To redirect http://domain to https://domain you need to put the following redirect rule in .htaccess under public_html.

RewriteEngine on
Options FollowSymLinks
RewriteCond %{SERVER_PORT} !^443$
RewriteRule ^.*$ https://%{SERVER_NAME}%{REQUEST_URI} [L,R]

To use this rule mod_rewrite module should be installed on the server by default.