On the Conformal Frames in <i>f</i>(<i>R</i>) Gravity
We discuss gravitational physics in the Jordan and Einstein frames of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo>...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/8/2/69 |
| _version_ | 1797476226898591744 |
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| author | Yuri Shtanov |
| author_facet | Yuri Shtanov |
| author_sort | Yuri Shtanov |
| collection | DOAJ |
| description | We discuss gravitational physics in the Jordan and Einstein frames of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity coupled to the Standard Model. We elucidate the way in which the observed gravitational coupling arises in the Einstein frame for generic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula>. We point out that the effect of “running units” in the Einstein frame is related to the fact that the explicit and implicit quantum parameters of the Standard Model, such as the Higgs vacuum expectation value and the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="sans-serif">Λ</mi><mi>QCD</mi></msub></semantics></math></inline-formula>, are modified by the conformal transformation of the metric and matter fields and become scalaron-dependent. Considering the scalaron of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity describing dark matter, we show that the effect of running units in this case is extremely weak, making two frames practically equivalent. |
| first_indexed | 2024-03-09T20:55:57Z |
| format | Article |
| id | doaj.art-e4838981961d4d10814b89fce5b839d3 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T20:55:57Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-e4838981961d4d10814b89fce5b839d32023-11-23T22:22:50ZengMDPI AGUniverse2218-19972022-01-01826910.3390/universe8020069On the Conformal Frames in <i>f</i>(<i>R</i>) GravityYuri Shtanov0Bogolyubov Institute for Theoretical Physics, Metrologichna St. 14-b, 03143 Kiev, UkraineWe discuss gravitational physics in the Jordan and Einstein frames of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity coupled to the Standard Model. We elucidate the way in which the observed gravitational coupling arises in the Einstein frame for generic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula>. We point out that the effect of “running units” in the Einstein frame is related to the fact that the explicit and implicit quantum parameters of the Standard Model, such as the Higgs vacuum expectation value and the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="sans-serif">Λ</mi><mi>QCD</mi></msub></semantics></math></inline-formula>, are modified by the conformal transformation of the metric and matter fields and become scalaron-dependent. Considering the scalaron of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity describing dark matter, we show that the effect of running units in this case is extremely weak, making two frames practically equivalent.https://www.mdpi.com/2218-1997/8/2/69modified gravity |
| spellingShingle | Yuri Shtanov On the Conformal Frames in <i>f</i>(<i>R</i>) Gravity Universe modified gravity |
| title | On the Conformal Frames in <i>f</i>(<i>R</i>) Gravity |
| title_full | On the Conformal Frames in <i>f</i>(<i>R</i>) Gravity |
| title_fullStr | On the Conformal Frames in <i>f</i>(<i>R</i>) Gravity |
| title_full_unstemmed | On the Conformal Frames in <i>f</i>(<i>R</i>) Gravity |
| title_short | On the Conformal Frames in <i>f</i>(<i>R</i>) Gravity |
| title_sort | on the conformal frames in i f i i r i gravity |
| topic | modified gravity |
| url | https://www.mdpi.com/2218-1997/8/2/69 |
| work_keys_str_mv | AT yurishtanov ontheconformalframesinifiirigravity |