Anisotropic evolution of 5D Friedmann-Robertson-Walker spacetime
- Department of Physical and Environmental Sciences, Colorado Mesa University (formerly Mesa State College), Grand Junction, Colorado 81501 (United States)
- Department of Physics, Purdue University, West Lafayette, Indiana 47907 (United States)
We examine the time evolution of the five-dimensional Einstein field equations subjected to a flat, anisotropic Robertson-Walker metric, where the 3D and higher-dimensional scale factors are allowed to dynamically evolve at different rates. By adopting equations of state relating the 3D and higher-dimensional pressures to the density, we obtain an exact expression relating the higher-dimensional scale factor to a function of the 3D scale factor. This relation allows us to write the Friedmann-Robertson-Walker field equations exclusively in terms of the 3D scale factor, thus yielding a set of 4D effective Friedmann-Robertson-Walker field equations. We examine the effective field equations in the general case and obtain an exact expression relating a function of the 3D scale factor to the time. This expression involves a hypergeometric function and cannot, in general, be inverted to yield an analytical expression for the 3D scale factor as a function of time. When the hypergeometric function is expanded for small and large arguments, we obtain a generalized treatment of the dynamical compactification scenario of Mohammedi [Phys. Rev. D 65, 104018 (2002)] and the 5D vacuum solution of Chodos and Detweiler [Phys. Rev. D 21, 2167 (1980)], respectively. By expanding the hypergeometric function near a branch point, we obtain the perturbative solution for the 3D scale factor in the small time regime. This solution exhibits accelerated expansion, which, remarkably, is independent of the value of the 4D equation of state parameter w. This early-time epoch of accelerated expansion arises naturally out of the anisotropic evolution of 5D spacetime when the pressure in the extra dimension is negative and offers a possible alternative to scalar field inflationary theory.
- OSTI ID:
- 21607946
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 84, Issue 8; Other Information: DOI: 10.1103/PhysRevD.84.085013; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ANISOTROPY
COMPACTIFICATION
DENSITY
EINSTEIN FIELD EQUATIONS
EQUATIONS OF STATE
EXPANSION
HYPERGEOMETRIC FUNCTIONS
MANY-DIMENSIONAL CALCULATIONS
MATHEMATICAL SOLUTIONS
METRICS
SCALAR FIELDS
SPACE-TIME
TIME DEPENDENCE
EQUATIONS
FIELD EQUATIONS
FUNCTIONS
PHYSICAL PROPERTIES