~(1 + 2 \ln [R_0] - r \ln [R_0]~) \Big] ~~\end{aligned}$$ and $$\begin{aligned}
C_2  =&  -\frac{R_0^{1-r}}{2(q-r)} \Big[2(2q - \delta +  q \delta) - \alpha \sqrt{R_0}~(3 - 2q) - 2\beta R_0~ (2 -q) - \nonumber \\
& 2\gamma R_0 ~(1 + 2 \ln [R_0] - q \ln [R_0]~) \Big] ~~.\end{aligned}$$ For the scale factor in deSitter space $H$ is constant. The future event horizon is located at $$L = a L = a \int_t^{\infty} \frac{d t}{a} = \frac{1}{H} = \sqrt{\frac{12}{R}} ~~,$$ where $H$ is given by eqn.(\[conh\]). So we can write the GUP motivated energy density from eqn.(\[hd\]) as $$\rho_{\Lambda} = \frac{n^2 m_p^2}{4} ~R + \frac{a ~m_p}{12^{\frac{3}{2}}} ~R^{\frac{3}{2}} + \frac{b}{144~ m_p^2}~R^2 \ln \left(\frac{12~m_p^2}{R}\right) + \frac{c}{144~ m_p^2} ~R^2 ~~.$$ So eqn.(\[maineq\]) takes the form $$R f'(R) - 2 f(R) = \frac{4 \rho_{\Lambda}}{m_p^2} ~~.$$ The solution of this equation can be written in the form $$f(R) = -n^2 ~R + C_1~R^2 - \frac{a}{3\sqrt{3}~m_p}~R^{\frac{3}{2}} - \frac{b}{72~m_p^2}~R^2~\left\{\ln \left(\frac{12~m_p^2}{R}\right)\right\}^2 + \frac{c}{36~m_p^2}~R^2~\ln (R) ~~,$$ where $C_1$ is the arbitrary integration constant to be fixed by boundary conditions. The GUP motivated terms in $f(R)$ are important for inflationary scenario. We have instances for the $R^2$ term in literature to explain early time inflation [@sud59] as a curvature driven 