The QCD mass gap and quark deconfinement scales as mass bounds in strong
  gravity
  Though not a part of mainstream physics, Salam's theory of strong gravity
remains a viable effective model for the description of strong interactions in
the gauge singlet sector of QCD, capable of producing particle confinement and
asymptotic freedom, but not of reproducing interactions involving $SU(3)$
colour charge. It may therefore be used to explore the stability and
confinement of gauge singlet hadrons, though not to describe scattering
processes that require colour interactions. It is a two-tensor theory of both
strong interactions and gravity, in which the strong tensor field is governed
by equations formally identical to the Einstein equations, apart from the
coupling parameter, which is of order $1 \ \rm GeV^{-1}$. We revisit the strong
gravity theory and investigate the strong gravity field equations in the
presence of a mixing term which induces an effective {\it strong cosmological
constant}, $\Lambda_{f}$. This introduces a {\it strong de Sitter radius} for
strongly interacting fermions, producing a confining bubble, which allows us to
identify $\Lambda_{f}$ with the `bag constant' of the MIT bag model, $B \simeq
2 \times 10^{14} \rm gcm^{-3}$. Assuming a static, spherically symmetric
geometry, we derive the strong gravity TOV equation, which describes the
equilibrium properties of compact hadronic objects. From this, we determine the
generalised Buchdahl inequalities for a strong gravity `particle', giving rise
to upper and lower bounds on the mass/radius ratio of stable, compact, strongly
interacting objects. We show, explicitly, that the existence of the lower mass
bound is induced by the presence of $\Lambda_f$, producing a mass gap, and that
the upper bound corresponds to a deconfinement phase transition. The physical
implications of our results for holographic duality in the context of the
AdS/QCD and dS/QCD correspondences are also discussed.
