Joomla! home (default menu item) page only module position with multi-lingual support.

gistfile1.phtml

<?php
$app = JFactory::getApplication();
$menu   = $app->getMenu();
$lang   = JFactory::getLanguage();
$isHome = $menu->getActive() == $menu->getDefault($lang->getTag());
?>

<?php if ($isHome) : ?>
	<jdoc:include type="modules" name="home"/>
<?php endif ?>



PROTIP: You can extend the logic of $isHome to be language specific, such as $isHomeEn = $menu->getActive() == $menu->getDefault('en-GB');