Expansion, Geometry, and Gravity

Abstract

In general-relativistic cosmological models, the expansion history, matter content, and geometry are closely intertwined. In this brief paper, we clarify the distinction between the effects of geometry and expansion history on the luminosity distance. We show that the cubic correction to the Hubble law, measured recently with high-redshift supernovae, is the first cosmological measurement, apart from the cosmic microwave background, that probes directly the effects of spatial curvature. We illustrate the distinction between geometry and expansion with a toy model for which the supernova results already indicate a curvature radius larger than the Hubble distance.

4 pages, 1 color figure

References in corpus (24)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution
• Cosmological Imprint of an Energy Component with General Equation of State
• A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state
• Discovery of a Supernova Explosion at Half the Age of the Universe and its Cosmological Implications
• A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation
• Phantom Energy and Cosmic Doomsday
• Cosmological Results from High-z Supernovae
• The High-Z Supernova Search: Measuring Cosmic Deceleration and Global Cur vature of the Universe Using Type Ia Supernovae
• MAXIMA-1: A Measurement of the Cosmic Microwave Background Anisotropy on angular scales of 10 arcminutes to 5 degrees
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Inflation
• Supernova Limits on the Cosmic Equation of State
• DASI First Results: A Measurement of the Cosmic Microwave Background Angular Power Spectrum
• CDM Models with a Smooth Component
• The cosmon model for an asymptotically vanishing time-dependent cosmological ``constant''
• A Measurement of the Angular Power Spectrum of the CMB from l = 100 to 400
• The Anisotropy of the Microwave Background to l = 3500: Deep Field Observations with the Cosmic Background Imager
• Dynamical Lambda Models of Structure Formation
• The Luminosity Distance, the Equation of State, and the Geometry of the Universe
• Small-Scale Cosmic Microwave Background Anisotropies as a Probe of the Geometry of the Universe
• Cosmology in a String-Dominated Universe
• Estimates of Cosmological Parameters Using the CMB Angular Power Spectrum of ACBAR
• A Low-Density Closed Universe

Cited by in corpus (60)

• The Carnegie-Chicago Hubble Program. VIII. An Independent Determination of the Hubble Constant Based on the Tip of the Red Giant Branch
• Reconciling dark energy models with f(R) theories
• The Physics of Cosmic Acceleration
• Cosmography: Cosmology without the Einstein equations
• A kinematical approach to dark energy studies
• Cosmic dynamics in the era of Extremely Large Telescopes
• Cosmography and constraints on the equation of state of the Universe in various parametrizations
• Safety in numbers: Gravitational Lensing Degradation of the Luminosity Distance-Redshift Relation
• Interacting holographic dark energy
• The dark degeneracy: On the number and nature of dark components
• The Carnegie Supernova Project: First Near-Infrared Hubble Diagram to z~0.7
• Probing for dynamics of dark energy and curvature of universe with latest cosmological observations
• Cosmographic Hubble fits to the supernova data
• Statefinders, higher-order energy conditions and sudden future singularities
• The Holographic dark energy reexamined
• Phantom Friedmann Cosmologies and Higher-Order Characteristics of Expansion
• New holographic scalar field models of dark energy in non-flat universe
• Probing the cosmographic parameters to distinguish between dark energy and modified gravity models
• Cosmological model with energy transfer
• Rational approximations of $f(R)$ cosmography through Padé polynomials
• Curvature constraints from Large Scale Structure
• Interacting new agegraphic tachyon, K-essence and dilaton scalar field models of dark energy in non-flat universe
• On Precision Measurement of the Mean Curvature
• Interacting Ricci Dark Energy with Logarithmic Correction
• Non-parametric reconstruction of the cosmological \textit{jerk} parameter
• High-redshift cosmography: Application and comparison with different methods
• Unified universe history through phantom extended Chaplygin gas
• Exploring scalar field dynamics with Gaussian processes
• Cosmic Behavior, Statefinder Diagnostic and $w-w^{\prime }$ Analysis for Interacting NADE model in Non-flat Universe
• Holographic dark energy in a non-flat universe with Granda-Oliveros cut-off
• Redshift drift in varying speed of light cosmology
• Can high-redshift Hubble diagrams rule out the standard model of cosmology in the context of cosmographic method?
• Cosmological tests of sudden future singularities
• Cosmography: Extracting the Hubble series from the supernova data
• Geometrical Constraints on Dark Energy
• Testing flatness of the universe with probes of cosmic distances and growth
• Testing cosmic anisotropy with Pade approximation and Pantheon+ sample
• Gibbons-Hawking Boundary Terms and Junction Conditions for Higher-Order Brane Gravity Models
• A statefinder luminosity distance formula in varying speed of light cosmology
• Interacting entropy-corrected holographic dark energy with apparent horizon as an infrared cutoff
• Future state of the Universe
• Is dark energy evolving?
• Interacting entropy-corrected holographic scalar field models in non-flat universe
• Interacting generalized ghost dark energy in non-flat universe
• Joint Constraints on the Hubble Constant, Spatial Curvature, and Sound Horizon from the Late-time Universe with Cosmography
• Constraints on Cosmographic Functions of Cosmic Chronometers Data Using Gaussian Processes
• Angular distribution of cosmological parameters as a probe of inhomogeneities: a kinematic parametrisation
• Dark-energy dependent test of general relativity at cosmological scales
• Dodging the dark matter degeneracy while determining the dynamics of dark energy
• Ghost dark energy with sign-changeable interaction term
• Reconstructions of $f(\mathcal{P})$ and $f(\mathcal{Q})$ gravity models from $(m,n)$-type Barrow Holographic Dark Energy: Analysis and Observational Constraints
• Spacetime averaging of exotic singularity universes
• Non-exotic conformal structure of weak exotic singularities
• Statefinders and observational measurement of superenergy
• Cosmic Acceleration in a Model of Fourth Order Gravity
• The Energy Density of "Wound" Fields in a Toroidal Universe
• Reconstructions of Einstein-Aether Gravity from Barrow Agegraphic and New Barrow Agegraphic Dark Energy models: Examinations and Observational Limits
• Quarkonia and heavy flavors at the LHC
• Observational Imprints of Our Lost Twin Anti-Universe
• Cosmological models with Big rip and Pseudo rip Scenarios in extended theory of gravity