{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,12]],"date-time":"2026-01-12T22:14:59Z","timestamp":1768256099295,"version":"3.49.0"},"reference-count":32,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,11,26]],"date-time":"2021-11-26T00:00:00Z","timestamp":1637884800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The work was \ufb01nancially supported by the Ministry of Education and Science of the Republic of Kazakhstan","award":["AP08957287"],"award-info":[{"award-number":["AP08957287"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>It is shown that the inflationary model is the result of the symmetry of the generalized F(R,T,X,\u03c6)-cosmological model using the Noether symmetry. It leads to a solution, a particular case of which is Starobinsky\u2019s cosmological model. It is shown that even in the more particular case of cosmological models F(R,X,\u03c6) and F(T,X,\u03c6) the Monge\u2013Amp\u00e8re equation is still obtained, one of the solutions including the Starobinsky model. For these models, it is shown that one can obtain both power-law and exponential solutions for the scale factor from the Euler\u2013Lagrange equations. In this case, the scalar field \u03c6 has similar time dependences, exponential and exponential. The resulting form of the Lagrangian of the model allows us to consider it as a model with R2 or X2. However, it is also shown that previously less studied models with a non-minimal relationship between R and X are important, as one of the possible models. It is shown that in this case the power-law model can have a limited evolutionary period with a negative value of the kinetic term.<\/jats:p>","DOI":"10.3390\/sym13122254","type":"journal-article","created":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T03:12:40Z","timestamp":1638328360000},"page":"2254","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Inflation from the Symmetry of the Generalized Cosmological Model"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0732-2080","authenticated-orcid":false,"given":"Koblandy","family":"Yerzhanov","sequence":"first","affiliation":[{"name":"Department of General and Theoretical Physics, L.N. Gumilyov Eurasian National University, Nur-Sultan Z01C0X1, Kazakhstan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8410-6640","authenticated-orcid":false,"given":"Gulnur","family":"Bauyrzhan","sequence":"additional","affiliation":[{"name":"Department of General and Theoretical Physics, L.N. Gumilyov Eurasian National University, Nur-Sultan Z01C0X1, Kazakhstan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9254-7027","authenticated-orcid":false,"given":"Aziza","family":"Altaibayeva","sequence":"additional","affiliation":[{"name":"Department of General and Theoretical Physics, L.N. Gumilyov Eurasian National University, Nur-Sultan Z01C0X1, Kazakhstan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5274-0815","authenticated-orcid":false,"given":"Ratbay","family":"Myrzakulov","sequence":"additional","affiliation":[{"name":"Department of General and Theoretical Physics, L.N. Gumilyov Eurasian National University, Nur-Sultan Z01C0X1, Kazakhstan"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1086\/307221","article-title":"Measurements of \u03a9 and \u039b from 42 High-Redshift Supernovae","volume":"517","author":"Perlmutter","year":"1999","journal-title":"Astroph. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1086\/300499","article-title":"Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant","volume":"116","author":"Riess","year":"1988","journal-title":"Astron. J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1753","DOI":"10.1142\/S021827180600942X","article-title":"Dynamics of dark energy","volume":"15","author":"Copeland","year":"2006","journal-title":"Int. J. Mod. Phys. 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