How to specify default options in a checkbox field using Field API
Try this for your instance creation:



field_create_instance(
  array(
    'field_name' =&gt; $default_notification_field_name,
    'entity_type' =&gt; 'user',
    'bundle' =&gt; 'user',
    'label' =&gt; t('Default settings for notifications'), 
    'description' =&gt; t('Select the ​​default notification options for the groups to which you subscribe, the contents you send and the replies to (your) comments. These default options can then be modified on a per-group, content or comment bases.'),
    'required' =&gt; FALSE,
    'widget' =&gt; array(
      'type' =&gt; 'options_buttons',
    ),
    'default_value' =&gt; array(
      0 =&gt; array(
        'value' =&gt; 'comment',
      ),
      1 =&gt; array(
        'value' =&gt; 'content',
      ),
    ),
  ));


To assist you in knowing the array structure, try this:


Install the devel module
Go to the page /devel/php on your site
Run this code to see all field information on your site:




// Show all fields.
dpm(field_info_fields());
// Show all field instances.
dpm(field_info_instances());