Inflaton

The inflaton field is a hypothetical scalar field that is conjectured to have driven cosmic inflation in the very early universe.^[1]^[2]^[3] The field, originally postulated by Alan Guth,^[1] provides a mechanism by which a period of rapid expansion from 10⁻³⁵ to 10⁻³⁴ seconds after the initial expansion can be generated, forming a universe that is not inconsistent with observed spatial isotropy and homogeneity.

Cosmological inflation

The basic^{[clarification needed]} model of inflation proceeds in three phases:^[4]

Expanding vacuum state with high potential energy
Phase transition to true vacuum
Slow roll and reheating

Expanding vacuum state with high potential energy

A "vacuum" or "vacuum state" in quantum field theory is a state of quantum fields that is at locally minimal potential energy. Quantum particles are excitations that deviate from this minimal potential energy state, therefore a vacuum state has no particles in it. Depending on the specifics of a quantum field theory, it can have more than one vacuum state. Different vacua, despite all "being empty" (having no particles), will generally have different vacuum energy. Quantum field theory stipulates that the pressure of the vacuum energy is always negative and equal in magnitude to its energy density.

Inflationary theory postulates that there is a vacuum state with very large vacuum energy, caused by a non-zero vacuum expectation value of the inflaton field. Any region of space in this state will rapidly expand. Even if initially it is not empty (contains some particles), very rapid exponential expansion dilutes any particles that might have previously been present to essentially zero density.

Transition to true vacuum

Inflationary theory further postulates that this "inflationary vacuum" state is not the state with globally the lowest energy; rather, it is a "false vacuum", also known as a metastable state^[5].

Historically, the first proposals of inflation^[6] suggested that the transition from the "false" to the "true vacuum" follows a quantum tunnelling process, where the inflaton field passes through the potential barrier of the two phases (this would correspond to a first-order phase transition). However, it was realised^[7] that this procedure would create a very inhomogeneous Universe on the large scales, contrary to what we observe.

Example of a field with a "false vacuum". Similar potentials had been considered for inflation. Note however that the simple, "slow-roll" potential has a smoother transition between the "false" and "true vacuum".

The theory was soon refined^[8]^[9] to allow a smooth transition between the two phases, where the inflaton field "rolls down" its potential.

Slow roll and reheating

In simple, modern models of inflation, the inflaton originally has much bigger potential energy than kinetic energy ("slow-roll"), which leads the inflationary potential to act as an effective cosmological constant. As an effect, one expects a period of exponential expansion.

When the inflaton reaches its true vacuum, it needs to be connected to the standard cosmological model. At that point, the field has "lost" its original potential energy, but gained kinetic energy. To introduce the standard model at this point, the idea is that this energy needs to be transferred to the observed Standard Model particles.^[10]^[11] This procedure is known as "reheating". When complete, the Universe is radiation dominated and its expansion decelerates. The decay of the inflaton fills the space with new particles, which interact with each other and finally reach the hot and dense state of the Big Bang theory.^[12]

Field quanta

Just like every other quantum field, excitations of the inflaton field are expected to be quantized. The field quanta of the inflaton field are known as inflatons. Depending on the modeled potential energy density, the inflaton field's ground state might, or might not, be zero.

The term inflaton follows the typical style of other quantum particles’ names – such as photon, gluon, boson, and fermion – deriving from the word inflation. The term was first used in a paper by Nanopoulos, Olive & Srednicki (1983).^[13] The nature of the inflaton field is currently not known. One of the obstacles for narrowing its properties is that current quantum theory is not able to correctly predict the observed vacuum energy, based on the particle content of a chosen theory (see vacuum catastrophe).

The confirmation of the Higgs boson led to the suggestion that it is possible that no new field is necessary – that a modified version of the Higgs field could suffice.^[14] However this early proposal and others that followed have faced criticism on fundamental grounds.^[15]^[16]

Non-minimally coupled inflation

Non-minimally coupled inflation is an inflationary model in which the constant which couples gravity to the inflaton field is not small. The coupling constant is usually represented by $\xi$ (letter xi), which features in the action (constructed by modifying the Einstein–Hilbert action):^[17]^: 1–2

S=\int d^{4}x{\sqrt {-g}}\left[{\tfrac {1}{2}}m_{P}^{2}R-{\tfrac {1}{2}}\partial ^{\mu }\phi \partial _{\mu }\phi -V(\phi )-{\tfrac {1}{2}}\xi R\phi ^{2}\right],

with $\xi$ representing the strength of the interaction between $R$ and ⁠ $\phi$ ⁠, which respectively relate to the curvature of space and the magnitude of the inflaton field.

