New tests are proposed to constrain possible deviations from local Lorentz invariance and local position invariance in the gravity sector .
By using precise timing results of two binary pulsars , i.e. , PSRs J1012+5307 and J1738+0333 , we are able to constrain ( strong-field ) parametrized post-Newtonian parameters \hat { \alpha } _ { 1 } , \hat { \alpha } _ { 2 } , \hat { \xi } to high precision , among which , | \hat { \xi } | < 3.1 \times 10 ^ { -4 } ( 95 % C.L . )
is reported here for the first time .