That doesnt mean that there is a default connection string, but that you dont have to provide a param that references the connection. Check out the example on php: pg_query
$conn = pg_pconnect("dbname=publisher");
if (!$conn) {
echo "An error occured.\n";
exit;
}
$result = pg_query($conn, "SELECT author, email FROM authors");
if (!$result) {
echo "An error occured.\n";
exit;
}
In this example there is $conn = pg_pconnect("dbname=publisher") and in the call to pg_query they pass a long $conn. That is the connection reference. Now you could also just use
$conn = pg_pconnect("dbname=publisher");
$result = pg_query("SELECT author, email FROM authors");
pg_query will now automatically use the last opened connection (which is $conn)
Update:
You cannot get the resource, PHP uses an internal method php_pgsql_get_default_link to get the default connection but will not return it anywhere (See php-5.4.9\ext\pgsql\pgsql.c in the source).
You can get information on the database name or user using pg_dbname or pg_parameter_status
pg-options()a try, but I'm not very sure what data it will give you (nor what data you're actually after).