References

^ ^a ^b Guth, Alan H. (1997). The Inflationary Universe: The Quest for a New Theory of Cosmic Origins. Basic Books. pp. 233–234. ISBN 978-0201328400.
^ Steinhardt, Paul J.; Turok, Neil (2007). Endless Universe: Beyond the Bang. Random House. p. 114. ISBN 978-0-7679-1501-4.
^ Steinhardt, Paul J. (April 2011). "Inflation Debate: Is the theory at the heart of modern cosmology deeply flawed?" (PDF). Scientific American. Archived from the original (PDF) on 2014-08-24. Retrieved 2013-12-31.
^ Tsujikawa, Shinji (2003). "Introductory review of cosmic inflation". arXiv:hep-ph/0304257.
^ Peter, Patrick; Uzan, Jean-Philippe; Peter, Patrick (2013). "Chapter 8". Primordial cosmology. Oxford graduate texts (1. publ. in paperback ed.). Oxford: Oxford University Press. ISBN 978-0-19-966515-0.
^ Guth, Alan H. (1981-01-15). "Inflationary universe: A possible solution to the horizon and flatness problems". Physical Review D. 23 (2): 347–356. Bibcode:1981PhRvD..23..347G. doi:10.1103/PhysRevD.23.347.
^ Guth, Alan H.; Weinberg, Erick J. (1983). "Could the universe have recovered from a slow first-order phase transition?". Nuclear Physics B. 212 (2): 321–364. Bibcode:1983NuPhB.212..321G. doi:10.1016/0550-3213(83)90307-3.
^ Linde, A.D. (1982). "A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems". Physics Letters B. 108 (6): 389–393. Bibcode:1982PhLB..108..389L. doi:10.1016/0370-2693(82)91219-9.
^ Albrecht, Andreas; Steinhardt, Paul J. (1982-04-26). "Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking". Physical Review Letters. 48 (17): 1220–1223. Bibcode:1982PhRvL..48.1220A. doi:10.1103/PhysRevLett.48.1220.
^ Kofman, Lev; Linde, Andrei; Starobinsky, Alexei (1994-10-12). "Reheating after Inflation". Physical Review Letters. 73 (24): 3195–3198. arXiv:hep-th/9405187. Bibcode:1994PhRvL..73.3195K. doi:10.1103/PhysRevLett.73.3195. PMID 10057315.
^ The Physics of Inflation, Daniel Baumann link
^ Strassler, Matt (17 March 2014). "Inflation". History of the Universe. Of Particular Significance (profmattstrassler.com) (blog). Relativity, space, astronomy, and cosmology. Retrieved 3 August 2024. ... by the author of Waves in an Impossible Sea.
^ Nanopoulos, D.V.; Olive, D.A.; Srednicki, M. (1983). "After primordial inflation" (PDF). Physics Letters B. 127 (1–2): 30–34. Bibcode:1983PhLB..127...30N. doi:10.1016/0370-2693(83)91624-6.
^ Bezrukov, Fedor; Shaposhnikov, Mikhail (2008-01-24). "The Standard Model Higgs boson as the inflaton". Physics Letters B. 659 (3): 703–706. arXiv:0710.3755. Bibcode:2008PhLB..659..703B. doi:10.1016/j.physletb.2007.11.072. ISSN 0370-2693.
^ Atkins, Michael; Calmet, Xavier (2011-02-21). "Remarks on Higgs inflation". Physics Letters B. 697 (1): 37–40. arXiv:1011.4179. Bibcode:2011PhLB..697...37A. doi:10.1016/j.physletb.2011.01.028. ISSN 0370-2693.
^ Atkins, Michael (2011). "Could the Higgs boson be the inflaton?" (PDF). Meyrin, CH: CERN – via cern.ch.
^ Hertzberg, Mark P. (2010). "On Inflation with Non-minimal Coupling". Journal of High Energy Physics. 2010 (11) 23. arXiv:1002.2995. Bibcode:2010JHEP...11..023H. doi:10.1007/JHEP11(2010)023. S2CID 54886582.

