set enable_seqscan=off;
CREATE TABLE test_time (
	i time
);
INSERT INTO test_time VALUES 
	( '03:55:08' ),
	( '04:55:08' ),
	( '05:55:08' ),
	( '08:55:08' ),
	( '09:55:08' ),
	( '10:55:08' )
;
CREATE INDEX idx_time ON test_time USING gin (i);
SELECT * FROM test_time WHERE i<'08:55:08'::time ORDER BY i;
    i     
----------
 03:55:08
 04:55:08
 05:55:08
(3 rows)

SELECT * FROM test_time WHERE i<='08:55:08'::time ORDER BY i;
    i     
----------
 03:55:08
 04:55:08
 05:55:08
 08:55:08
(4 rows)

SELECT * FROM test_time WHERE i='08:55:08'::time ORDER BY i;
    i     
----------
 08:55:08
(1 row)

SELECT * FROM test_time WHERE i>='08:55:08'::time ORDER BY i;
    i     
----------
 08:55:08
 09:55:08
 10:55:08
(3 rows)

SELECT * FROM test_time WHERE i>'08:55:08'::time ORDER BY i;
    i     
----------
 09:55:08
 10:55:08
(2 rows)