TeVeS Cosmology : Covariant formalism for the background evolution and linear perturbation theory

Abstract

A relativistic theory of gravity has recently been proposed by Bekenstein, where gravity is mediated by a tensor, a vector and a scalar field, thus called TeVeS. The theory aims at modifying gravity in such a way as to reproduce Milgrom's MOdified Newtonian Dynamics (MOND) in the weak field, non-relativistic limit, which provides a framework to solve the missing mass problem in galaxies without invoking dark matter. In this paper I apply a covariant approach to formulate the cosmological equations for this theory, for both the background and linear perturbations. I derive the necessary perturbed equations for scalar, vector and tensor modes without adhering to a particular gauge. Special gauges are considered in the appendix.

33 pages, no figures, submitted to PRD

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• Cosmological Tests of Gravity
• Observational Tests of Modified Gravity
• Cosmic Microwave Weak lensing data as a test for the dark universe
• The Tensor-Vector-Scalar theory and its cosmology
• The Parameterized Post-Friedmann Framework for Theories of Modified Gravity: Concepts, Formalism and Examples
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• From galactic bars to the Hubble tension: weighing up the astrophysical evidence for Milgromian gravity
• Can Cosmic Structure form without Dark Matter?
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• Detecting a Lorentz-Violating Field in Cosmology
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• Nonlocal metric formulations of MOND with sufficient lensing
• Tests of Gravity from Imaging and Spectroscopic Surveys
• On the growth of structure in theories with a dynamical preferred frame
• Spherical Collapse in f(R) Gravity
• TeVeS gets caught on caustics
• Preferred frame parameters in the tensor-vector-scalar theory of gravity and its generalization
• The cosmological behavior of Bekenstein's modified theory of gravity
• Vertical dynamics of disk galaxies in MOND
• Cosmological fluctuation growth in bimetric MOND
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• Gravity Gets There First with Dark Matter Emulators
• Weak Lensing of Galaxy Clusters in MOND
• Galaxy-CMB Cross-Correlation as a Probe of Alternative Models of Gravity
• Three-Point Correlations in f(R) Models of Gravity
• Testing gravity theories using tensor perturbations
• Scalars, Vectors and Tensors from Metric-Affine Gravity
• Modifying Gravity: You Can't Always Get What You Want
• Tensor-vector-scalar-modified gravity: from small scale to cosmology
• Cosmological evolution of interacting dark energy in Lorentz violation
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• Nonlinearities in modified gravity cosmology I: signatures of modified gravity in the nonlinear matter power spectrum
• Gravitational instability on the brane: the role of boundary conditions
• Restricting Fourth Order Gravity via Cosmology
• The D-material universe
• Testing Alternative Theories of Dark Matter with the CMB
• Dark Matter, Modified Gravity and the Mass of the Neutrino
• Testing the tensor-vector-scalar Theory with the latest cosmological observations
• Stringy Models of Modified Gravity: Space-time defects and Structure Formation
• Cosmology of the Galileon extension of Bekenstein's theory of relativistic Modified Newtonian Dynamics
• Post-Newtonian parameters in the tensor-vector-scalar theory
• Structure Formation in Nonlocal MOND
• Modified Gravitational Equations on Braneworld with Lorentz Invariant Violation
• A Possible Late Time $\Lambda$CDM-like Background Cosmology in Relativistic MOND Theory
• Revisiting metric perturbations in tensor-vector-scalar theory
• On the problem of deformed spherical systems in Modified Newtonian Dynamics
• Power-law solutions for TeVeS
• Tensor Potential Description of Matter and Space, III. Gravitation
• The Effects of Gravitational Slip on the Higher-Order Moments of the Matter Distribution