What is the fastest public transit to take from Davis Square to Harvard Square?
user
The fastest public transit from Davis Square to Harvard Square is the MBTA Red Line. It should take approximately 8 minutes to reach the Harvard station from Davis.
assistant
How much would that cost?
user
The Price of the One-Way of the Massachusetts BayTransportation Authority MBTA costs $2.40
with CharlieCard, CharlieTicket, or Cash. and $1.10 with reduced fare card 1-Day Pass

There is also the option of 
$11.00

Unlimited travel for 24 hours

CharlieCard and CharlieTicket valid on:
 Subway
 Local Bus
 Silver Line

7-Day Pass

$22.50

Unlimited travel for 7 days.

$90.00

Unlimited travel for 1 calendar month

This information was found in the official MBTA website https://www.mbta.com/fares/
assistant