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We examine a class of braneworld models in which the expanding universeencounters a "quiescent" future singularity. At a quiescent singularity, theenergy density and pressure of the cosmic fluid as well as the Hubble parameterremain finite while all derivatives of the Hubble parameter diverge (i.e.,${\dot H}$, ${\ddot H}$, etc. $\to \infty$). Since the Kretschmann invariantdiverges ($R_{iklm}R^{iklm} \to \infty$) at the singularity, one expectsquantum effects to play an important role as the quiescent singularity isapproached. We explore the effects of vacuum polarization due to masslessconformally coupled fields near the singularity and show that these can eithercause the universe to recollapse or, else, lead to a softer singularity atwhich $H$, ${\dot H}$, and ${\ddot H}$ remain finite while ${\dddot H}$ andhigher derivatives of the Hubble parameter diverge. An important aspect of thequiescent singularity is that it is encountered in regions of low density,which has obvious implications for a universe consisting of a cosmic web ofhigh and low density regions -- superclusters and voids. In addition to vacuumpolarization, the effects of quantum particle production of non-conformalfields are also likely to be important. A preliminary examination shows thatintense particle production can lead to an accelerating universe whose Hubbleparameter shows oscillations about a constant value.Comment: 19 pages, 3 figures, text slightly improved and references added.  Accepted for publication in Classical and Quantum Gravit

Quantum effects, soft singularities and the fate of the universe in a braneworld cosmology