Effective field theory of dark matter from membrane inflationary paradigm

In this article, we have studied the cosmological and particle physics constraints on dark matter relic abundance from effective field theory of inflation from 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 (${\Omega }_{\mathrm{DM}}{h}^2$) 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, $\sigma \le O\left(10^{-9}\right)M_p^4$, bulk mass scale $M_5\le O(0.04-0.05)M_p$, and cosmological constant ${\tilde{\Lambda }}_5\ge -O\left(10^{-15}\right)M_p^5$, 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 in RSII membrane. 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 data sets. Using all of these derived results we have shown that to satisfy the bound on, ${\Omega }_{\mathrm{DM}}{h}^2=0.1199\pm 0.0027$, as from Planck 2015 data, it is possible to put further stringent constraint on $r$ within, $0.01\le r\le 0.12$, for thermally averaged annihilation cross-section of dark matter, $〈\sigma v〉\approx O(10^{-28}-10^{-27}){\mathrm{cm}}^3/s$, which are very useful to constrain various membrane inflationary models.