We present a comprehensive study of the cosmological solutions of 6D braneworld models with azimuthal symmetry in the extra dimensions, moduli stabilization by flux or a bulk scalar field, and which contain at least one 3-brane that could be identified with our world. We emphasize an unusual property of these models: their expansion rate depends on the 3-brane tension either not at all, or in a nonstandard way, at odds with the naive expected dimensional reduction of these systems to 4D general relativity at low energies. Unlike other braneworld attempts to find a self-tuning solution to the cosmological constant problem, the apparent failure of decoupling in these models is not associated with the presence of unstabilized moduli; rather it is due to automatic cancellation of the brane tension by the curvature induced by the brane. This provides some corroboration for the hope that these models provide a distinctive step toward understanding the smallness of the observed cosmological constant. However, we point out some challenges for obtaining realistic cosmology within this framework.

It has been suggested that codimension-two braneworlds might naturally explain the vanishing of the 4D effective cosmological constant, due to the automatic relation between the deficit angle and the brane tension. To investigate whether this cancellation happens dynamically, and within the context of a realistic cosmology, we study a codimension-two braneworld with spherical extra dimensions compactified by magnetic flux. Assuming Einstein gravity, we show that when the brane contains matter with an arbitrary equation of state, the 4D metric components are not regular at the brane, unless the brane has nonzero thickness. We construct explicit 6D solutions with thick branes, treating the brane matter as a perturbation, and find that the universe expands consistently with standard Friedmann-Robertson-Walker (FRW) cosmology. The relation between the brane tension and the bulk deficit angle becomes $\Delta=2\pi G_6(\rho-3 p)$ for a general equation of state. However, this relation does not imply a self-tuning of the effective 4D cosmological constant to zero; perturbations of the brane tension in a static solution lead to deSitter or anti-deSitter braneworlds. Our results thus confirm other recent work showing that codimension-two braneworlds in nonsupersymmetric Einstein gravity do not lead to a dynamical relaxation of the cosmological constant, but they leave open the possibility that supersymmetric versions can be compatible with self-tuning.Comment: Revtex4, 17 pages, references added, typos corrected, minor points clarified. Matches published versio

We derive the corrections to the Friedmann equation of order ρ 2 in the RandallSundrum (RS) model, where two 3-branes bound a slice of five-dimensional Anti-deSitter space. The effects of radion stabilization by the Goldberger-Wise mechanism are taken into account. Surprisingly, we find that an inflaton on either brane will experience no order ρ 2 corrections in the Hubble rate H due to its own energy density, although an observer on the opposite brane does see such a correction. Thus there is no enhancement of the slow-roll condition unless inflation is simultaneously driven by inflatons on both branes. Similarly, during radiation domination, the ρ 2 correction to H on a given brane vanish unless there is nonvanishing energy density on the opposite brane. During the electroweak phase transition the correction can be large, but is has the wrong sign for causing sphalerons to go out of thermal equilibrium, so it cannot help electroweak baryogenesis. We discuss the differences between our results and exact solutions in RS-II cosmology.

We investigate in detail recent suggestions that codimension-two braneworlds in six dimensional supergravity might circumvent Weinberg's no-go theorem for selftuning of the cosmological constant. The branes are given finite thickness in order to regularize mild singularities in their vicinity, and we allow them to have an arbitrary equation of state. We study perturbatively the time evolution of the solutions by solving the equations of motion linearized around a static background. Even allowing for the most general possibility of warping and nonconical singularities, the geometry does not relax to a static solution when the brane stress-energies are perturbed.Rather, both the internal and external geometries become time-dependent, and the system does not exhibit any self-tuning behavior.

It has recently been proposed that the Universe might be accelerating as a consequence of extra dimensions with time-varying size. We show that, although these scenarios can lead to acceleration, they run into serious difficulty when taking into account the limits on the time variation of the four-dimensional Newton constant. On the other hand, models of ''Cardassian'' expansion based on extra dimensions which have been constructed so far violate the weak energy condition for the bulk stress energy, for parameters that give an accelerating Universe.