  Mimetic gravity analysis has been studied as a theory in various types of
general relativity extensions, such as mimetic f(R) gravity, mimetic f(R, T)
gravity, mimetic f(R, G) gravity, etc., in the literature. This paper presents
a set of equations arising from mimetic conditions and studies cosmic inflation
with a combination of mimetic f(G) gravity and swampland dS conjectures. We
analyze and evaluate these results. Therefore, we first thoroughly introduce
the mimetic f(G) gravity and calculate some cosmological parameters such as the
scalar spectral index, the tensor-to-scalar ratio, and the slow-roll
parameters. Also, we investigate the potential according to the mimetic f(G)
gravity. Then we will challenge the swampland dS conjectures with this
condition. By expressing the coefficient of swampland dS conjectures viz
$C_{1}$ and $C_2$ in terms of $n_{s}$ and $r$, we plot some figures and
determine the allowable range for each of these cosmological parameters and
these coefficients, and finally, compare these results with observable data
such as Planck and BICEP2/Keck array data. We show $C_{1}$ and $C_2$ are not
$\mathcal{O}(1)$, so the refining swampland dS conjecture is not satisfied for
this inflationary model. Then we examine it with further refining swampland dS
conjecture, which has a series of free parameters such as $a,b>0$, $q>2$, and
$a+b=1$. By adjusting these parameters, the compatibility of the mentioned
conjecture with the inflationary model can be discussed. We determine the
further refining swampland dS conjecture is satisfied. when $a <
\frac{1}{1.00489}=0.99513$, we can always find $a$, $b$ and $q$ whose value is
larger than 2, viz for $q=2.4$, we find $0.99185\leq a < 1$, which we can
choose $a=0.99235$ according to the condition $a < 0.99513$. Also we know
$b=1-a$, so we will have $1-0.99235=0.00765 > 0$.

General Relativity and Quantum Cosmology;High Energy Physics - Theory