On the question of measuring spatial curvature in an inhomogeneous universe

Abstract

The curvature of a spacetime, either in a topological sense, or averaged over super-horizon-sized patches, is often equated with the global curvature term that appears in Friedmann's equation. In general, however, the Universe is inhomogeneous, and gravity is a nonlinear theory, thus any curvature perturbations violate the assumptions of the FLRW model; it is not necessarily true that local curvature, averaged over patches of constant-time surfaces, will reproduce the observational effects of global symmetry. Further, the curvature of a constant-time hypersurface is not an observable quantity, and can only be inferred indirectly. Here, we examine the behavior of curvature modes on hypersurfaces of an inhomogeneous spacetime non-perturbatively in a numerical relativistic setting, and how this curvature corresponds with that inferred by observers. We also note the point at which observations become sensitive to the impact of curvature sourced by inhomogeneities on inferred average properties, finding general agreement with past literature.

arXiv comment15 pages, 10 figures

References in corpus (44)

• Efficient Computation of CMB anisotropies in closed FRW models
• Cosmological parameters from CMB and other data: a Monte-Carlo approach
• The Complete Light-curve Sample of Spectroscopically Confirmed Type Ia Supernovae from Pan-STARRS1 and Cosmological Constraints from The Combined Pantheon Sample
• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• On the Numerical Integration of Einstein's Field Equations
• Cosmic Topology
• Hubble Parameter and Baryon Acoustic Oscillation Measurement Constraints on the Hubble Constant, the Deviation from the Spatially-Flat $\Lambda$cdm Model, The Deceleration-Acceleration Transition Redshift, and Spatial Curvature
• A general test of the Copernican Principle
• General Cosmography Model with Spatial Curvature
• Topology and the Cosmic Microwave Background
• Effects of nonlinear inhomogeneity on the cosmic expansion with numerical relativity
• Departures from the FLRW Cosmological Model in an Inhomogeneous Universe: A Numerical Examination
• Constraints on backreaction in dust universes
• A Lockdown Perspective on the Hubble Tension (with comments from the SH0ES team)
• Emerging spatial curvature can resolve the tension between high-redshift CMB and low-redshift distance ladder measurements of the Hubble constant
• Evaluating backreaction with the peak model of structure formation
• How flat can you get? A model comparison perspective on the curvature of the Universe
• Average expansion rate and light propagation in a cosmological Tardis spacetime
• Topological Lensing in Spherical Spaces
• Spatial Curvature Falsifies Eternal Inflation
• Can COBE see the shape of the universe?
• Einstein's Universe: Cosmological structure formation in numerical relativity
• Integration of inhomogeneous cosmological spacetimes in the BSSN formalism
• On Precision Measurement of the Mean Curvature
• Simulating Cosmic Microwave Background maps in multi-connected spaces
• Bias and scatter in the Hubble diagram from cosmological large-scale structure
• Spatial curvature and cosmological tests of general relativity
• Constraints on the Topology of the Universe: Extension to General Geometries
• Solving the curvature and Hubble parameter inconsistencies through structure formation-induced curvature
• Another look at redshift drift and the backreaction conjecture
• Model independent constraints on the cosmological expansion rate
• Redshift and distances in a ΛCDM cosmology with non-linear inhomogeneities
• The trouble with Hubble: Local versus global expansion rates in inhomogeneous cosmological simulations with numerical relativity
• Comparing Fully General Relativistic and Newtonian Calculations of Structure Formation
• Relativistic numerical cosmology with Silent Universes
• The Limited Accuracy of Linearized Gravity
• Light propagation through black-hole lattices
• Towards statistically homogeneous and isotropic perfect fluid universes with cosmic backreaction
• General Relativistic Corrections to the Weak Lensing Convergence Power Spectrum
• Kinematic Constraints on Spatial Curvature from Supernovae Ia and Cosmic Chronometers
• Topological lens effects in universes with non-Euclidean compact spatial sections
• Dynamical spatial curvature as a fit to type Ia supernovae
• Emergence of spatial curvature
• Light path averages in spacetimes with non-vanishing average spatial curvature

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• Is the Observable Universe Consistent with the Cosmological Principle?
• What is flat ΛCDM, and may we choose it?
• Cosmological distances with general-relativistic ray tracing: framework and comparison to cosmographic predictions
• Cosmology using numerical relativity
• First investigation of void statistics in numerical relativity simulations
• The art of building a smooth cosmic distance ladder in a perturbed universe
• EBWeyl: a Code to Invariantly Characterize Numerical Spacetimes
• Remarks on overestimating the effects of inhomogeneities on the Hubble constant
• Spatial anisotropies from long wavelength scalar and tensor modes
• Backreaction and the Role of Spatial Curvature in the Cosmic Neighborhood