Editing Andrei Sakharov (section)

===Particle physics and cosmology===
After 1965 Sakharov returned to [[fundamental science]] and began working on [[particle physics]] and [[physical cosmology]].<ref name="Sakharov 1966">{{cite journal
 |last1=Sakharov |first1=A. D.
 |date=July 1965
 |script-title=ru:Начальная стадия расширения Вселенной и возникновение неоднородности распределения вещества
 |journal=[[Journal of Experimental and Theoretical Physics|Pi'sma ZhÉTF]]
 |volume=49 
 |issue=1
 |pages=345–358
 |language=ru
}} Translated as: {{cite journal
 |last1=Sakharov |first1=A. D.
 |date=January 1966
 |title=The Initial Stage of an Expanding Universe and the Appearance of a Nonuniform Distribution of Matter
 |journal=[[Journal of Experimental and Theoretical Physics|JETP]]
 |volume=22 
 |issue=1
 |pages=241–249
 |url= http://jetp.ac.ru/cgi-bin/dn/e_022_01_0241.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://jetp.ac.ru/cgi-bin/dn/e_022_01_0241.pdf |archive-date=2022-10-09 |url-status=live
 |bibcode = 1966JETP...22..241S }}</ref><ref name="Sakharov 1967b">{{cite journal |last1=Sakharov |first1=A. D. |date=January 1967 |script-title=ru:Кварк–мюонные токи и нарушение СР–инвариантности |journal=Pi'sma ZhÉTF |language=ru |volume=5 |issue=1 |pages=36–39}} Translated as: {{cite journal |last1=Sakharov |first1=A. D. |date=January 1967 |title=Quark-Muonic Currents and Violation of CP Invariance |url=http://www.jetpletters.ac.ru/ps/1643/article_25090.pdf |url-status=live |journal=JETP Letters |volume=5 |issue=1 |pages=27–30 |bibcode=1967JETPL...5...27S |archive-url=https://ghostarchive.org/archive/20221009/http://www.jetpletters.ac.ru/ps/1643/article_25090.pdf |archive-date=2022-10-09}}</ref><ref>Dokl. Akad. Nauk SSSR 177, 70 (1967) [trans. Sov. Phys.-Dokl. 12, 1040 (1968)]</ref><ref name="Sakharov 1969">{{cite journal
 |last1=Sakharov |first1=A. D.
 |date=1969
 |script-title=ru:Антикварки во Вселенной
 |trans-title=Antiquarks in the Universe
 |language=ru
 |journal=Problems in Theoretical Physics
 |pages=35–44
}} Dedicated to the 30th anniversary of [[Nikolay Bogolyubov|N. N. Bogolyubov]].</ref><ref>Paper at seminar, Phys. Inst. Acad. Sci., June 1970</ref>
[[File:2D didactic image of Sakharov's twin universe model.svg|thumb|300px|right|2D didactic image of Sakharov's model of the universe with reversal of the arrow of time]]
He tried to explain the [[baryon asymmetry]] of the universe; in that regard, he was the first to give a theoretical motivation for [[proton decay]]. Proton decay was suggested by Wigner in 1949 and 1952.<ref>E. P. Wigner, Proc. Am. Philos. Soc. 93, 521 (1949); Proc. Natl.Ac'ad. Sci. (U. S.) 38, 449 (1952)</ref>
Proton decay experiments had been performed since 1954 already.<ref>F. Reines, C.L. Cowan, M. Goldhaber, Phys.Rev. 96 (1954) 1157.</ref> Sakharov was the first to consider [[CPT symmetry|CPT-symmetric]] events occurring ''before'' the [[Big Bang]]:<blockquote>We can visualize that neutral spinless maximons (or photons) are produced at <nowiki>''</nowiki>t<nowiki>''</nowiki> < 0 from contracting matter having an excess of antiquarks, that they pass "one through the other" at the instant <nowiki>''</nowiki>t<nowiki>''</nowiki> = 0 when the density is infinite, and decay with an excess of quarks when <nowiki>''</nowiki>t<nowiki>''</nowiki> > 0, realizing total CPT symmetry of the universe. All the phenomena at t < 0 are assumed in this hypothesis to be CPT reflections of the phenomena at t > 0.<ref name="Sakharov 1967a">{{cite journal |last1=Sakharov |first1=A. D. |date=January 1967 |script-title=ru:Нарушение СР–инвариантности, С–асимметрия и барионная асимметрия Вселенной |journal=Pi'sma ZhÉTF |language=ru |volume=5 |issue=1 |pages=32–35}} Translated as: {{cite journal |last1=Sakharov |first1=A. D. |date=January 1967 |title=Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe |url=http://www.jetpletters.ac.ru/ps/1643/article_25089.pdf |url-status=live |journal=JETP Letters |volume=5 |issue=1 |pages=24–26 |bibcode=1967JETPL...5...24S |archive-url=https://ghostarchive.org/archive/20221009/http://www.jetpletters.ac.ru/ps/1643/article_25089.pdf |archive-date=2022-10-09}} Republished as {{cite journal |last1=Sakharov |first1=A. D. |date=May 1991 |title=Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe |url=http://ayuba.fr/pdf/sakharov1991.pdf |url-status=live |journal=[[Physics-Uspekhi|Soviet Physics Uspekhi]] |volume=34 |issue=5 |pages=392–393 |bibcode=1991SvPhU..34..392S |doi=10.1070/PU1991v034n05ABEH002497 |archive-url=https://ghostarchive.org/archive/20221009/http://ayuba.fr/pdf/sakharov1991.pdf |archive-date=2022-10-09}}</ref></blockquote> His legacy in this domain are the famous [[Baryon asymmetry#Sakharov conditions|conditions]] named after him:<ref name="Sakharov 1967a" /> Baryon number violation, C-symmetry and CP-symmetry violation, and interactions out of thermal equilibrium.

