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Axion
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== Axion dark matter == QCD effects produce an effective periodic potential in which the axion field moves.<ref name="peccei2008"/> Expanding the potential about one of its minima, one finds that the product of the axion mass with the axion decay constant is determined by the topological susceptibility of the QCD vacuum. An axion with mass much less than {{val|60|u=keV/c2}} is long-lived and weakly interacting, a perfect dark matter candidate. The oscillations of the axion field about the minimum of the effective potential, the so-called misalignment mechanism, generate a cosmological population of cold axions with an abundance depending on the mass of the axion.<ref name="auto">{{cite journal |last1=Preskill |first1=J. |author1-link=John Preskill |last2=Wise |first2=M. |author2-link=Mark B. Wise |last3=Wilczek |first3=F. |author3-link=Frank Wilczek |date=6 January 1983 |journal=Physics Letters B |volume=120 |issue=1β3 |pages=127β132 |title=Cosmology of the invisible axion |doi=10.1016/0370-2693(83)90637-8 |bibcode=1983PhLB..120..127P |url=http://www.theory.caltech.edu/~preskill/pubs/preskill-1983-axion.pdf |citeseerx=10.1.1.147.8685 }}</ref><ref name="A cosmological bound on the invisib">{{cite journal |last1=Abbott |first1=L. |last2=Sikivie |first2=P. |year=1983 |journal=Physics Letters B |volume=120 |issue=1β3 |pages=133β136 |title=A cosmological bound on the invisible axion |bibcode=1983PhLB..120..133A |doi=10.1016/0370-2693(83)90638-X |citeseerx=10.1.1.362.5088}}</ref><ref name="The not-so-harmless axion">{{cite journal |last1=Dine |first1=M. |last2=Fischler |first2=W. |year=1983 |journal=Physics Letters B |volume=120 |issue=1β3 |pages=137β141 |title=The not-so-harmless axion |doi=10.1016/0370-2693(83)90639-1 |bibcode=1983PhLB..120..137D}}</ref> With a mass above 5 [[electron-volt|ΞΌeV/{{mvar|c}}<sup>2</sup>]] ({{10^|β11}} times the [[electron mass]]) axions could account for [[dark matter]], and thus be both a dark-matter candidate and a solution to the strong CP problem. If inflation occurs at a low scale and lasts sufficiently long, the axion mass can be as low as 1 peV/{{mvar|c}}<sup>2</sup>.<ref>{{cite journal |last1=di Luzio |first1=L. |last2=Nardi |first2=E. |last3=Giannotti |first3=M. |last4=Visinelli |first4=L. |date=25 July 2020 |journal=Physics Reports |volume=870 |pages=1β117 |title=The landscape of QCD axion models |bibcode=2020PhR...870....1D |doi=10.1016/j.physrep.2020.06.002 |arxiv=2003.01100 |s2cid=211678181 }}</ref><ref>{{cite journal |last1=Graham |first1=Peter W. |last2=Scherlis |first2=Adam |title=Stochastic axion scenario |journal=Physical Review D |date=9 August 2018 |volume=98 |issue=3 |page=035017 |doi=10.1103/PhysRevD.98.035017 |arxiv=1805.07362 |bibcode=2018PhRvD..98c5017G |s2cid=119432896 }}</ref><ref>{{cite journal |last1=Takahashi |first1=Fuminobu |last2=Yin |first2=Wen |last3=Guth |first3=Alan H. |title=The QCD Axion Window and Low Scale Inflation |journal=Physical Review D |date=31 July 2018 |volume=98 |issue=1 |pages=015042 |doi=10.1103/PhysRevD.98.015042 |arxiv=1805.08763 |bibcode=2018PhRvD..98a5042T |s2cid=54584447 }}</ref> There are two distinct scenarios in which the axion field begins its evolution, depending on the following two conditions: {| |- style="vertical-align:top;" | (a) || The PQ symmetry is spontaneously broken during inflation. This condition is realized whenever the axion energy scale is larger than the Hubble rate at the end of inflation. |- style="vertical-align:top;" | (b) || The PQ symmetry is never restored after its spontaneous breaking occurs. This condition is realized whenever the axion energy scale is larger than the maximum temperature reached in the post-inflationary Universe. |} Broadly speaking, one of the two possible scenarios outlined in the two following subsections occurs: === Pre-inflationary scenario === If both (a) and (b) are satisfied, [[Inflation (cosmology)|cosmic inflation]] selects one patch of the Universe within which the spontaneous breaking of the PQ symmetry leads to a homogeneous value of the initial value of the axion field. In this "pre-inflationary" scenario, [[topological defect]]s are inflated away and do not contribute to the axion energy density. However, other bounds that come from [[isocurvature mode]]s severely constrain this scenario, which require a relatively low-energy scale of inflation to be viable.