Is there a function or a way to invoke the comment object? I want to use the $comment object in page.tpl.php. 
Is there a function or a way to use it?
The page.tpl.php template file is used for any page output from Drupal; it is not said the page is being output for a node. It would be rather better to use node.tpl.php, which is always used for a node, except when a different template is being suggested and that file exists.

The code I am reporting is valid for page.tpl.php, but with few changes it can be used also for node.tpl.php.
I am taking the assumption you are interested in the comments for the node being shown.

if (!empty($node)) {
  $result = db_query('SELECT * FROM {comments} WHERE nid = %d', $node-&gt;nid);
  while ($comment_obj = db_fetch_object($result)) {
    // $comment_obj contains the comment object.
    // ...
  }
}


In the case the code is used in node.tpl.php, it is not necessary to verify if $node is not empty, as the template is surely used to visualize a node.
I called the variable $comment_obj because in node.tpl.php there is already a variable named $comment, but that variable doesn't contain any comment object; it contains the comment settings for the node.

As pointed out from Jeremy French, such code should never go inside a template file, which should just contain presentation code (i.e. code that prints out the content of variables). That code could be the body of a function (contained in template.php of a theme) that builds up the output shown from the template file; alternatively, similar code should be used in a preprocess function.

In this case, the code is similar to the following one.

function mymodule_preprocess_node(&amp;$variables) {
  $variables['comment_output'] = '';

  if (!empty($variables[node])) {
    $result = db_query('SELECT * FROM {comments} WHERE nid = %d', $variables[node]-&gt;nid);
    while ($comment_obj = db_fetch_object($result)) {
      // $comment_obj contains the comment object.
      // ...
      $variables['comment_output'] .= // ...
    }
  }
}


page.tpl.php should then print the content of $variables['comment_output'].

print $comment_output;


To notice also that Drupal uses comment.tpl.php, to which is passed a comment object. Depending on what you are trying to do, that could be the template file you are really interested in.