The Feynman rules for quantum electrodynamics (QED) are correct within the framework of QED itself. They have been extensively tested and are in agreement with experimental observations to a very high degree of precision. However, when it comes to including gravity within the framework of quantum field theory (QFT), things become more complicated.
The problem lies in the fact that the theory of gravity, general relativity, and QFT do not easily mesh together. Attempts to combine the two theories have led to a number of challenges and unresolved issues, such as the problem of infinities in certain calculations (known as ultraviolet divergences) and the absence of a fully consistent and mathematically rigorous theory of quantum gravity.
The Feynman rules used in QED, which work well in the context of electromagnetic interactions, do not directly apply to gravitational interactions. Gravity is not described by a gauge theory like QED, but rather by the curvature of spacetime in general relativity. Therefore, a consistent and complete framework for incorporating gravity within the framework of quantum field theory is still an area of ongoing research.
The combination of quantum field theory and gravity is an active field of theoretical physics, and various approaches and frameworks have been proposed, such as string theory, loop quantum gravity, and other approaches to quantum gravity. These attempts seek to reconcile the principles of quantum mechanics with the theory of gravity and to provide a more complete description of physical phenomena.
In summary, the Feynman rules for QED are valid and highly successful within the context of QED itself. However, when it comes to including gravity within the framework of QFT, we face challenges and open questions that require further theoretical development and investigation.