Updated December 17, 2023

*Image: JWST NASA's James Webb Space Telescope (Public domain). *

The vast majority of the Universe (70%) is in an unknown form.

Under the standard ΛCDM (Lambda Cold Dark Matter) model, the accelerated expansion of the universe is attributed to a form of dark energy, generally called dark energy. The standard ΛCDM model is the most accepted cosmological model in 2023. It describes the universe as being composed of 68% dark energy, 27% dark matter, and 5% ordinary matter. Dark energy is absolutely everywhere.

The ΛCDM model is compatible with a wide range of observations, including Hubble's law, the distribution of galaxies and the composition of the universe. However, it poses some theoretical problems, including the nature of dark energy and the fact that it makes up such a large fraction of the universe.

The explanation can simply come from the cosmological constant induced by general relativity which would have a non-zero value.

This constant Λ, added by Albert Einstein to his equations of general relativity (1915), in February 1917, explains this expansion provided that it is given a very precise value.

For some cosmologists this is not satisfactory, which is why they look beyond it.

There are a large number of alternative theories or extensions of the model that seek to explain this acceleration in different ways.

These alternative theories have been proposed to explain the expansion of the universe without involving dark energy. They can be classified into two categories: those which modify the composition of the universe and those which modify the theory of gravitation.

• **Quintessence** posits the existence of a dynamic scalar field, called the quintessence field, which fills the universe with energy that evolves over time. This development may lead to changes in the acceleration of the expansion of the universe during cosmic epochs.

• **K-essence** implies the existence of a dynamic scalar field that fills the universe. Unlike a scalar field with a simple equation of state (like that associated with a quintessence field), the K-essence field can have a more complex equation of state.

• The **Phantom dark energy** resides in a "phantom" state equation where the density of dark energy increases with time, which leads to an acceleration of the expansion of the universe which becomes faster and faster. Unlike standard dark energy which leads to accelerated but limited expansion, phantom dark energy suggests expansion which becomes infinite in a finite time, which may have interesting and speculative implications for the ultimate fate of the universe. .

• The **Coupled Quintessence** explains the observed acceleration of the expansion of the universe, by introducing additional degrees of freedom compared to the simple cosmological constant Λ of the ΛCDM model.

• **Chaplygin gas** introduces a negative pressure associated with the Chaplygin equation of state. It could lead to a repulsive force, thus simulating the effect of dark energy.

• **Janus** is a cosmological theory proposed by the physicist Julian Barbour. The key idea is to consider that time is not a fundamental entity, but rather an emergent concept. Barbour proposes that the time we perceive results from a particular symmetry, called Janus symmetry, which links the preferential states of two mirror universes. These two universes are described by theory, and Janus symmetry connects them in such a way that a concept of time emerges in each of them.

• **Janus-Petit**, is based on the same principles as Barbour's original theory, but it introduces a new hypothesis. Petit's hypothesis is that the negative metric of Janus theory is associated with a form of matter or energy that exists in an additional dimension. This additional dimension is hidden from our observation, but it interacts with the spatial dimension that we perceive.

• The **Gauss-Bonnet** theory is an extension of general relativity that includes additional terms in the gravitational field equations. More precisely, it incorporates the Gauss-Bonnet term, which is a particular combination of quadratic curvature terms in the gravitational action.

• The **Einstein-Æther** theory is an alternative approach to Albert Einstein's general relativity. It proposes a modification of the theory of gravity by introducing a vector field, called the Aether field, which is a unit vector linked to space-time. This theory was developed to explore scenarios where Lorentz symmetry (which describes the invariance of physical laws under Lorentz transformations) can be spontaneously broken.

• **Cascading Gravity** is based on the idea that the space-time we observe can contain several additional dimensions, beyond the four dimensions we commonly perceive (three spatial dimensions and one temporal dimension). . These additional dimensions are compacted on a very small scale, and it is their influence on the cosmological scale that is explored in this theory.

• **The Fab Four** is a cosmological theory proposed by physicists John Moffat and Paul Wesson. It is based on the idea that the expansion of the universe is due to the presence of a new form of matter or energy, called "Wesson matter".

• The **Galileon** theory is a class of scalar field theories in the context of gravity that generalizes the symmetry properties of Galileo. The name "Galileon" comes from the fact that these theories share similar symmetries to Galilean motion in classical mechanics.

• The **DGP** theory (Dvali-Gabadadze-Porrati) is a theory of gravity that was formulated by Gia Dvali, Gregory Gabadadze, and Massimo Porrati in the 2000s. The main feature of DGP theory is the introduction of additional dimensions of spacetime, in addition to the four dimensions we commonly observe (three spatial dimensions and one temporal dimension). These extra dimensions are often called "branes" (short for membranes) in the context of string theory and extra dimensions.

• The **Brans-Dicke** theory was designed to explore possibilities beyond standard Einsteinian gravity, by introducing an additional scalar field (sometimes called a "dilaton") into the gravity equations.

• **Bigravity** is a theoretical proposition in the field of physics that explores the possibility that gravity results from the interaction of two distinct gravitational fields rather than just one.

• The **Horndeski** theory is a special class of alternative gravity theories that encompasses scalar-tensor gravity models. It was formulated by Gregory Horndeski in 1974 and is characterized by the presence of a fifth force, distinct from standard Newtonian gravity, which arises from a scalar field not minimally coupled to gravity.

• The **f(R)** theory is a class of modified gravity theories that generalizes Einstein's gravity by introducing an arbitrary function f(R) into the field equations. The theory f(R) assumes that the curvature constant of general relativity is a function of the curvature of spacetime. This means that gravitation can be different at different scales.

• **Massive gravity** is an extension of Einstein's general gravity which explores the possibility that the particles responsible for transmitting gravitational force, called gravitons, have non-zero mass. Unlike general gravity, where gravitons are considered massless, massive gravity proposes that these particles have a certain mass.

• The **Randall-Sundrum** theory proposes an extension to the usual dimension of space-time by including an additional dimension, often called a "compact" additional dimension. The main features of the theory are described in two models, generally referred to as RS1 and RS2.

Scientists do not lack creativity. There are many other alternative theories in the field of theoretical physics and cosmology, seeking to explain phenomena such as dark energy or the accelerating expansion of the universe. Some of these theories are more speculative than others and may have implications beyond current observations.

Research in these areas is active, but no alternative theory has yet been widely accepted as a complete and definitive explanation of phenomena observed in the universe. However, they represent a promising way to resolve the theoretical problems of the ΛCDM model.

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