Parameterized Post-Newtonian Cosmology

Abstract

Einstein's theory of gravity has been extensively tested on solar system scales, and for isolated astrophysical systems, using the perturbative framework known as the parameterized post-Newtonian (PPN) formalism. This framework is designed for use in the weak-field and slow-motion limit of gravity, and can be used to constrain a large class of metric theories of gravity with data collected from the aforementioned systems. Given the potential of future surveys to probe cosmological scales to high precision, it is a topic of much contemporary interest to construct a similar framework to link Einstein's theory of gravity and its alternatives to observations on cosmological scales. Our approach to this problem is to adapt and extend the existing PPN formalism for use in cosmology. We derive a set of equations that use the same parameters to consistently model both weak fields and cosmology. This allows us to parameterize a large class of modified theories of gravity and dark energy models on cosmological scales, using just four functions of time. These four functions can be directly linked to the background expansion of the universe, first-order cosmological perturbations, and the weak-field limit of the theory. They also reduce to the standard PPN parameters on solar system scales. We illustrate how dark energy models and scalar-tensor and vector-tensor theories of gravity fit into this framework, which we refer to as "parameterized post-Newtonian cosmology" (PPNC).

30 pages, no figures, v2: matches published version

References in corpus (54)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Planck 2015 results. XIII. Cosmological parameters
• Dynamics of dark energy
• Modified Gravity and Cosmology
• The Confrontation between General Relativity and Experiment
• The Supernova Legacy Survey: Measurement of Omega_M, Omega_Lambda and w from the First Year Data Set
• Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples
• The Hubble Space Telescope Cluster Supernova Survey: V. Improving the Dark Energy Constraints Above z>1 and Building an Early-Type-Hosted Supernova Sample
• Chameleon Fields: Awaiting Surprises for Tests of Gravity in Space
• Chameleon Cosmology
• Beyond the Cosmological Standard Model
• Gravity Probe B: Final Results of a Space Experiment to Test General Relativity
• The Effective Field Theory of Dark Energy
• A Parameterized Post-Friedmann Framework for Modified Gravity
• Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity
• An introduction to the Vainshtein mechanism
• Dark Energy or Modified Gravity? An Effective Field Theory Approach
• Backreaction in late-time cosmology
• Hubble Space Telescope and Ground-Based Observations of Type Ia Supernovae at Redshift 0.5: Cosmological Implications
• The Parameterized Post-Friedmann Framework for Theories of Modified Gravity: Concepts, Formalism and Examples
• Junction Conditions in f(R) Theories of Gravity
• Effective Field Theory of Cosmological Perturbations
• Parametrized Post-Friedmann Signatures of Acceleration in the CMB
• Effective action approach to cosmological perturbations in dark energy and modified gravity
• Towards a fully consistent parameterization of modified gravity
• Geometrical Constraint on Curvature with BAO experiments
• An exact quantification of backreaction in relativistic cosmology
• Black Hole Universe: Time Evolution
• Evolution of a periodic eight-black-hole lattice in numerical relativity
• The Parameterised Post-Newtonian Limit of Fourth-Order Theories of Gravity
• A sub-horizon framework for probing the relationship between the cosmological matter distribution and metric perturbations
• Consistent cosmological modifications to the Einstein equations
• A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories
• On the absence of the usual weak-field limit, and the impossibility of embedding some known solutions for isolated masses in cosmologies with f(R) dark energy
• Black Hole Universe: Construction and Analysis of Initial Data
• Evolution of a family of expanding cubic black-hole lattices in numerical relativity
• Black Hole Universe with $\Lambda$
• Cosmology Without Averaging
• Backreaction and continuum limit in a closed universe filled with black holes
• Parameterizing dark sector perturbations via equations of state
• Post-Newtonian Cosmological Modelling
• The Parametrized Post-Newtonian-Vainshteinian Formalism
• Solving the Einstein constraints in periodic spaces with a multigrid approach
• Relativistic Perihelion Precession of Orbits of Venus and the Earth
• Back-Reaction in Relativistic Cosmology
• Cosmological backreaction in the presence of radiation and a cosmological constant
• Piecewise Silence in Discrete Cosmological Models
• On the vacuum Einstein equations along curves with a discrete local rotational and reflection symmetry
• Nonlinear effects of general relativity from multiscale structure
• On the Emergence of Accelerating Cosmic Expansion in f(R) Theories of Gravity
• The Parameterised Post-Newtonian Limit of Bimetric Theories of Gravity
• The Magnetic Part of the Weyl Tensor, and the Expansion of Discrete Universes
• Cosmic Acceleration and Brans-Dicke Theory

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• Gauge-invariant approach to the parametrized post-Newtonian formalism
• xPPN: An implementation of the parametrized post-Newtonian formalism using xAct for Mathematica
• Will-Nordtvedt PPN formalism applied to renormalization group extensions of general relativity
• Scale-Dependent Gravitational Couplings in Parameterised Post-Newtonian Cosmology
• Multi-Scale Perturbation Theory I: Methodology and Leading-Order Bispectrum Corrections in the Matter-Dominated Era
• Quasilocal Newtonian limit of general relativity and galactic dynamics
• The momentum constraint equation in Parameterised Post-Newtonian Cosmology
• Consistent cosmological structure formation on all scales in relativistic extensions of MOND
• Construction of the cosmological model with periodically distributed inhomogeneities with growing amplitude
• A New Paradigm for Testing Gravity: Theory-Independent Constraints Using Data From All Astrophysical and Cosmological Scales
• A viable relativistic scalar theory of gravitation
• Parametrized post-Newtonian formalism in higher-order Teleparallel Gravity