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The problem is that you are using an undefined variable `$cookie`. This will cause `setcookie()` to "set" a cookie with name "cookie" and value `null`. Obviously PHP deletes the cookie in that case, as you can observe with curl (also note the expiration time in the past):

    curl $URL_OF_YOUR_WEBSITE -i
    [...]
    set-cookie: cookie=deleted; expires=Thu, 01-Jan-1970 00:00:01 GMT; Max-Age=0; path=/; domain=$YOURDOMAIN
    [...]

Therefore, after the reload, the browser will not send the cookie (as it is expired = deleted), which brings us in the same situation as in the first request. Thus, the browser is running into an infinite loop of reloads.

(The same happens, by the way, if you set the cookie to value "".)

To fix the problem, set the cookie to a non-empty string, as in 

    if(!isset($_COOKIE['cookie'])){
        $domain = $_SERVER['SERVER_NAME'];
        setcookie('cookie', 'yes', time() + 31536000, '/', $domain);
        header('Location: '.$_SERVER['REQUEST_URI']);   // reload
    }

Then, the cookie will actually be set (and not deleted) and the browser should be fine. With curl, you can see that the cookie is really set and has an expiration time in the future:

    curl $URL_OF_YOUR_WEBSITE -i
    [...]
    set-cookie: cookie=yes; expires=Sat, 22-Jun-2024 21:02:32 GMT; Max-Age=31536000; path=/; domain=$YOUR_DOMAIN
    [...]