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Ground-based and space-borne observatories studying exoplanetary transits nowand in the future will considerably increase the number of known exoplanets andthe precision of the measured times of transit minima. Variations in thetransit times can not only be used to infer the presence of additional planets,but might also provide opportunities for testing new physics in the placesbeyond the Solar system. In this work, we take deviation from theinverse-square law of gravity as an example, focus on the fifth-force-likeYukawa-type correction to the Newtonian gravitational force which parameterizesthis deviation, investigate its effects on the secular transit timingvariations and analyze their observability in exoplanetary systems. It is foundthat the most optimistic values of Yukawa-type secular transit timingvariations are at the level of $\sim 0.1$ seconds per year. Those valuesunfortunately appear only in rarely unique cases and, most importantly, theyare still at least two orders of magnitude below the current capabilities ofobservations. Such a deviation from the inverse-square law of gravity is likelytoo small to detect for the foreseeable future. Meanwhile, systematicuncertainties, such as the presence of additional and unknown planets, willlikely be exceptionally difficult to remove from a signal that should be seen.

On the (im)possibility of testing new physics in exoplanets using transit timing variations: deviation from inverse-square law of gravity