Sakharov was also interested in explaining why the curvature of the universe is so small. This led him to consider cyclic models, where the universe oscillates between contraction and expansion phases.<ref name="Sakharov 1982">{{cite journal |last1=Sakharov |first1=A. D. |date=October 1982 |script-title=ru:Многолистные модели Вселенной |journal=Pi'sma ZhÉTF |language=ru |volume=82 |issue=3 |pages=1233–1240}} Translated as: {{cite journal |last1=Sakharov |first1=A. D. |date=October 1982 |title=Many-sheeted models of the universe (Multisheet models of the universe) |url=http://www.jetp.ac.ru/cgi-bin/dn/e_056_04_0705.pdf |url-status=live |journal=JETP |volume=56 |issue=4 |pages=705–709 |archive-url=https://ghostarchive.org/archive/20221009/http://www.jetp.ac.ru/cgi-bin/dn/e_056_04_0705.pdf |archive-date=2022-10-09}}</ref><ref name="Sakharov 1980">{{cite journal |last1=Sakharov |first1=A. D. |date=September 1980 |script-title=ru:Космологические модели Вселенной с поворотом стрелы времени |journal=Pi'sma ZhÉTF |language=ru |volume=79 |issue=3 |pages=689–693}}Translated as: {{cite journal |last1=Sakharov |first1=A. D. |date=September 1980 |title=Cosmological models of the Universe with reversal of time's arrow |url=http://www.jetp.ac.ru/cgi-bin/dn/e_052_03_0349.pdf |url-status=live |journal=JETP Letters |volume=52 |issue=3 |pages=349–351 |bibcode=1980JETP...52..349S |archive-url=https://ghostarchive.org/archive/20221009/http://www.jetp.ac.ru/cgi-bin/dn/e_052_03_0349.pdf |archive-date=2022-10-09}}</ref> In those models, after a certain number of cycles the curvature naturally becomes infinite even if it had not started this way: Sakharov considered three starting points, a flat universe with a slightly negative cosmological constant, a universe with a positive curvature and a zero cosmological constant, and a universe with a negative curvature and a slightly negative cosmological constant. Those last two models feature what Sakharov calls a reversal of the time arrow, which can be summarized as follows: He considers times t > 0 after the initial Big Bang singularity at t = 0 (which he calls "Friedman singularity" and denotes Φ) as well as times t < 0 before that singularity. He then assumes that entropy increases when time increases for t > 0 as well as when time decreases for t < 0, which constitutes his reversal of time. Then he considers the case when the universe at t < 0 is the image of the universe at t > 0 under CPT symmetry but also the case when it is not so: the universe has a non-zero CPT charge at t = 0 in this case. Sakharov considers a variant of this model where the reversal of the time arrow occurs at a point of maximum entropy instead of happening at the singularity. In those models there is no dynamic interaction between the universe at t < 0 and t > 0.

In his first model the two universes did not interact, except via local matter accumulation whose density and pressure become high enough to connect the two sheets through a bridge without spacetime between them, but with a continuity of geodesics beyond the Schwarzschild radius with no singularity{{citation needed|date=March 2021}}, allowing an exchange of matter between the two conjugated sheets, based on an idea after [[Igor Dmitriyevich Novikov]].<ref name="Novikov 1966">{{cite journal
 |last1=Novikov |first1=I. D.
 |date=March 1966
 |title=The Disturbances of the Metric when a Collapsing Sphere Passes below the Schwarzschild Sphere
 |journal=JETP Letters
 |volume=3
 |issue=5
 |pages=142–144
 |url=http://www.jetpletters.ac.ru/ps/1614/article_24731.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.jetpletters.ac.ru/ps/1614/article_24731.pdf |archive-date=2022-10-09 |url-status=live
 |bibcode = 1966JETPL...3..142N }}</ref> Novikov called such singularities a ''collapse'' and an ''anticollapse'', which are an alternative to the couple [[black hole]] and [[white hole]] in the [[wormhole]] model. Sakharov also proposed the idea of [[induced gravity]] as an alternative theory of [[quantum gravity]].<ref name="Sakharov QVF">
{{cite journal
 |last1=Sakharov |first1=A. D.
 |date=1967
 |script-title=ru:Вакуумные квантовые флуктуации в искривленном пространстве и теория гравитации
 |journal=[[Proceedings of the USSR Academy of Sciences]]
 |volume=177
 |issue=1
 |pages=70–71
 |language=ru
}} Translated as: {{cite journal
 |last1=Sakharov |first1=A. D.
 |date=1991
 |title=Vacuum Quantum Fluctuations in Curved Space and the theory of gravitation
 |journal=Soviet Physics Uspekhi
 |volume=34
 |issue=5
 |pages=394
 |doi=10.1070/PU1991v034n05ABEH002498
 |url=http://ayuba.fr/pdf/sakharov_qvf.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://ayuba.fr/pdf/sakharov_qvf.pdf |archive-date=2022-10-09 |url-status=live
 |bibcode = 1991SvPhU..34..394S }}</ref>