Modals of speculation (past, present, future)

We can use modal verbs for deduction – guessing if something is true using the available information.

It shows how certain we are about the possibility.

We use must have + past participle when we feel SURE about what happened.

Example: Who told the newspapers about the prime minister's plans? It must have been someone close to him.

We can use might have or may have + past participle when we think it's possible that something happened. 

Example: I think I might have left the air conditioning on. Please can you check?

May have is more formal than might have. Could have is also possible in this context but less common.

We use can't have and couldn't have + past participle when we think it's not possible that something happened.

She can't have driven there. Her car keys are still here.

Use must when we feel sure that something is true or it's the only realistic possibility.

Example: This must be her house. I can see her car in the garage.

Use might, may or could to say that we think something is possible but we're not sure. 

She's not here yet. She might be stuck in traffic.

Note: They all have the same meaning, but may is more formal than might and could.

Use can't when we feel sure that something is not possible.

It can't be far now. We've been driving for hours.