# Quintessence (physics)

In physics, quintessence is a hypothetical form of dark energy, more precisely a scalar field, postulated as an explanation of the observation of an accelerating rate of expansion of the universe. The first example of this scenario was proposed by Ratra and Peebles (1988).[1] The concept was expanded to more general types of time-varying dark energy and the term "quintessence" was first introduced in a paper by Robert R. Caldwell, Rahul Dave and Paul Steinhardt.[2] It has been proposed by some physicists to be a fifth fundamental force.[3][4][5] Quintessence differs from the cosmological constant explanation of dark energy in that it is dynamic; that is, it changes over time, unlike the cosmological constant which, by definition, does not change. Quintessence can be either attractive or repulsive depending on the ratio of its kinetic and potential energy. Those working with this postulate believe that quintessence became repulsive about ten billion years ago, about 3.5 billion years after the Big Bang.[6]

## Scalar field

Quintessence (Q) is a scalar field with an equation of state where wq, the ratio of pressure pq and density ${\displaystyle \rho }$q, is given by the potential energy ${\displaystyle V(Q)}$ and a kinetic term:

${\displaystyle w_{q}={\frac {p_{q}}{\rho _{q}}}={\frac {{\frac {1}{2}}{\dot {Q}}^{2}-V(Q)}{{\frac {1}{2}}{\dot {Q}}^{2}+V(Q)}}}$

Hence, quintessence is dynamic, and generally has a density and wq parameter that varies with time. By contrast, a cosmological constant is static, with a fixed energy density and wq = 1.

## Tracker behavior

Many models of quintessence have a tracker behavior, which according to Ratra and Peebles (1988) and Paul Steinhardt et al. (1999) partly solves the cosmological constant problem.[7] In these models, the quintessence field has a density which closely tracks (but is less than) the radiation density until matter-radiation equality, which triggers quintessence to start having characteristics similar to dark energy, eventually dominating the universe. This naturally sets the low scale of the dark energy.[8] When comparing the predicted expansion rate of the universe as given by the tracker solutions with cosmological data, a main feature of tracker solutions is that one needs four parameters to properly describe the behavior of their equation of state,[9][10] whereas it has been shown that at most a two-parameter model can optimally be constrained by mid-term future data (horizon 2015–2020).[11]

## Specific models

Some special cases of quintessence are phantom energy, in which wq < 1,[12] and k-essence (short for kinetic quintessence), which has a non-standard form of kinetic energy. If this type of energy were to exist, it would cause a big rip[13] in the universe due to the growing energy density of dark energy which would cause the expansion of the universe to increase at a faster-than-exponential rate.

### Holographic dark energy

Holographic dark energy models compared with cosmological constant models, imply a high degeneracy.[14] It has been suggested that dark energy might originate from quantum fluctuations of spacetime, and are limited by the event horizon of the universe.[15]

Studies with quintessence dark energy found that it dominates gravitational collapse in a spacetime simulation, based on the holographic thermalization. These results show that the smaller the state parameter of quintessence is, the harder it is for the plasma to thermalize.[16]

## Quintom scenario

In 2004, when scientists fitted the evolution of dark energy with the cosmological data, they found that the equation of state had possibly crossed the cosmological constant boundary (w = –1) from above to below. A proven no-go theorem indicates this situation, called the Quintom scenario, requires at least two degrees of freedom for dark energy models.[17]

## Terminology

The name comes from quinta essentia (fifth element) so called in Latin starting from the Middle Ages, was the element added by Aristotle to the other four ancient classical elements, because he thought it was the essence of the celestial world. Aristotle called this element aether, that had to be a pure, fine and primigenial element. Similarly, modern quintessence would be the fifth known "dynamical, time-dependent and spatially inhomogeneous" contribution to the overall mass–energy content of the universe. The other four components are not the classical elements, but rather "baryons, neutrinos, dark matter, [and] radiation." Although neutrinos are sometimes considered radiation, the term "radiation" here refers only to photons. Spatial curvature (which has not been detected) is excluded because it is non-dynamical and homogeneous; the cosmological constant would not be considered a fifth component in this sense because it is non-dynamical, homogeneous, and time-independent.[2]

