is synchronization on method passing local variables as parameters needed

[reddzer]

i have the following code

	public void doGet (HttpServletRequest req, HttpServletResponse res) throws ServletException,IOException
	{
		res.setContentType ("text/html");
		PrintWriter out = res.getWriter();

		//check to see if the session cookie has been created and that user has been fully authenticated
		//if the cookie doesnt exist they have just logged in and must be forwarded to cookieAuthentication
		//or the user doesnt have cookies enabled
		//no need to synchronize because local variables being used
		Cookie[] cookies = req.getCookies();
		String user = req.getRemoteUser();
		boolean authenticated = checkCookie(out, cookies, user);

		if (authenticated == true)	//user authenticated continue
		{
			//create html welcome page
			createWelcome(out, user);	
		}
		else
		{
			res.sendRedirect("login");	//cookie not created, send to login servlet (cookieAuthentication.java)
		}

	}

	private boolean checkCookie(PrintWriter out, Cookie[] cookies, String user) 
	{			
		boolean val = false;
		if (cookies!=null)	//if cookies retrieved check them
		{
			for (int i=0; i<cookies.length; i++)
			{
				if (cookies[i].getName().equals(user))
				{
					//if cookie name is the same as logged in user 
					//then cookie has been created, return true
					val = true;	
				}
			}
		}
		return val;
	}

i was wondering do i need to add synchronization to checkCookie() when i call it to keep "cookies" and "user" thread safe when passing them the method or are they ok because they are local variables not instance variables.
i.e in the doGet change

boolean authenticated = checkCookie(out, cookies, user);

to

synchronized (this) 
{
   boolean authenticated = checkCookie(out, cookies, user);
}