According to the standard model of cosmology, also known as ΛCDM (Lambda Cold Dark Matter) model, about 95% of our Universe is invisible or undetectable, or possibly both. Various alternative models have been proposed to describe our Universe without the need of dark matter or dark energy. One of them, called Modified Gravity (MOG) does not require either dark matter or dark energy. So far, it seems to be consistent with observational data.

The need for dark matter and dark energy appeared with various observations. Rotational speeds of galaxies, or gravitational lensing by galaxy clusters for example, are very well explained by the presence of some invisible, transparent dark matter. The observation of type Ia supernovae showed that the Universe seems to be expanding at an accelerating rate: cosmologists concluded that some form of energy acting repulsively caused the acceleration of the expansion. They called it dark energy. The nature of both dark matter and dark energy remains completely unknown today.

Because the standard model is in very good agreement with observations, any attempt to give an alternative explanation will have to match observations at least as well as the ΛCDM model does.

Scalar-tensor-vector gravity (STVG) theory, often referred to as MOG (MOdified Gravity), was developed by John Moffat, from the Perimeter Institute for Theoretical Physics in Waterloo, Ontario. It is a fully relativistic theory of gravitation that is derived from the action principle, which does not require any dark matter or dark energy. MOG postulates the existence of a massive vector field, which is motivated by the desire to introduce a repulsive modification of the law of gravitation at short range. In other words, far from a source gravity is stronger than the Newtonian prediction; at shorter distances, it is counteracted by a repulsive “fifth force” due to the vector field.

So far, MOG has been able to account for a range of key cosmological observations: galaxy rotation curves, galaxy cluster masses, lensing, the distribution of mass in the Universe (matter power spectrum), and the acoustic peaks in the cosmic microwave background radiation (CMB).

Regarding the matter power spectrum, MOG and the ΛCDM model notably differ: while the ΛCDM cosmology shows a significant dampening of baryonic oscillations, these are present in MOG. The current resolution of the available data is not high enough to tell whether these oscillations are here: as galaxy surveys are growing in size, the resolution will improve and tell if MOG is correct.

It is also important to note that the angular power spectrum of the CMB was calculated using a semi-analytical approximation. This is not as accurate as numerical software, which is generally used: in the case of MOG, these software packages cannot be easily adapted. However, the results of the semi-analytical approach achieves agreement with observational data.

Additionally, on the scale of the solar system, MOG predicts no deviation from the previous results of Newton and Einstein.

Curiously, while MOG may be able to describe our Universe without requiring any additional dark component, the theory doesn’t seem to be as popular as other alternatives like MOND (which actually fails at describing various cosmological observations, such as gravitational lensing)… Finally, further studies to obtain interior solutions to the MOG field equations and the development of N-body simulations, may be able to show MOG as a solid and exciting alternative to the standard model of cosmology.



Moffat, J. W. (2006). Scalar-Tensor-Vector Gravity TheoryJournal of Cosmology and Astroparticle Physics.  doi:10.1088/1475-7516/2006/03/004  arXiv:gr-qc/0506021v7

Moffat, J. W. (2010). Modified gravity or dark matter? arXiv:1101.1935v2

Moffat, J. W., Toth, V. T. (2011). Cosmological observations in a modified theory of gravity (MOG). arXiv:1104.2957v1

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