The existence of anomalous astrophysical and cosmological phenomena like the cosmic acceleration and the dynamics of clusters of galaxies and gas in galaxies themselves recently
boosted the growth of several long-range modifications of the usual laws of gravitation

Gravitation

Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

. Indeed, the aforementioned phenomena did not found satisfactorily explanations
in terms of the standard Newton

Isaac Newton

Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

–Einstein

Albert Einstein

Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

 gravitational physics, unless exotic and still undetected forms of matter

Matter

Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...

-energy

Energy

In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

 are postulated. Examples of such entities are, e.g, dark matter

Dark matter

In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...

 and dark energy

Dark energy

In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...

, identified with the Cosmological Constant

Cosmological constant

In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...

. At galactic scales, the most famous modified model of gravity is, perhaps, the MOdified Newtonian Dynamics (MOND

Mond

Mond may refer to:* MOND - Modified Newtonian Dynamics. A proposed adjustment to the classical inverse-square law of gravity.* Der Mond, an opera in one act* Mond Nickel Company, a defunct mining company...

) proposed in 1983 by Mordehai Milgrom

Mordehai Milgrom

Mordehai Milgrom is an Israeli physicist and professor in the department of Condensed Matter Physics at the Weizmann Institute in Rehovot, Israel. He is most famous for his proposal of Modified Newtonian dynamics as an alternative to the dark matter and galaxy rotation curve problems, in 1981...

 . More recently, also the MOdified Gravity (MOG) by John Moffat

John Moffat

John W. Moffat is a Professor Emeritus in physics at the University of Toronto.He is also an adjunct Professor in physics at the University of Waterloo and a resident affiliate member of the Perimeter Institute for Theoretical Physics....

  took place.

MOND and MOG

While MOND

Mond

Mond may refer to:* MOND - Modified Newtonian Dynamics. A proposed adjustment to the classical inverse-square law of gravity.* Der Mond, an opera in one act* Mond Nickel Company, a defunct mining company...

 modifies Newton's inverse square law at a characteristic acceleration

Acceleration

In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...

 scale , MOG's modifications occur at large distances, i.e. MOG is a length scale-dependent model.

DGP model

Another proposal to accommodate the cosmic acceleration without invoking the concept of dark energy

Dark energy

In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...

 is the multidimensional braneworld model by Gia Dvali

Gia Dvali

Georgi Dvali is a professor of physics at LMU Munich and a director at the Max Planck Institute for Physics. He received his Ph.D. in high energy physics and cosmology from Tbilisi State University, Georgia in 1992...

, Gregory Gabadadze

Gregory Gabadadze

Gregory Gabadadze is a Georgian theoretical physicist. He is currently member of the Department of Physics at New York University. He is known for the Dvali-Gabadadze-Porrati multidimensional braneworld model of gravity, also known as DGP model....

 and Massimo Porrati

Massimo Porrati

Massimo Porrati is a professor of physics, and a member of the Center for Cosmology and Particle Physics, at New York University. He graduated from the Scuola Normale Superiore di Pisa, Italy with a "Diploma di Scienze" degree in 1985. Later he worked as a postdoctoral fellow at UCLA and UC...

 (DGP model

DGP model

The DGP model is a model of gravity proposed by Gia Dvali, Gregory Gabadadze, and Massimo Porrati in 2000. The model is popular among some model builders, but has resisted being embedded into string theory....

). In it our ordinary space-time is a 3+1 dimensional brane embedded in a five-dimensional bulk space.