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Incoming links: Dark radiation on a cosmological brane
Dark radiation on a cosmological brane 2026-10-14
Projected bulk Weyl tensor can contribute a radiation-scaling term to the brane Friedmann equation, even without ordinary brane photons. For an anti-de Sitter black-hole bulk the integration constant is related to its mass. This dark radiation on a cosmological brane changes the expansion rate tested by Big Bang nucleosynthesis and Cosmic microwave background anisotropy; it should not automatically be identified with a freely specifiable thermal particle species.
Past exam of the mathematics course of the University of Cambridge 2002 iii Paper 75 4 i Solution Created 2026-10-03 Updated 2026-10-14
In the one-brane Randall–Sundrum model, gravity localization in a noncompact warped dimension produces a normalizable massless graviton despite the infinite proper fifth dimension. At long distances its zero mode reproduces four-dimensional gravity; bulk Kaluza-Klein modes give corrections. This localization mechanism, rather than a large compact volume, is the reason an infinite dimension need not destroy the usual Newton law, as established in the original single-brane warped-gravity construction. Its observational tests include:
- Short-distance gravity experiments. Massive bulk modes supplement the localized zero mode, changing the gravitational potential near the AdS curvature length. Torsion balances, microscopic force measurements and suitable precision gravitational tests can seek departures from the inverse-square law. The relevant scale is the warp curvature length, not a finite compactification radius.
- Collider missing energy. If the bulk gravitational scale and couplings are accessible, collisions can emit gravitons into the fifth dimension; a visible jet or photon recoils against unobserved energy. Virtual bulk modes can also change scattering rates and angular distributions. The minimal one-brane spectrum is a continuum, not the discrete resonant tower of a two-brane model, so those predictions must not be interchanged.
- Gravitational-radiation tests. Additional bulk propagation channels can modify energy loss, waveforms or propagation at sufficiently high frequencies. Binary timing and gravitational-wave measurements probe such departures. The localized low-energy mode makes four-dimensional propagation a good approximation; large long-distance leakage is not automatic.
- Astrophysical energy loss. Dense hot objects could radiate accessible bulk modes, changing cooling histories. Supernova and compact-star observations can limit such channels, with rates determined by the specific warped spectrum and coupling.
For an expanding brane, its motion in the bulk and the Israel junction conditions modify the four-dimensional cosmological expansion. In the tuned low-energy regime it approaches ordinary cosmology, but high-energy braneworld expansion has a density-squared correction when the matter density approaches the brane tension. Faster early expansion changes weak-interaction freeze-out and light-element yields, so Big Bang nucleosynthesis is a sensitive test. It also changes time-temperature relations, recombination distances and acoustic scales in the Cosmic microwave background anisotropy.
The bulk can supply dark radiation on a cosmological brane, a projected-Weyl contribution that scales like radiation and is related to a bulk black-hole mass in the simplest vacuum construction. Nucleosynthesis and CMB measurements constrain its contribution to the expansion. Energy transferred from a hot brane into bulk gravitons can further modify the radiation history. None of these terms must be identified with an ordinary thermal particle component without a model.
Inflation on the brane can alter scalar and tensor production at high energy; the gravitational-wave zero-mode normalization and coupling to bulk modes can change primordial spectra. CMB temperature/polarization, primordial gravitational waves and later structure growth can test these effects. Projected bulk perturbations may introduce nonlocal corrections to the brane's effective perturbation equations, so a background expansion law alone does not determine all observables. Late-time measurements of expansion and structure also test residual departures, although the basic tuned model does not automatically predict dark-energy acceleration.
All proposed signals depend on the curvature scale, fundamental gravitational scale, brane tension, reheating history and bulk state. The minimal single-brane construction has no second-brane separation radion; an arbitrary radion fifth-force prediction from a two-brane compactification cannot simply be imported here. The main probes are corrected gravity, accessible bulk radiation, and high-energy/dark-radiation changes to cosmological evolution.