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We study the expectation value of the $\mathrm{T}\overline{\mathrm{T}}$operator in spacetimes with constant curvature. We define an diffeomorphisminvariant biscalar whose coinciding limit gives the expectation value of the$\mathrm{T}\overline{\mathrm{T}}$ operator. We show that this biscalar is aconstant in flat spacetime, which reproduces Zamolodchikov's result in 2004.For spacetimes with non-zero curvature, we show that this is no longer true andthe expectation value of the $\mathrm{T}\overline{\mathrm{T}}$ operator dependson both the one-point and two-point functions of the stress-energy tensor.

Expectation value of $\mathrm{T}\overline{\mathrm{T}}$ operator in curved spacetimes