Some pensions penalize you in their formula for taking it early and give better benefits if you delay them, is that what is inspiring this possibility?
Nothing published in their formula that I can find for age affecting payout. It's a pretty simple 2.3% of (final average 36 month) salary per year of service.
The percentage per year of service changes slightly with age for most plans, if it does not for Texas state employees, that's great for someone who gets a state job young and chooses to retire early. In my system the benefit factor ranges from 1.092% at age 50 to 2.418% at age 63 or older.
It does not vary by age for Texas state employees in ERS. It's also not inflation adjusted - what you get is what you will continue to get.
I have not investigated the other plans (Teachers have a separate plan, municipal employees have one, Law Enforcement has one, etc.)
However, when you can take it gets complicated.
As a pre-2009 employee, I need one of the following for the pension + medical:
Age + Years of Service = 80, and Years of Service >=10
Age = 65, Years of Service >=10.
For pension only, no medical
Age + Years of Service = 80, and Years of Service >=5
Age = 60, Years of Service >=5.
I already have > 10 years of service, plus I purchased 3 years of service time (the max.)
For those who started on or after September 1, 2009 it gets more restrictive.