Dark Matter from a Second Warped Throat: Gravitational Freeze‑In in the DBQTM Framework

Abstract

We extend the Dual-Brane Quantum Tunneling Model (DBQTM) to incorporate 
dark matter through a multi-throat compactification on a Calabi--Yau manifold.
While the first Klebanov--Strassler throat ($K_1=203$, $M_1=17$, $kd_1 \approx 375$) 
generates the observed cosmological constant via vacuum energy suppression, 
a second throat ($K_2=39$, $M_2=35$, $kd_2 \approx 35$) produces a natural 
dark matter candidate: the lightest scalar glueball of the confined gauge theory, 
with mass $m_\mathrm{DM} = k\,e^{-kd_2} \approx 133$~GeV.
Dark matter is produced via UV-dominated gravitational freeze-in through 
zero-mode graviton exchange, yielding the observed relic abundance 
$\Omega_\mathrm{DM} h^2 = 0.12$ for an inflationary Hubble rate 
$H_\mathrm{inf} \sim 10^{13}$~GeV, which predicts a tensor-to-scalar 
ratio $r \sim 0.001$--$0.01$ testable by LiteBIRD and CMB-S4.
The dark matter is absolutely stable on cosmological timescales 
($\tau \approx 1.6 \times 10^{32}$~yr) and undetectable via direct detection 
($\sigma_\mathrm{SI} \sim 10^{-98}$~cm$^2$).
Both the cosmological constant and the dark matter mass are determined 
by five discrete parameters $(K_1, M_1, K_2, M_2, g_s)$, with $k$ 
fixed by the RS geometry and $g_s$ fixed in the first throat to 
reproduce the observed $\rho_\Lambda$~\cite{DBQTM-Paper1}. The 
cross-prediction $kd_1/kd_2 = K_1 M_2/(K_2 M_1)$ is verified exactly.
The tadpole constraint $K_1 M_1 + K_2 M_2 = 4816$ requires a Calabi--Yau 
with Euler characteristic $\chi \geq 115{,}584$.

\medskip
\noindent\textit{v2.0}: Adds perturbative brane backreaction analysis
confirming RS consistency ($\varepsilon_\mathrm{BR}\sim10^{-34}$,
Appendix~C) and detailed gravitational freeze-in derivation including
warped lifetime ($\tau\approx2.9\times10^{33}$~yr) and decay branching
fractions (Appendix~D). Core predictions unchanged.

inflation, Randall--Sundrum, Klebanov--Strassler, 
Starobinsky, warped extra dimensions, dark matter, string cosmology