  In this article, we have studied the cosmological and particle physics
constraints on dark matter relic abundance from effective field theory of
inflation using tensor-to-scalar ratio ($r$), in case of Randall-Sundrum single
membrane (RSII) paradigm. Using semi-analytical approach we establish a direct
connection between the dark matter relic abundance ($\Omega_{DM}h^2$) and
primordial gravity waves ($r$), which establishes a precise connection between
inflation and generation of dark matter within the framework of effective field
theory in RSII membrane. Further assuming the UV completeness of the effective
field theory perfectly holds good in the prescribed framework, we have
explicitly shown that the membrane tension, $\sigma$, bulk mass scale $M_5$,
and cosmological constant $\tilde{\Lambda}_{5}$, in RSII membrane plays the
most significant role to establish the connection between dark matter and
inflation, using which we have studied the features of various mediator mass
scale suppressed effective field theory "relevant operators" induced from the
localized $s$, $t$ and $u$ channel interactions. Taking a completely model
independent approach, we have studied an exhaustive list of tree-level Feynman
diagrams for dark matter annihilation within the prescribed setup and to check
the consistency of the obtained results, further we apply the constraints as
obtained from recently observed Planck 2015 data and Planck+BICEP2+Keck Array
joint datasets. Using all of these derived results we have shown that to
satisfy the bound on, $\Omega_{DM}h^2=0.1187\pm 0.0017$, as from Planck 2015
data, it is possible to put further stringent constraint on $r$ within,
$0.01\leq r\leq 0.12$, for thermally averaged annihilation cross-section of
dark matter, $\langle \sigma v\rangle\approx {\cal O}(10^{-28}-10^{-27}){\rm
cm^3 /s}$, which are very useful to constrain various membrane inflationary
models.
