Search query for posts within certain period of time - mysql

Question

The query below is searching for posts that are followed by users (if user follows category, user or topic).
It is working if it doesn't use $time_interval.
I would like to select posts from a certain period of time (last week, last month etc.).
I hardcoded 1 month and $filter for this example. But as soon as I try to select posts from last month, the query stops working.
I tried with methods that I used in other places, but this query is much more complex and by even putting the query to work to this point was very long process of errors, so I am not sure if it is written in the best possible way.
$current_user_id = get_current_user_id();
$term_relat_table = ;// table with term relationships
$topic_follow_table = ;// contains which topic user follows
$cat_follow_table = ;// contains which category user follows
$posts_table = ;// table with posts
$user_follow_user_table = ;// contains which users current user follows
$votes_stats_table = ;// table with votes
$perPage = 10; // hardcoded for this example
$orderby = "ORDER BY vote_rating DESC, total_votes DESC"; // hardcoded for this example
$time_interval = date('Y-m-d H:i:s', strtotime('-1 month')); // wasnt able to include in query
//I tried placing p.post_date > $time_interval in different places in query but none seem to work.
$all_results = $wpdb->get_results($wpdb->prepare("
SELECT v.topic_id AS post_id
, v.votes_rating AS vote_rating
, v.total_votes AS total_votes
FROM $votes_stats_table v
JOIN
( SELECT tf.discussion_id AS post_id
FROM $topic_follow_table AS tf
WHERE tf.current_user = %d
UNION ALL
SELECT p.ID AS post_id
FROM $user_follow_user_table AS uf
JOIN $posts_table AS p
ON p.post_author = uf.followed_user
WHERE uf.current_user = %d
-- tried placing p.post_date > %s here, and $time_interval below next to other variables
UNION ALL
SELECT r.object_id AS post_id
FROM $term_relat_table AS r
JOIN $cat_follow_table AS cf
ON cf.cat_id = r.term_taxonomy_id
WHERE cf.user_id = %d
) AS i
ON i.post_id = v.topic_id
GROUP
BY v.topic_id
$orderby
LIMIT %d
OFFSET $offset", $current_user_id, $current_user_id, $current_user_id, $perPage));