Scalar Field Source Teleparallel Robertson–Walker <i>F</i>(<i>T</i>) Gravity Solutions
This paper investigates the teleparallel Robertson–Walker (TRW) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></...
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2025-01-01
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| author | Alexandre Landry |
| author_facet | Alexandre Landry |
| author_sort | Alexandre Landry |
| collection | DOAJ |
| description | This paper investigates the teleparallel Robertson–Walker (TRW) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity solutions for a scalar field source. We use the TRW <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity field equations (FEs) for each <i>k</i>-parameter value case added by a scalar field to find new teleparallel <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> solutions. For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>, we find an easy-to-compute <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> solution formula applicable for any scalar field source. Then, we obtain, for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>=</mo><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula> situations, some new analytical <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> solutions, only for specific <i>n</i>-parameter values and well-determined scalar field cases. We can find by those computations a large number of analytical teleparallel <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> solutions independent of any scalar potential <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mo>(</mo><mi>ϕ</mi><mo>)</mo></mrow></semantics></math></inline-formula> expression. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mo>(</mo><mi>ϕ</mi><mo>)</mo></mrow></semantics></math></inline-formula> independence makes the FE solving and computations easier. The new solutions will be relevant for future cosmological applications in dark matter, dark energy (DE) quintessence, phantom energy and quintom models of physical processes. |
| format | Article |
| id | doaj-art-9f64d60de07a4d8888d5fe6702d5fcec |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-9f64d60de07a4d8888d5fe6702d5fcec2025-08-20T02:12:25ZengMDPI AGMathematics2227-73902025-01-0113337410.3390/math13030374Scalar Field Source Teleparallel Robertson–Walker <i>F</i>(<i>T</i>) Gravity SolutionsAlexandre Landry0Department of Mathematics and Statistics, Dalhousie University, Halifax, NS B3H 3J5, CanadaThis paper investigates the teleparallel Robertson–Walker (TRW) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity solutions for a scalar field source. We use the TRW <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity field equations (FEs) for each <i>k</i>-parameter value case added by a scalar field to find new teleparallel <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> solutions. For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>, we find an easy-to-compute <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> solution formula applicable for any scalar field source. Then, we obtain, for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>=</mo><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula> situations, some new analytical <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> solutions, only for specific <i>n</i>-parameter values and well-determined scalar field cases. We can find by those computations a large number of analytical teleparallel <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> solutions independent of any scalar potential <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mo>(</mo><mi>ϕ</mi><mo>)</mo></mrow></semantics></math></inline-formula> expression. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mo>(</mo><mi>ϕ</mi><mo>)</mo></mrow></semantics></math></inline-formula> independence makes the FE solving and computations easier. The new solutions will be relevant for future cosmological applications in dark matter, dark energy (DE) quintessence, phantom energy and quintom models of physical processes.https://www.mdpi.com/2227-7390/13/3/374scalar field sourceteleparallel gravityteleparallel Robertson–Walkercosmological teleparallel solutionsdark energyquintessence |
| spellingShingle | Alexandre Landry Scalar Field Source Teleparallel Robertson–Walker <i>F</i>(<i>T</i>) Gravity Solutions Mathematics scalar field source teleparallel gravity teleparallel Robertson–Walker cosmological teleparallel solutions dark energy quintessence |
| title | Scalar Field Source Teleparallel Robertson–Walker <i>F</i>(<i>T</i>) Gravity Solutions |
| title_full | Scalar Field Source Teleparallel Robertson–Walker <i>F</i>(<i>T</i>) Gravity Solutions |
| title_fullStr | Scalar Field Source Teleparallel Robertson–Walker <i>F</i>(<i>T</i>) Gravity Solutions |
| title_full_unstemmed | Scalar Field Source Teleparallel Robertson–Walker <i>F</i>(<i>T</i>) Gravity Solutions |
| title_short | Scalar Field Source Teleparallel Robertson–Walker <i>F</i>(<i>T</i>) Gravity Solutions |
| title_sort | scalar field source teleparallel robertson walker i f i i t i gravity solutions |
| topic | scalar field source teleparallel gravity teleparallel Robertson–Walker cosmological teleparallel solutions dark energy quintessence |
| url | https://www.mdpi.com/2227-7390/13/3/374 |
| work_keys_str_mv | AT alexandrelandry scalarfieldsourceteleparallelrobertsonwalkerifiitigravitysolutions |