Editing Axion (section)

=== 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&nbsp;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=69–71 |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]]–[[Mikhail Shifman|Shifman]]–[[Arkady Vainshtein|Vainshtein]]–{{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&nbsp;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>