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As an alternative to the LCDM concordance model, Scalar-Tensor-Vector Modified Gravity (MOG) theory reproduces key cosmological observations without postulating the presence of an exotic dark matter component. MOG is a field theory based on…

General Relativity and Quantum Cosmology · Physics 2015-03-17 Viktor T. Toth

We consider the cosmological consequences of a special scalar-tensor-vector theory of gravity, known as MOG (for MOdified Gravity), proposed to address the dark matter problem. This theory introduces two scalar fields $G(x)$ and $\mu(x)$,…

General Relativity and Quantum Cosmology · Physics 2018-02-14 Sara Jamali , Mahmood Roshan , Luca Amendola

Deviations from the standard $\Lambda$CDM model motivate an interpretation of early universe cosmology using the Scalar-Tensor-Vector-Gravity (STVG) theory. A constraint analysis carried out by Valentino, Melchiorri and Silk, revealed…

Cosmology and Nongalactic Astrophysics · Physics 2015-11-27 J. W. Moffat

We investigate the cosmological consequences of a scalar-vector-tensor theory of gravity known as MOG. In MOG, in addition to metric tensor, there are two scalar fields $G(x)$ and $\mu(x)$, and one vector field $\phi_{\alpha}(x)$. Using the…

General Relativity and Quantum Cosmology · Physics 2016-09-13 Sara Jamali , Mahmood Roshan

In this work, we investigate the MOdified Gravity (MOG) theory for dynamics of the universe and compare the results with the $\Lambda$CDM cosmology. We study the background cosmological properties of the MOG model and structure formation at…

Cosmology and Nongalactic Astrophysics · Physics 2021-08-17 Zahra Davari , Sohrab Rahvar

We investigate the linear cosmological perturbations in the context of the so-called energy-momentum squared gravity (EMSG) theory. Recent researches show that the EMSG theory can reproduce viable background cosmological evolution…

Cosmology and Nongalactic Astrophysics · Physics 2025-02-17 Qi-Ming Fu , Xin Zhang

We show that Scalar-Tensor-Vector Gravity (STVG-MOG) is observationally equivalent to the standard model $\Lambda$CDM cosmological model for all probes that depend on isotropic and linear gravitational dynamics, including galaxy rotation…

Cosmology and Nongalactic Astrophysics · Physics 2026-02-04 John W. Moffat

The Modified Gravity Model (MOG) has been proposed as a solution to the dark matter problem, but it does not meet the gauge invariant condition. The aim of this work is to propose a gauge-invariant theory, which suggests that symmetry can…

General Relativity and Quantum Cosmology · Physics 2023-11-02 Shahin Rouhani , Sohrab Rahvar

Our modified gravity theory (MOG) is a gravitational theory without exotic dark matter, based on an action principle. MOG has been used successfully to model astrophysical phenomena such as galaxy rotation curves, galaxy cluster masses, and…

Cosmology and Nongalactic Astrophysics · Physics 2013-06-25 J. W. Moffat , V. T. Toth

The subject of this paper is to investigate the weak regime covariant scalar-tensor-vector gravity (STVG) theory, known as the MOdified gravity (MOG) theory of gravity. First, we show that the MOG in the absence of scalar fields is…

General Relativity and Quantum Cosmology · Physics 2018-10-09 M. Khurshudyan , N. S. Mazhari , D. Momeni , R. Myrzakulov , M. Raza

The observed accelerated expansion of the Universe may be explained by dark energy or the breakdown of general relativity (GR) on cosmological scales. When the latter case, a modified gravity scenario, is considered, it is often assumed…

Cosmology and Nongalactic Astrophysics · Physics 2020-08-04 Jiro Matsumoto , Teppei Okumura , Misao Sasaki

Scalar-tensor-vector gravity, also known as modified gravity (MOG), has emerged as an alternative to General Relativity (GR). It aims to explain astrophysical phenomena without invoking dark matter. The S-stars orbiting the supermassive…

General Relativity and Quantum Cosmology · Physics 2026-05-21 Ioannis Liodis , Gernot Heissel , Rita Mastroioanni , Jai Grover , Dario Izzo

We present a fully covariant and gauge-invariant analysis of linear cosmological perturbations in Energy-Momentum Squared Gravity. Working within the 1+3 formalism, we derive the exact propagation equations for scalar, vector, and tensor…

General Relativity and Quantum Cosmology · Physics 2025-11-10 Peter K. S. Dunsby , Maria-Alexia Caldis , Eduardo Bittencourt

A covariant scalar-tensor-vector gravity theory is developed which allows the gravitational constant $G$, a vector field coupling $\omega$ and the vector field mass $\mu$ to vary with space and time. The equations of motion for a test…

General Relativity and Quantum Cosmology · Physics 2021-11-22 J. W. Moffat

We reconsider the gravitational wave spectrum induced by scalar perturbations in spatially flat Friedmann-Lema\^itre-Robertson-Walker spacetimes, focusing on the matter- and $\Lambda$-dominated epochs. During matter domination, sub-horizon…

Cosmology and Nongalactic Astrophysics · Physics 2023-03-31 Marvin Sipp , Bjoern Malte Schaefer

Viable models of modified gravity designed to produce cosmic acceleration at the current epoch, closely mimic the $\Lambda$CDM model at the level of background cosmology. However, this degeneracy is generically broken at the level of linear…

Cosmology and Nongalactic Astrophysics · Physics 2009-11-05 Alessandra Silvestri

The recent data release by the Planck satellite collaboration presents a renewed challenge for modified theories of gravitation. Such theories must be capable of reproducing the observed angular power spectrum of the cosmic microwave…

General Relativity and Quantum Cosmology · Physics 2021-04-28 J. W. Moffat , V. T. Toth

We study the evolution of matter density perturbations in the framework of massive conformal gravity (MCG). Starting from the conservation of the energy-momentum tensor, we find the continuity and Euler equations for the conformal perfect…

General Relativity and Quantum Cosmology · Physics 2026-02-03 F. F. Faria , G. S. Silva

Scalar-Tensor-Vector Gravity (STVG), also referred as MOdified Gravity (MOG), is an alternative theory of the gravitational interaction. Its weak field approximation has been successfully used to described Solar System observations, galaxy…

General Relativity and Quantum Cosmology · Physics 2017-02-02 Federico G. Lopez Armengol , Gustavo E. Romero

A modified gravitational theory explains early universe and late time cosmology, galaxy and galaxy cluster dynamics. The modified gravity (MOG) theory extends general relativity (GR) by three extra degrees of freedom: a scalar field $G$,…

General Relativity and Quantum Cosmology · Physics 2020-10-30 J. W. Moffat
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