The Averaging Problem in Cosmology and Macroscopic Gravity
arXiv:0801.3256 · doi:10.1142/S0217751X08040032
Abstract
The averaging problem in cosmology and the approach of macroscopic gravity to resolve the problem is discussed. The averaged Einstein equations of macroscopic gravity are modified on cosmological scales by the macroscopic gravitational correlation tensor terms as compared with the Einstein equations of general relativity. This correlation tensor satisfies a system of structure and field equations. An exact cosmological solution to the macroscopic gravity equations for a constant macroscopic gravitational connection correlation tensor for a flat spatially homogeneous, isotropic macroscopic space-time is presented. The correlation tensor term in the macroscopic Einstein equations has been found to take the form of either a negative or positive spatial curvature term. Thus, macroscopic gravity provides a cosmological model for a flat spatially homogeneous, isotropic Universe which obeys the dynamical law for either an open or closed Universe.
8 pages, LaTeX, ws-ijmpa.cls, few style and typo corrections. Based on the plenary talk given at the Second Stueckelberg Workshop, ICRANet Coordinating Center, Pescara, Italy, September 3-7, 2007. To appear in International Journal of Modern Physics A (2008)
References in corpus (6)
- Cosmological Solutions in Macroscopic Gravity
- Averaging in Cosmology
- Space-time Averages in Macroscopic Gravity and Volume-preserving Coordinates
- On the Domain of Applicability of General Relativity
- The Gravitational Polarization in General Relativity: Solution to Szekeres' Model of Quadrupole Polarization
- Averaging Einstein's Equations: The Linearized Case
Cited by in corpus (31)
- Does the growth of structure affect our dynamical models of the universe? The averaging, backreaction and fitting problems in cosmology
- A new framework for analyzing the effects of small scale inhomogeneities in cosmology
- Light propagation in statistically homogeneous and isotropic dust universes
- Backreaction: directions of progress
- Light propagation in statistically homogeneous and isotropic universes with general matter content
- Inhomogeneity effects in Cosmology
- Applicability of the linearly perturbed FRW metric and Newtonian cosmology
- Cosmic spherical void via coarse-graining and averaging non-spherical structures
- Backreaction and continuum limit in a closed universe filled with black holes
- A Complete Cosmological Solution to the Averaged Einstein Field Equations as found in Macroscopic Gravity
- Backreaction in Cosmology
- Black-Hole Lattices as Cosmological Models
- Post-Newtonian Celestial Dynamics in Cosmology: Field Equations
- Mori-Zwanzig formalism for general relativity: a new approach to the averaging problem
- Dynamic Field Theory and Equations of Motion in Cosmology
- Light propagation in the averaged universe
- Ricci Flow Approach to The Cosmological Constant Problem
- Backreaction mechanism in multifluid and extended cosmologies
- A Statistical Fields Theory underlying the Thermodynamics of Ricci Flow and Gravity
- Trace Anomaly, Perelman's Functionals and the Cosmological Constant
- Gauge-invariant perturbations at a quantum gravity bounce
- Averaged universe confronted with cosmological observations: A fully covariant approach
- Applications of the Hawking Energy in Inhomogeneous Cosmology
- The Ricci Flow and the Early Universe
- On the Effects of Non-metricity in an Averaged Universe
- An Almost-FLRW Universe as the Averaged Geometry in Macroscopic Gravity
- Limits on the Inferred Hubble Constant Bias from a Local McVittie Gravitational Field
- Cosmological perturbations on an averaged background
- Spherical and Plane Symmetric Solutions in Macroscopic Gravity
- Mori-Zwanzig formalism for early cosmic inflation
- Self-interaction in a cosmic dark fluid: The four-kernel rheological extension of the equations of state