We know that gravity works at an infinite distance. By Einstein's theory of gravity it is the result of space time curvature. So can we say that the curvature is infinitely long? How can this be even possible? Can something be infinite?
Infinities are attributes of classical frameworks, and general relativity has not been definitively quantized yet. Infinities disappear when effective quantization is used.
The effective quantizations used in cosmological models assumes the existence of gravitons, elementary particles of spin 2, that are the (to be proven) gauge bosons of gravity. These have zero mass and thus travel with the velocity of light c. This transfers the infinity to the coordinate systems used , approached with the velocity of light because the gravitational field in a quantized version cannot travel faster than c.