I have a query that is used to display search results from search. The query is in search.php. It shows custom posts and pages in the search result, which is what I want. I have a custom post type called 'event', each post has a date stored in _event_start_date. I want to compare _event_start_date (a meta key) with the current date and exclude event posts that are in the past from the search result.

My working query:

if ( have_posts() ) : ?>
<h1 class="page-title"><?php printf( __( 'Search Results for: %s', 'shape' ), '<span>' . get_search_query() . '</span>' ); ?></h1>
<?php while ( have_posts() ) : the_post(); ?>
 <a href="<?php echo get_permalink(  ); ?>"><?php echo the_title(); ?></a>
 <?php endwhile; ?>
 <?php else : ?>
 <p> there were no results </p>
 <?php endif; ?>

How can I include _event_start_date in the above code, so that if an event has already started it is not shown in the search result? The date is formatted as 2015-05-01 in _event_start_date