1. Simple infinitive in combination with can/can't refers the action to the present, future or to no particular time in
a) the meaning of ability or possibility.
- She can dance.
- She can do it tomorrow.
- It can be true.
b) the meaning of doubt in questions.
- Can she lift such a heavy thing?
- Can it be true?
c) the meaning of negative deduction (present time reference with stative verbs).
-It can't be true.
Could with simple infinitive shows either ability in the past, or unreality in the present.
-She could swim when she was younger.
-She could swim, but she doesn't feel like swimming.
2.Continuous infiitive in combination with can/can't shows that the action is or not in progress at the moment of speaking in the meaning of possibility (deduction), doubt, negative deduction.
-He can be cleaning his flat now. He told me he was going home.
-Can he really be cleaning his flat now?
-He can't be cleaning his flat. I saw him just now.
3.Perfect infinitive in combination with can/can't shows deduction or doubt (only can) about something in the past.
He can have gone home. His office is closed.
He can't have gone home. His office is still opened.
Can he have gone home? His office is still opened.
Could in similar sentences is milder than can.
Could in combination with perfect infinitive can express unreality in the past.
- I could have done it if I they had given me more time.