  In this paper, we consider stochastic reaction-diffusion equations with
super-linear drift on the real line $\mathbb{R}$ driven by space-time white
noise. A Freidlin-Wentzell large deviation principle is established by a
modified weak convergence method on the space $C([0,T], C_{tem}(\mathbb{R}))$.
Obtaining the main result in this paper is challenging due to the setting of
unbounded domain, the space-time white noise, and the superlinear drift term
without dissipation. To overcome these difficulties, the special designed norm
on $C([0,T], C_{tem}(\mathbb{R}))$, one order moment estimates of the
stochastic convolution and two nonlinear Gronwall-type inequalities play an
important role.
