  For first passage percolation on $\mathbb{Z}^2$ with i.i.d. bounded edge
weights, we consider the upper tail large deviation event; i.e., the rare
situation where the first passage time between two points at distance $n$, is
macroscopically larger than typical. It was shown by Kesten (1986) that the
probability of this event decays as $\exp (-\Theta(n^2))$. However the question
of existence of the rate function i.e., whether the log-probability normalized
by $n^2$ tends to a limit, had remained open. We show that under some
additional mild regularity assumption on the passage time distribution, the
rate function for upper tail large deviation indeed exists. Our proof can be
generalized to work in higher dimensions and for the corresponding problem in
last passage percolation as well. The key intuition behind the proof is that a
limiting metric structure which is atypical causes the upper tail large
deviation event. The formal argument then relies on an approximate version of
the above which allows us to dilate the large deviation environment to compare
the upper tail probabilities for various values of $n.$
