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We use the Hartree approximation to the Einstein equation on de Sitterbackground to solve for the one loop correction to the graviton mode function.This should give a reasonable approximation to how the ensemble of inflationarygravitons affects a single external graviton. At late times we find that theone loop correction to the plane wave mode function $u(\eta,k)$ goes like $GH^2 \ln(a)/a^2$, where $a$ is the inflationary scale factor. One consequence isthat the one loop corrections to the "electric" components of the linearizedWeyl tensor grow compared to the tree order result.

Hartree Approximation to the One Loop Quantum Gravitational Correction to the Graviton Mode Function on de Sitter