Appending parameter to URL without refresh

You can use the pushState or replaceState methods, i.e. :

window.history.pushState("object or string", "Title", "new url");

OR

window.history.replaceState(null, null, "?arg=123");

Example with argument:

var refresh = window.location.protocol + "//" + window.location.host + window.location.pathname + '?arg=1';    
window.history.pushState({ path: refresh }, '', refresh);