Craft 2 - Date Comparison In Criteria - Impossible to access an attribute ("today") on a string variable (">=")

Question

I am working with a template in Craft 2, and I am setting up the criteria for entries to be displayed.
Here is my code (below).

{% set today = now|date('Y-m-d') %}

{% set criteria = {
    section: 'bulletin',
    order: 'postDate',
    expiryDate: '>=' . today
} %}

{% set initialEntry = craft.entries(criteria).first() %}
{% set finalEntry = craft.entries(criteria).last() %}

I get this error:

Impossible to access an attribute ("today") on a string variable (">="). 

How would I set expiryDate >= today?