Reinventing spacetime on a dynamical hypersurface

Abstract

In braneworld models, Space-Time-Matter and other Kaluza-Klein theories, our spacetime is devised as a four-dimensional hypersurface {\it orthogonal} to the extra dimension in a five-dimensional bulk. We show that the FRW line element can be "reinvented" on a dynamical four-dimensional hypersurface, which is {\it not} orthogonal to the extra dimension, without any internal contradiction. This hypersurface is selected by the requirement of continuity of the metric and depends explicitly on the evolution of the extra dimension. The main difference between the "conventional" FRW, on an orthogonal hypersurface, and the new one is that the later contains higher-dimensional modifications to the regular matter density and pressure in 4D. We compare the evolution of the spacetime in these two interpretations. We find that a wealth of "new" physics can be derived from a five-dimensional metric if it is interpreted on a dynamical (non-orthogonal) 4D hypersurface. In particular, in the context of a well-known cosmological metric in $5D$, we construct a FRW model which is consistent with the late accelerated expansion of the universe, while fitting simultaneously the observational data for the deceleration parameter. The model predicts an effective equation of state for the universe, which is consistent with observations.

References added to the Introduction, and Abstract modified. Accepted for publication in Mod. Phys. Lett. A

References in corpus (4)

• New Constraints on ${\Omega }_M$, ${\Omega }_{\Lambda }$, and w from an Independent Set of Eleven High-Redshift Supernovae Observed with HST
• Brane-world gravity
• Five-Dimensional Cosmological Scaling Solution
• Accelerated expansion from braneworld models with variable vacuum energy

Cited by in corpus (19)

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• Modified Saez-Ballester scalar-tensor theory from 5D space-time
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• Late time cosmic acceleration from vacuum Brans-Dicke theory in 5D
• Stellar models with Schwarzschild and non-Schwarzschild vacuum exteriors
• Kaluza-Klein solitons reexamined
• Time-dependent extra dimension and higher-dimensional modifications to the matter content in FRW spacetimes
• Phantom cosmology with a decaying cosmological function $\Lambda (t)$ induced from five-dimensional (5D) geometrical vacuum
• Pre-big bang collapsing universe from modern Kaluza-Klein theory of gravity
• Static exteriors for nonstatic braneworld stars
• Self-similar cosmologies in 5D: Our universe as a topological separation from an empty 5D Minkowski space
• Passing to an effective 4D phantom cosmology from 5D vacuum theory of gravity
• Quintessential inflation from 5D warped product spaces on a dynamical foliation
• Kaluza-Klein Cosmology: the bulk metric
• 3+2 Cosmology: unifying FRW metrics in the bulk
• Wave-like Solutions for Bianchi type-I cosmologies in 5D
• Super exponential inflation from a dynamical foliation of a 5D vacuum state
• Inflation from the bang of a white hole induced from a 6D vacuum state