Brane-World Gravity (1004.3962v2)

Abstract: The observable universe could be a 1+3-surface (the "brane") embedded in a 1+3+\textit{d}-dimensional spacetime (the "bulk"), with Standard Model particles and fields trapped on the brane while gravity is free to access the bulk. At least one of the \textit{d} extra spatial dimensions could be very large relative to the Planck scale, which lowers the fundamental gravity scale, possibly even down to the electroweak ($\sim$ TeV) level. This revolutionary picture arises in the framework of recent developments in M theory. The 1+10-dimensional M theory encompasses the known 1+9-dimensional superstring theories, and is widely considered to be a promising potential route to quantum gravity. At low energies, gravity is localized at the brane and general relativity is recovered, but at high energies gravity "leaks" into the bulk, behaving in a truly higher-dimensional way. This introduces significant changes to gravitational dynamics and perturbations, with interesting and potentially testable implications for high-energy astrophysics, black holes, and cosmology. Brane-world models offer a phenomenological way to test some of the novel predictions and corrections to general relativity that are implied by M theory. This review analyzes the geometry, dynamics and perturbations of simple brane-world models for cosmology and astrophysics, mainly focusing on warped 5-dimensional brane-worlds based on the Randall--Sundrum models. We also cover the simplest brane-world models in which 4-dimensional gravity on the brane is modified at \emph{low} energies -- the 5-dimensional Dvali--Gabadadze--Porrati models. Then we discuss co-dimension two branes in 6-dimensional models.

• The paper investigates how gravity confined to a brane emerges from higher-dimensional bulk curvature, yielding modified gravitational dynamics.
• It applies string theory and M-theory concepts to show that gravitational leakage can lower the interaction scale and alter Newtonian potentials.
• The study links high-energy physics with cosmological phenomena, revealing novel insights into black holes, cosmic inflation, and holographic dualities.

Brane-World Gravity

The concept of brane-world gravity as outlined by Maartens and Koyama explores the possibility that our observable universe resides within a four-dimensional surface, referred to as a "brane," embedded within a higher-dimensional spacetime, known as the "bulk." This framework emerges from developments in string theory, particularly M-theory, and has implications for both high-energy physics and cosmological models.

M-theory suggests that the universe is inherently multidimensional, incorporating different dimensions that influence various phenomena at fundamental levels. The brane-world hypothesis postulates that while the standard model particles are confined to the brane, gravity uniquely extends into the bulk. This departure raises intriguing possibilities, especially with regard to lowering the scale of fundamental interactions, potentially even to the electroweak scale.

Key Concepts

In the brane-world scenario:

• Dimensional Reduction: Gravity reduction on the brane arises not from compactification but from bulk curvature, elucidated through the anti-de Sitter (AdS) space in idealized models like Randall-Sundrum (RS).
• Dynamic Gravity: High-energy behavior of gravity deviates from the standard four-dimensional model, with gravitational "leakage" into the bulk indicating higher-dimensional dynamics.
• Phenomenological Correlations: The RS models, especially through RS 1 and RS 2 configurations, suggest testable predictions that deviate from general relativity, offering corrections at high energy levels potentially observable in astrophysical phenomena or particle colliders.

Theoretical Implications

Several consequential outcomes emerge from the brane-world model:

• Effective Gravity: Brane-world models investigate how gravitational dynamics are effectively manifested on the brane, leading to modified Newtonian potentials and deviations in high-energy astrophysical contexts. Notably, they provide a mode to account for enhanced gravitational interactions at small scales.
• Holography: Insights into possible holographic relationships are highlighted, establishing connections between bulk dynamics and boundary conditions, represented by AdS/CFT dualities.
• Black Holes and Cosmology: Solutions like the black string and others reflect on embedding black holes within this framework, elucidating on new parameters such as tidal charge.
• Cosmological Phenomena: Friedmann-Robertson-Walker (FRW) cosmologies find new formulations in these scenarios, offering fresh insights into early universe dynamics and cosmic inflation models with novel inflationary potentials.

Future Directions

Exploration of the brane-world project points to various inquiries needing further investigation:

• High-Energy Experiments: Collider experiments could potentially reveal effects of extra dimensions, considering that the RS models predict collider signatures under certain conditions.
• Numerical Modeling: There is a sustained need for numerical simulations supporting brane-world gravity by bridging theoretical models with observable phenomena.
• Theoretical Extensions: Extending brane-world frameworks to include additional higher-dimensional corrections, such as incorporating bulk scalar fields, or considering multiple intersecting branes, to address gaps like stabilization challenges and addressing the cosmological constant problem.
• Alternative Models: The Dvali-Gabadadze-Porrati (DGP) model represents a distinct framework modifying gravity at low energies, amplifying the discourse around alternatives to dark energy and cosmic acceleration.

The brane-world model, rich in its theoretical constructs, continues to bridge concepts from quantum gravity towards observable high-energy physics. It offers a fertile ground for understanding cosmic phenomena, underscoring a myriad of ongoing experiments and theoretical advancements aimed at unraveling the fabric of our universe through the lens of multidimensional theories.