I know we cannot use "present perfect tense" to talk about a finished action that have mentioned time frame. But my question is different. Suppose, something happened yesterday but I do not want to mention the time rather I want to describe what happened.
Hi, Subhajit: You can use a sentence like "I bought a new cell phone" without a time adverbial if the context in which you are using the sentence contains an implicit indication of the time frame. For example, if you are talking with a friend of yours and are asked, "What have you been up to?," you could reply, "I bought a new cell phone." It would be clear implicitly, from the surrounding social context, that you meant that you had bought a new cell phone recently.
Otherwise, without an implicit indication of a time frame, if you want to use the simple past, you need to use a time adverbial. It doesn't need to be an adverbial so specific as "yesterday." The adverb "recently" would work perfectly well. Sentences in the simple past need to be anchored to a time frame, explicitly or implicitly. Otherwise, how would your interlocutor know whether "I bought a new cell phone" meant that you did so recently or, say, fifteen years ago?