lorentz violation at the $10^{-6}$ to $10^{-11}$ level in these parameters.