Measuring Space-Time Geometry over the Ages

Abstract

Theorists are often told to express things in the "observational plane". One can do this for space-time geometry, considering "visual" observations of matter in our universe by a single observer over time, with no assumptions about isometries, initial conditions, nor any particular relation between matter and geometry, such as Einstein's equations. Using observables as coordinates naturally leads to a parametrization of space-time geometry in terms of other observables, which in turn prescribes an observational program to measure the geometry. Under the assumption of vorticity-free matter flow we describe this observational program, which includes measurements of gravitational lensing, proper motion, and redshift drift. Only 15% of the curvature information can be extracted without long time baseline observations, and this increases to 35% with observations that will take decades. The rest would likely require centuries of observations. The formalism developed is exact, non-perturbative, and more general than the usual cosmological analysis.

Originally written for the Gravity Research Foundation 2012 Awards for Essays on Gravitation and received Honorable Mention

References in corpus (6)

• Weak Gravitational Lensing
• Dark Energy and the Accelerating Universe
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Power Spectra and WMAP-Derived Parameters
• The Hubble Constant
• Direct Measurement of Cosmological Parameters from the Cosmic Deceleration of Extragalactic Objects
• Gamma-Ray Bursts From Neutron Star Phase Transitions

Cited by in corpus (9)

• Observables and unobservables in dark energy cosmologies
• Giving Cosmic Redshift Drift a Whirl
• Forecasts of redshift drift constraints on cosmological parameters
• The Copernican principle in light of the latest cosmological data
• Redshift drift of gravitational lensing
• Measuring the Homogeneity of the Universe Using Polarization Drift
• A first model-independent radial BAO constraint from the final BOSS sample
• Spectral Distortion in a Radially Inhomogeneous Cosmology
• Quasilinear observables in dark energy cosmologies