There exists an experiment at CERN, an international collaboration called ALPHA which at the moment aims to check for differences between particles and antiparticles.
In a news bulletin the intent is stated to extend the experiment :
Though ALPHA-2 has only just arrived, discussions have already begun on a possible new experiment for the collaboration: ALPHA-3, which would investigate the properties of gravity. In order to make space for this possible expansion, a new platform was created over the experimental area for the ALPHA-2 electronics
There is no proposal pending for studying gravitational differences between hydrogen and antihydrogen. From their web page:
Eventually, we will use this technique to compare the structure of antihydrogen and hydrogen atoms, to search for difference between matter and antimatter, but In this first experiment, we do not yet have enough precision to test these fundamental symmetries. This is important, as the Universe has shown a preference for matter over antimatter as it has evolved, but so far, no measurements can explain why this came about. If matter and antimatter were truely identical, the Universe as we know it could not have come about. The next step at ALPHA is to construct an apparatus that will allow us to make these more precise measurements, using both microwave radiation, and laser light.
Maybe they aim at such a precision as to test how hydrogen and antihydrogen interact with gravity, but they have no open publication discussing this, except the cryptic sentence given with the CERN news bulletin.
Edit given the link in the comments above, it seems that the article is talking of a "gleam in the researcher's eye" . The only specific proposals of testing gravity in accelerators has come from the ALPHA collaboration as stated above, and the relevant papers are restricted to the collaboration, but have to do with using interferometry to test the gravitational field of hydrogen with respect to antihydrogen, old proposals (T. J. Philips, Hyp. Int. 109 (1997) 357. which is reference 3 in an older experiment.
The article in the Times of India was probably written by somebody who listened to the presentations, and is probably referring to the expectation of current physics models that the unification of all forces, including gravity, will allow to study the behavior of particles closer to the energies of the Big Bang . A verification of the theories, which predict a lot of new particles, would be a study of gravity.
There also exists the Aegis experiment also at CERN using the beams.
The principle of universality of free fall (or weak equivalence principle, WEP) states that all bodies fall with the same acceleration, independent of mass and composition. The WEP has been tested with very high precision for matter but never for antimatter. AEgIS is an experiment to test the WEP with antiprotons at the European laboratory CERN, using the antiproton decelerator (AD). AEgIS is a collaboration of physicists from all around the world.