Viability of Baryon to Entropy Ratio in Modified Hořava–Lifshitz Gravity
In this paper, we study the matter–antimatter imbalance in the universe through baryogenesis (also known as baryosynthesis), which is a physical process that took off just a little while after the big bang explosion, producing a supremacy of matter over antimatter. In this work, we commit the reprod...
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MDPI AG
2023-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/4/824 |
| _version_ | 1797603441093115904 |
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| author | Abdul Jawad Abdul Malik Sultan Shamaila Rani |
| author_facet | Abdul Jawad Abdul Malik Sultan Shamaila Rani |
| author_sort | Abdul Jawad |
| collection | DOAJ |
| description | In this paper, we study the matter–antimatter imbalance in the universe through baryogenesis (also known as baryosynthesis), which is a physical process that took off just a little while after the big bang explosion, producing a supremacy of matter over antimatter. In this work, we commit the reproduction of the baryon to entropy ratio (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfrac><msub><mi>η</mi><msub><mrow></mrow><mi>B</mi></msub></msub><mi>S</mi></mfrac><mo>=</mo><mfrac><mrow><msub><mi>η</mi><msub><mrow></mrow><mi>β</mi></msub></msub><mo>−</mo><msub><mi>η</mi><mover accent="true"><msub><mrow></mrow><mi>β</mi></msub><mo>¯</mo></mover></msub></mrow><mi>S</mi></mfrac></mrow></semantics></math></inline-formula>), where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>η</mi><msub><mrow></mrow><mi>β</mi></msub></msub><mrow><mo>(</mo><msub><mi>η</mi><mover accent="true"><msub><mrow></mrow><mi>β</mi></msub><mo>¯</mo></mover></msub><mo>)</mo></mrow></mrow></semantics></math></inline-formula> is a baryon(anti-baryon) number and <i>S</i> is the entropy of the universe in the presence of modified Hořava-Lifshitz <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, which is also called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mo>)</mo></mrow></semantics></math></inline-formula>-gravity. We inspect different baryogenesis interactions proportional to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>R</mi><mo>˜</mo></mover></semantics></math></inline-formula> (where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>R</mi><mo>˜</mo></mover></semantics></math></inline-formula> is the argument of general function <i>F</i> used for the development of modified Hořava-Lifshitz gravity). For this study, we examine two models by choosing different values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mo>)</mo></mrow></semantics></math></inline-formula>. In the first model, the functional value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mrow><mo>(</mo><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mo>)</mo></mrow><mo>=</mo><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mo>+</mo><mi>α</mi><msup><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mn>2</mn></msup></mrow></semantics></math></inline-formula> (where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> is a real constant). The second model is more generalized and extended as compare to first one. Mathematically, this model is given by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mrow><mo>(</mo><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mo>)</mo></mrow><mo>=</mo><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mo>+</mo><mi>α</mi><msup><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mn>2</mn></msup><mo>+</mo><mi>β</mi><msup><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mi>m</mi></msup></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> are real constants and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>></mo><mn>2</mn></mrow></semantics></math></inline-formula> is a real model parameter. Our results for both models and different values of <i>m</i> point out that matter-antimatter asymmetry does not vanish under the effect of the modified Hořava-Lifshitz theory of gravity, which shows a consistent and compatible fact of gravitational baryogenesis with recent observational data. |
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| spelling | doaj.art-8e34900b4d0547db92c4b84d4be0d2032023-11-17T21:33:15ZengMDPI AGSymmetry2073-89942023-03-0115482410.3390/sym15040824Viability of Baryon to Entropy Ratio in Modified Hořava–Lifshitz GravityAbdul Jawad0Abdul Malik Sultan1Shamaila Rani2Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, PakistanDepartment of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, PakistanDepartment of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, PakistanIn this paper, we study the matter–antimatter imbalance in the universe through baryogenesis (also known as baryosynthesis), which is a physical process that took off just a little while after the big bang explosion, producing a supremacy of matter over antimatter. In this work, we commit the reproduction of the baryon to entropy ratio (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfrac><msub><mi>η</mi><msub><mrow></mrow><mi>B</mi></msub></msub><mi>S</mi></mfrac><mo>=</mo><mfrac><mrow><msub><mi>η</mi><msub><mrow></mrow><mi>β</mi></msub></msub><mo>−</mo><msub><mi>η</mi><mover accent="true"><msub><mrow></mrow><mi>β</mi></msub><mo>¯</mo></mover></msub></mrow><mi>S</mi></mfrac></mrow></semantics></math></inline-formula>), where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>η</mi><msub><mrow></mrow><mi>β</mi></msub></msub><mrow><mo>(</mo><msub><mi>η</mi><mover accent="true"><msub><mrow></mrow><mi>β</mi></msub><mo>¯</mo></mover></msub><mo>)</mo></mrow></mrow></semantics></math></inline-formula> is a baryon(anti-baryon) number and <i>S</i> is the entropy of the universe in the presence of modified Hořava-Lifshitz <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, which is also called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mo>)</mo></mrow></semantics></math></inline-formula>-gravity. We inspect different baryogenesis interactions proportional to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>R</mi><mo>˜</mo></mover></semantics></math></inline-formula> (where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>R</mi><mo>˜</mo></mover></semantics></math></inline-formula> is the argument of general function <i>F</i> used for the development of modified Hořava-Lifshitz gravity). For this study, we examine two models by choosing different values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mo>)</mo></mrow></semantics></math></inline-formula>. In the first model, the functional value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mrow><mo>(</mo><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mo>)</mo></mrow><mo>=</mo><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mo>+</mo><mi>α</mi><msup><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mn>2</mn></msup></mrow></semantics></math></inline-formula> (where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> is a real constant). The second model is more generalized and extended as compare to first one. Mathematically, this model is given by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mrow><mo>(</mo><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mo>)</mo></mrow><mo>=</mo><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mo>+</mo><mi>α</mi><msup><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mn>2</mn></msup><mo>+</mo><mi>β</mi><msup><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mi>m</mi></msup></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> are real constants and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>></mo><mn>2</mn></mrow></semantics></math></inline-formula> is a real model parameter. Our results for both models and different values of <i>m</i> point out that matter-antimatter asymmetry does not vanish under the effect of the modified Hořava-Lifshitz theory of gravity, which shows a consistent and compatible fact of gravitational baryogenesis with recent observational data.https://www.mdpi.com/2073-8994/15/4/824gravitational baryogenesisbaryon to entropy ratiomodified Hořava-Lifshitz gravity |
| spellingShingle | Abdul Jawad Abdul Malik Sultan Shamaila Rani Viability of Baryon to Entropy Ratio in Modified Hořava–Lifshitz Gravity Symmetry gravitational baryogenesis baryon to entropy ratio modified Hořava-Lifshitz gravity |
| title | Viability of Baryon to Entropy Ratio in Modified Hořava–Lifshitz Gravity |
| title_full | Viability of Baryon to Entropy Ratio in Modified Hořava–Lifshitz Gravity |
| title_fullStr | Viability of Baryon to Entropy Ratio in Modified Hořava–Lifshitz Gravity |
| title_full_unstemmed | Viability of Baryon to Entropy Ratio in Modified Hořava–Lifshitz Gravity |
| title_short | Viability of Baryon to Entropy Ratio in Modified Hořava–Lifshitz Gravity |
| title_sort | viability of baryon to entropy ratio in modified horava lifshitz gravity |
| topic | gravitational baryogenesis baryon to entropy ratio modified Hořava-Lifshitz gravity |
| url | https://www.mdpi.com/2073-8994/15/4/824 |
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