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] and Wetterich (1988).[2][3] The concept was expanded to more general types of time-varying dark energy, and the term "quintessence" was first introduced in a 1998 paper by Robert R. Caldwell, Rahul Dave and Paul Steinhardt.[4] It has been proposed by some physicists to be a fifth fundamental force.[5][6][7][8] 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.[9]

A group of researchers argued in 2021 that observations of the Hubble tension may imply that only quintessence models with a nonzero coupling constant are viable.[10]


The name comes from quinta essentia (fifth element). So called in Latin starting from the Middle Ages, this was the (first) element added by Aristotle to the other four ancient classical elements because he thought it was the essence of the celestial world. Aristotle posited to be a pure, fine, and primigenial element. Later scholars identified this element with aether. Similarly, modern quintessence would be the fifth known "dynamical, time-dependent, and spatially inhomogeneous" contribution to the overall mass–energy content of the universe.

Of course, the other four components are not the ancient Greek classical elements, but rather "baryons, neutrinos, dark matter, [and] radiation." Although neutrinos are sometimes considered radiation, the term "radiation" in this context is only used to refer to massless photons. Spatial curvature of the cosmos (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.[4]

Scalar field

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

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.[11] 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.[12] 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,[13][14] whereas it has been shown that at most a two-parameter model can optimally be constrained by mid-term future data (horizon 2015–2020).[15]

Specific models

Some special cases of quintessence are phantom energy, in which wq < 1,[16] 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[17] 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.[18] It has been suggested that dark energy might originate from quantum fluctuations of spacetime, and are limited by the event horizon of the universe.[19]

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.[20]

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 involving ideal gases or scalar fields.[21]

See also


  1. Ratra, P.; Peebles, L. (1988). "Cosmological consequences of a rolling homogeneous scalar field". Physical Review D. 37 (12): 3406–3427. Bibcode:1988PhRvD..37.3406R. doi:10.1103/PhysRevD.37.3406. PMID 9958635.
  2. Wetterich, C. (1988-06-13). "Cosmology and the fate of dilatation symmetry". Nuclear Physics B. 302 (4): 668–696. arXiv:1711.03844. doi:10.1016/0550-3213(88)90193-9. ISSN 0550-3213. S2CID 118970077.
  3. Doran, Michael (2001-10-01). et al. "Quintessence and the Separation of Cosmic Microwave Background Peaks". The Astrophysical Journal. 559 (2): 501–506. doi:10.1086/322253. S2CID 119454400 via Iopscience.
  4. 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. S2CID 597168.
  5. Carroll, S.M. (1998). "Quintessence and the Rest of the World: Suppressing Long-Range Interactions". Phys. Rev. Lett. 81 (15): 3067–3070. arXiv:astro-ph/9806099. Bibcode:1998PhRvL..81.3067C. doi:10.1103/PhysRevLett.81.3067. S2CID 14539052.
  6. Wetterich, C. "Quintessence --a fifth force from variation of the fundamental scale" (PDF). Heidelberg University.
  7. Dvali, Gia; Zaldarriaga, Matias (2002). "Changing α With Time: Implications For Fifth-Force-Type Experiments And Quintessence" (PDF). Physical Review Letters. 88 (9): 091303. arXiv:hep-ph/0108217. Bibcode:2002PhRvL..88i1303D. doi:10.1103/PhysRevLett.88.091303. PMID 11863992. S2CID 32730355.
  8. Cicoli, Michele; Pedro, Francisco G.; Tasinato, Gianmassimo (23 July 2012). "Natural Quintessence in String Theory" via arXiv.org.
  9. Wanjek, Christopher. "Quintessence, accelerating the Universe?". Astronomy Today.
  10. Krishnan, Chethan; Mohayaee, Roya; Colgáin, Eoin Ó; Sheikh-Jabbari, M. M.; Yin, Lu (16 September 2021). "Does Hubble Tension Signal a Breakdown in FLRW Cosmology?". Classical and Quantum Gravity. 38 (18): 184001. arXiv:2105.09790. Bibcode:2021CQGra..38r4001K. doi:10.1088/1361-6382/ac1a81. ISSN 0264-9381. S2CID 234790314.
  11. 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. S2CID 119073006.
  12. 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. S2CID 40714104.
  13. 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. S2CID 118288188.
  14. 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. S2CID 17386518.
  15. 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. S2CID 14722329.
  16. 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. S2CID 9820570.
  17. 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. S2CID 18017360.
  18. 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. S2CID 118732915.
  19. Shan Gao (2013). "Explaining Holographic Dark Energy". Galaxies. 1 (3): 180–191. Bibcode:2013Galax...1..180G. doi:10.3390/galaxies1030180.
  20. 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. S2CID 119107827.
  21. 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. S2CID 8791054.

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