<ref>{{cite journal |last1= Crotty |first1=P. |last2=Garcia-Bellido |first2=J. |last3=Lesgourgues |first3=J. |last4=Riazuelo |first4=A. |year=2003 |journal=Physical Review Letters |volume=91 |pages=171301 |title=Bounds on isocurvature perturbations from CMB and LSS data |issue=17 |doi=10.1103/PhysRevLett.91.171301 |pmid=14611330 |bibcode=2003PhRvL..91q1301C |arxiv=astro-ph/0306286 |s2cid=12140847 }}</ref><ref>{{cite journal |last1= Beltran |first1=Maria |last2=Garcia-Bellido |first2=Juan |last3=Lesgourgues |first3=Julien |last4=Liddle |first4=Andrew R. |last5=Slosar |first5= Anze |year=2005 |journal=Physical Review D |volume=71 |issue=6 |pages= 063532 |title=Bayesian model selection and isocurvature perturbations |bibcode=2005PhRvD..71f3532B |doi=10.1103/PhysRevD.71.063532 |arxiv=astro-ph/0501477|s2cid=2220608 }}</ref><ref>{{cite journal |last1= Beltran |first1=Maria |last2=Garcia-Bellido |first2=Juan |last3=Lesgourgues |first3=Julien |year=2007 |journal=Physical Review D |volume=75 |issue=10 |pages= 103507 |title=Isocurvature bounds on axions revisited |doi=10.1103/PhysRevD.75.103507 |bibcode=2007PhRvD..75j3507B |arxiv=hep-ph/0606107 |s2cid=119451896 }}</ref> === Post-inflationary scenario === If at least one of the conditions (a) or (b) is violated, the axion field takes different values within patches that are initially out of [[causal contact]], but that today populate the volume enclosed by our [[Cosmological horizon#Hubble horizon|Hubble horizon]]. In this scenario, isocurvature fluctuations in the PQ field randomise the axion field, with no preferred value in the power spectrum. The proper treatment in this scenario is to solve numerically the equation of motion of the PQ field in an expanding Universe, in order to capture all features coming from the misalignment mechanism, including the contribution from topological defects like "axionic" [[cosmic string|strings]] and [[domain wall]]s. An axion mass estimate between 0.05 and 1.50 meV was reported by Borsanyi et al. (2016).<ref>{{cite journal |display-authors=6 |last1=Borsanyi |first1=S. |last2=Fodor |first2=Z. |last3=Guenther |first3=J. |last4=Kampert |first4=K.-H. |last5=Katz |first5=S. D. |last6=Kawanai |first6=T. |last7=Kovacs |first7=T. G. |last8=Mages |first8=S. W. |last9=Pasztor |first9=A. |last10=Pittler |first10=F. |last11=Redondo |first11=J. |last12=Ringwald |first12=A. |last13=Szabo |first13=K. K. |title=Calculation of the axion mass based on high-temperature lattice quantum chromodynamics |journal=Nature |date=3 November 2016 |volume=539 |issue=7627 |pages=69β71 |doi=10.1038/nature20115 |pmid=27808190 |bibcode=2016Natur.539...69B |s2cid=2943966 |url=https://bib-pubdb1.desy.de/record/311362 }}</ref> The result was calculated by simulating the formation of axions during the [[Inflation (cosmology)|post-inflation]] period on a [[supercomputer]].<ref>{{cite journal |first=Davide |last=Castelvecchi |date=3 November 2016 |title=Axion alert! Exotic-particle detector may miss out on dark matter |series=news |journal=[[Nature (journal)|Nature]] |doi=10.1038/nature.2016.20925 |s2cid=125299733 |doi-access=free }}</ref> Progress in the late 2010s in determining the present abundance of a KSVZ-type axion{{efn|At present, physics literature discusses "invisible axion" mechanisms in two forms, one of them is called KSVZ for [[Kim Jihn-eui|Kim]]β[[Mikhail Shifman|Shifman]]β[[Arkady Vainshtein|Vainshtein]]β{{nowrap|{{abbr|Zakharov|Valya Zakharov}}.<ref name=Kim-1979/><ref name=Shifman-etal-1980/>}} See discussion in the "Searches" section, [[#K-S-V-Z-vs-D-F-S-Z-anchor|below]].}} using numerical simulations lead to values between 0.02 and 0.1 meV,<ref>{{cite journal |last1=Klaer |first1=Vincent B. |last2=Moore |first2=Guy D. |year=2017 |journal=Journal of Cosmology and Astroparticle Physics |volume=2017 |pages= 049 |title=The dark-matter axion mass |issue=11 |doi=10.1088/1475-7516/2017/11/049 |bibcode=2017JCAP...11..049K |arxiv=1708.07521 |s2cid=119227153 }}</ref><ref>{{cite journal |last1= Buschmann |first1= Malte |last2= Foster |first2=Joshua W. |last3=Safdi |first3=Benjamin R. |year=2020 |journal=Physical Review Letters |volume=124 |issue=16 |pages=161103 |title=Early-Universe Simulations of the Cosmological Axion |doi=10.1103/PhysRevLett.124.161103 |pmid= 32383908 |bibcode=2020PhRvL.124p1103B |arxiv= 1906.00967 |s2cid= 174797749 }}</ref> although these results have been challenged by the details on the power spectrum of emitted axions from strings.<ref>{{cite journal |last1=Gorghetto |first1=Marco |last2=Hardy |first2=Edward |last3=Villadoro |first3=Giovanni |title=More axions from strings |journal=SciPost Physics |year=2021 |volume=10 |issue=2 |page=050 |doi=10.21468/SciPostPhys.10.2.050 |arxiv=2007.04990 |bibcode=2021ScPP...10...50G |s2cid=220486728 |doi-access=free }}</ref>
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