  In this paper, we study the upper tail large deviation for the
one-dimensional frog model. In this model, sleeping and active frogs are
assigned to vertices on $\mathbb Z$. While sleeping frogs do not move, the
active ones move as independent simple random walks and activate any sleeping
frogs. The main object of interest in this model is the asymptotic behavior of
the first passage time ${\rm T}(0,n)$, which is the time needed to activate the
frog at the vertex $n$, assuming there is only one active frog at $0$ at the
beginning. While the law of large numbers and central limit theorems have been
well established, the intricacies of large deviations remain elusive. Using
renewal theory, B\'erard and Ram\'irez have pointed out a slowdown phenomenon
where the probability that the first passage time ${\rm T}(0,n)$ is
significantly larger than its expectation decays sub-exponentially and lies
between $\exp(-n^{1/2+o(1)})$ and $\exp(-n^{1/3+o(1)})$. In this article, using
a novel covering process approach, we confirm that $1/2$ is the correct
exponent, i.e., the rate of upper large deviations is given by $n^{1/2}$.
Moreover, we obtain an explicit rate function that is characterized by
properties of Brownian motion and is strictly concave.
