Calendar fields "Default value" or value takes any strtotime value so "now" (without quotes) will set it to today's date or "+1 day" will set it to tomorrow, see https://php.net/manual/en/function.strtotime.phpfor more details or examples
Note: storage must be set to DateTime for this to work.
In search you can combine this with conditionals - create a dropdown with options like bellow, then use condition filledBy to fill calendar field (e.g. article_created) value from this dropdown and set matching to Future. This will search for items that were created before 1 week or before one year.