In supergravity theories combining

general relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...

and

supersymmetry Supersymmetry is a Theory, theoretical framework in physics that suggests the existence of a symmetry between Particle physics, particles with integer Spin (physics), spin (''bosons'') and particles with half-integer spin (''fermions''). It propo ...

, the gravitino () is the gauge fermion supersymmetric partner of the hypothesized graviton. It has been suggested as a candidate for

dark matter In astronomy, dark matter is an invisible and hypothetical form of matter that does not interact with light or other electromagnetic radiation. Dark matter is implied by gravity, gravitational effects that cannot be explained by general relat ...

. If it exists, it is a

fermion In particle physics, a fermion is a subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin (spin 1/2, spin , Spin (physics)#Higher spins, spin , etc.) and obey the Pauli exclusion principle. These particles i ...

of spin and therefore obeys the Rarita–Schwinger equation. The gravitino field is conventionally written as ''ψ_μα'' with a four-vector index and a spinor index. For one would get negative norm modes, as with every massless particle of spin 1 or higher. These modes are unphysical, and for

consistency In deductive logic, a consistent theory is one that does not lead to a logical contradiction. A theory T is consistent if there is no formula \varphi such that both \varphi and its negation \lnot\varphi are elements of the set of consequences ...

there must be a gauge symmetry which cancels these modes: , where ''ε_α''(''x'') is a spinor function of spacetime. This gauge symmetry is a local

transformation, and the resulting theory is supergravity. Thus the gravitino is the fermion mediating supergravity interactions, just as the

photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that can ...

is mediating

electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...

, and the graviton is presumably mediating

gravitation In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...

. Whenever supersymmetry is broken in supergravity theories, it acquires a mass which is determined by the scale at which supersymmetry is broken. This varies greatly between different models of supersymmetry breaking, but if supersymmetry is to solve the hierarchy problem of the

Standard Model The Standard Model of particle physics is the Scientific theory, theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions – excluding gravity) in the unive ...

, the gravitino cannot be more massive than about 1 TeV/c².

History

Murray Gell-Mann Murray Gell-Mann (; September 15, 1929 – May 24, 2019) was an American theoretical physicist who played a preeminent role in the development of the theory of elementary particles. Gell-Mann introduced the concept of quarks as the funda ...

and Peter van Nieuwenhuizen intended the spin-3/2 particle associated with supergravity to be called the 'hemitrion', meaning 'half-3', however the editors of '' Physical Review'' were not keen on the name and instead suggested 'massless Rarita–Schwinger particle' for their 1977 publication. The current name of gravitino was instead suggested by Sidney Coleman and Heinz Pagels, although this term was originally coined in 1954 by Felix Pirani to describe a class of negative energy excitations with zero rest mass.

Gravitino cosmological problem

If the gravitino indeed has a mass of the order of TeV, then it creates a problem in the standard model of cosmology, at least naïvely. One option is that the gravitino is stable. This would be the case if the gravitino is the lightest supersymmetric particle and R-parity is conserved (or nearly so). In this case the gravitino is a candidate for

; as such gravitinos will have been created in the very early universe. However, one may calculate the density of gravitinos and it turns out to be much higher than the observed

density. The other option is that the gravitino is unstable. Thus the gravitinos mentioned above would decay and will not contribute to the observed

density. However, since they decay only through gravitational interactions, their lifetime would be very long, of the order of in natural units, where ''M''_pl is the Planck mass and ''m'' is the mass of a gravitino. For a gravitino mass of the order of TeV this would be , much later than the era of nucleosynthesis. At least one possible channel of decay must include either a

, a charged lepton or a

meson In particle physics, a meson () is a type of hadronic subatomic particle composed of an equal number of quarks and antiquarks, usually one of each, bound together by the strong interaction. Because mesons are composed of quark subparticles, the ...

, each of which would be energetic enough to destroy a nucleus if it strikes one. One can show that enough such energetic particles will be created in the decay as to destroy almost all the nuclei created in the era of nucleosynthesis, in contrast with observations. In fact, in such a case the universe would have been made of

hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...

alone, and

star formation Star formation is the process by which dense regions within molecular clouds in interstellar space—sometimes referred to as "stellar nurseries" or "star-forming regions"—Jeans instability, collapse and form stars. As a branch of astronomy, sta ...

would probably be impossible. One possible solution to the cosmological gravitino problem is the split supersymmetry model, where the gravitino mass is much higher than the TeV scale, but other fermionic supersymmetric partners of standard model particles already appear at this scale. Another solution is that R-parity is slightly violated and the gravitino is the lightest supersymmetric particle. This causes almost all supersymmetric particles in the early Universe to decay into Standard Model particles via R-parity violating interactions well before the synthesis of primordial nuclei; a small fraction however decay into gravitinos, whose half-life is orders of magnitude greater than the age of the Universe due to the suppression of the decay rate by the Planck scale and the small R-parity violating couplings.

References

{{Authority control Fermions Quantum gravity Supersymmetry Hypothetical elementary particles

History

Gravitino cosmological problem

See also

References