Scalar Field Source Teleparallel Robertson–Walker <i>F</i>(<i>T</i>) Gravity Solutions

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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Bibliographic Details
Main Author:	Alexandre Landry
Format:	Article
Language:	English
Published:	MDPI AG 2025-01-01
Series:	Mathematics
Subjects:	scalar field source teleparallel gravity teleparallel Robertson–Walker cosmological teleparallel solutions dark energy quintessence
Online Access:	https://www.mdpi.com/2227-7390/13/3/374
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Summary:	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.
ISSN:	2227-7390