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Chappell further said he could not understand why left-handed batter Travis Head was dropped for the first Test in Nagpur.
India retained the Border-Gavaskar Trophy after crushing Australia inside three days in the first two Tests of the ongoing series.
The Australian skipper's mother 'is ill and in palliative care', according to media reports.
The left-arm spinner will link up with the squad ahead of the one-day leg next month.
With a highest score of 23 in his last 10 Test innings, Rahul's place has become untenable as India chase a third successive victory that would seal their place in the final of the World Test Championship in June.
Paceman Josh Hazlewood has already been ruled out with an Achilles injury.
Cummins bowled 13 overs in the first innings. But in defence of 115 against India, the captain didn't bowl at all as Australia slumped to a six-wicket loss inside three days.
The third Test will be played in Indore from March 1 and the fourth in Ahmedabad from March 9.
As a result of India's victory in the Delhi Test, the number of teams able to qualify for the final shrinks from four to three. South Africa are out of contention, leaving Sri Lanka as the lone challenger for a place in the final.
Chasing 115 for victory, India's top order did wobble but the meagre target meant their victory, which came in the second session on day three, was never in doubt.