[Guth1997-1] Guth, Alan H. (1997). The Inflationary Universe: The Quest for a New Theory of Cosmic Origins. Basic Books. pp. 233–234. ISBN 978-0201328400.

[2] Steinhardt, Paul J.; Turok, Neil (2007). Endless Universe: Beyond the Bang. Random House. p. 114. ISBN 978-0-7679-1501-4.

[3] Steinhardt, Paul J. (April 2011). "Inflation Debate: Is the theory at the heart of modern cosmology deeply flawed?" (PDF). Scientific American. Archived from the original (PDF) on 2014-08-24. Retrieved 2013-12-31.

[4] Tsujikawa, Shinji (2003). "Introductory review of cosmic inflation". arXiv:hep-ph/0304257.

[5] Peter, Patrick; Uzan, Jean-Philippe; Peter, Patrick (2013). "Chapter 8". Primordial cosmology. Oxford graduate texts (1. publ. in paperback ed.). Oxford: Oxford University Press. ISBN 978-0-19-966515-0.

[6] Guth, Alan H. (1981-01-15). "Inflationary universe: A possible solution to the horizon and flatness problems". Physical Review D. 23 (2): 347–356. Bibcode:1981PhRvD..23..347G. doi:10.1103/PhysRevD.23.347.

[7] Guth, Alan H.; Weinberg, Erick J. (1983). "Could the universe have recovered from a slow first-order phase transition?". Nuclear Physics B. 212 (2): 321–364. Bibcode:1983NuPhB.212..321G. doi:10.1016/0550-3213(83)90307-3.

[8] Linde, A.D. (1982). "A new inflationary universe scenario: A possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems". Physics Letters B. 108 (6): 389–393. Bibcode:1982PhLB..108..389L. doi:10.1016/0370-2693(82)91219-9.

[9] Albrecht, Andreas; Steinhardt, Paul J. (1982-04-26). "Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking". Physical Review Letters. 48 (17): 1220–1223. Bibcode:1982PhRvL..48.1220A. doi:10.1103/PhysRevLett.48.1220.

[10] Kofman, Lev; Linde, Andrei; Starobinsky, Alexei (1994-10-12). "Reheating after Inflation". Physical Review Letters. 73 (24): 3195–3198. arXiv:hep-th/9405187. Bibcode:1994PhRvL..73.3195K. doi:10.1103/PhysRevLett.73.3195. PMID 10057315.

[11] The Physics of Inflation, Daniel Baumann link

[12] Strassler, Matt (17 March 2014). "Inflation". History of the Universe. Of Particular Significance (profmattstrassler.com) (blog). Relativity, space, astronomy, and cosmology. Retrieved 3 August 2024. ... by the author of Waves in an Impossible Sea.

[13] Nanopoulos, D.V.; Olive, D.A.; Srednicki, M. (1983). "After primordial inflation" (PDF). Physics Letters B. 127 (1–2): 30–34. Bibcode:1983PhLB..127...30N. doi:10.1016/0370-2693(83)91624-6.

[14] Bezrukov, Fedor; Shaposhnikov, Mikhail (2008-01-24). "The Standard Model Higgs boson as the inflaton". Physics Letters B. 659 (3): 703–706. arXiv:0710.3755. Bibcode:2008PhLB..659..703B. doi:10.1016/j.physletb.2007.11.072. ISSN 0370-2693.

[15] Atkins, Michael; Calmet, Xavier (2011-02-21). "Remarks on Higgs inflation". Physics Letters B. 697 (1): 37–40. arXiv:1011.4179. Bibcode:2011PhLB..697...37A. doi:10.1016/j.physletb.2011.01.028. ISSN 0370-2693.

[16] Atkins, Michael (2011). "Could the Higgs boson be the inflaton?" (PDF). Meyrin, CH: CERN – via cern.ch.

[hertzberg12-17] Hertzberg, Mark P. (2010). "On Inflation with Non-minimal Coupling". Journal of High Energy Physics. 2010 (11) 23. arXiv:1002.2995. Bibcode:2010JHEP...11..023H. doi:10.1007/JHEP11(2010)023. S2CID 54886582.

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