Smith is nursing a tendon injury to his left wrist which will keep him sidelined for up to another four weeks. The report added that Starc is experiencing 'groin soreness'.
Cummins, who fractured his wrist during the fifth Ashes Test at the Oval (July 27-31), has been advised rest for six weeks.
Knowing the importance of Smith's wicket, England went for a review. However, third umpire Nitin Menon too ruled in favour of Smith as Stokes had not completed the catch.
One can be certain that many more records will be broken and new milestones achieved before Smith bids bye to international cricket.
India trail Australia by 318 runs after ending the second day at 151/5.
The present quartet of top batsmen emerged almost two decades after the retirement of the four great all-rounders.
Smith dived full length to his right to take a stunning one-handed catch off Sean Abbott's bowling.
Australia lost last six wickets for only 19 runs in a space of 7.5 overs
Regular captain Pat Cummins, who lost his mother recently, will not return for the three-match series.
Australia scored at a run-a-ball rate in the last nine overs of the day, after India had taken the second new ball, at the Narendra Modi Stadium.