## References

1. Ratra, P.; Peebles, L. (1988). "Cosmological consequences of a rolling homogeneous scalar field". Physical Review D. 37 (12): 3406. Bibcode:1988PhRvD..37.3406R. doi:10.1103/PhysRevD.37.3406.
2. Caldwell, R.R.; Dave, R.; Steinhardt, P.J. (1998). "Cosmological Imprint of an Energy Component with General Equation-of-State". Phys. Rev. Lett. 80 (8): 1582–1585. arXiv:astro-ph/9708069. Bibcode:1998PhRvL..80.1582C. doi:10.1103/PhysRevLett.80.1582.
3. Wetterich, C. "Quintessence --a fifth force from variation of the fundamental scale" (PDF). Heidelberg University.
4. Dvali, Gia; Zaldarriaga, Matias. "Changing α With Time: Implications For Fifth-Force-Type Experiments And Quintessence" (PDF). CERN.
5. Cicoli, Michele; Pedro, Francisco G.; Tasinato, Gianmassimo (23 July 2012). "Natural Quintessence in String Theory" via arXiv.org.
6. Wanjek, Christopher. "Quintessence, accelerating the Universe?". Astronomy Today.
7. Zlatev, I.; Wang, L.; Steinhardt, P. (1999). "Quintessence, Cosmic Coincidence, and the Cosmological Constant". Physical Review Letters. 82 (5): 896–899. arXiv:astro-ph/9807002. Bibcode:1999PhRvL..82..896Z. doi:10.1103/PhysRevLett.82.896.
8. Steinhardt, P.; Wang, L.; Zlatev, I. (1999). "Cosmological tracking solutions". Physical Review D. 59 (12): 123504. arXiv:astro-ph/9812313. Bibcode:1999PhRvD..59l3504S. doi:10.1103/PhysRevD.59.123504.
9. Linden, Sebastian; Virey, Jean-Marc (2008). "Test of the Chevallier-Polarski-Linder parametrization for rapid dark energy equation of state transitions". Physical Review D. 78 (2): 023526. arXiv:0804.0389. Bibcode:2008PhRvD..78b3526L. doi:10.1103/PhysRevD.78.023526.
10. Ferramacho, L.; Blanchard, A.; Zolnierowsky, Y.; Riazuelo, A. (2010). "Constraints on dark energy evolution". Astronomy & Astrophysics. 514: A20. arXiv:0909.1703. Bibcode:2010A&A...514A..20F. doi:10.1051/0004-6361/200913271.
11. Linder, Eric V.; Huterer, Dragan (2005). "How many cosmological parameters". Physical Review D. 72 (4): 043509. arXiv:astro-ph/0505330. Bibcode:2005PhRvD..72d3509L. doi:10.1103/PhysRevD.72.043509.
12. Caldwell, R. R. (2002). "A phantom menace? Cosmological consequences of a dark energy component with super-negative equation of state". Physics Letters B. 545 (1–2): 23–29. arXiv:astro-ph/9908168. Bibcode:2002PhLB..545...23C. doi:10.1016/S0370-2693(02)02589-3.
13. Antoniou, Ioannis; Perivolaropoulos, Leandros (2016). "Geodesics of McVittie Spacetime with a Phantom Cosmological Background". Phys. Rev. D. 93 (12): 123520. arXiv:1603.02569. Bibcode:2016PhRvD..93l3520A. doi:10.1103/PhysRevD.93.123520.
14. Hu, Yazhou; Li, Miao; Li, Nan; Zhang, Zhenhui (2015). "Holographic Dark Energy with Cosmological Constant". Journal of Cosmology and Astroparticle Physics. 2015 (8): 012. arXiv:1502.01156. Bibcode:2015JCAP...08..012H. doi:10.1088/1475-7516/2015/08/012.
15. Shan Gao (2013). "Explaining Holographic Dark Energy". Galaxies. 1 (3): 180–191. Bibcode:2013Galax...1..180G. doi:10.3390/galaxies1030180.
16. Zeng, Xiao-Xiong; Chen, De-You; Li, Li-Fang (2015). "Holographic thermalization and gravitational collapse in the spacetime dominated by quintessence dark energy". Physical Review D. 91 (4): 046005. arXiv:1408.6632. Bibcode:2015PhRvD..91d6005Z. doi:10.1103/PhysRevD.91.046005.
17. Hu, Wayne (2005). "Crossing the phantom divide: Dark energy internal degrees of freedom". Physical Review D. 71 (4): 047301. arXiv:astro-ph/0410680. Bibcode:2005PhRvD..71d7301H. doi:10.1103/PhysRevD.71.047301.