Jerk Parameter and Modified Theory
The accelerated expansion of the universe during recent times is well known in cosmology, whereas during early times, there was decelerated expansion. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvar...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/9/10/430 |
| _version_ | 1797572147534626816 |
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| author | Değer Sofuoğlu Aroonkumar Beesham |
| author_facet | Değer Sofuoğlu Aroonkumar Beesham |
| author_sort | Değer Sofuoğlu |
| collection | DOAJ |
| description | The accelerated expansion of the universe during recent times is well known in cosmology, whereas during early times, there was decelerated expansion. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Λ</mi></semantics></math></inline-formula>CDM model is consistent with most observations, but there are some issues with it. In addition, the transition from early deceleration to late-time acceleration cannot be explained by general relativity. Hence, it is worthwhile to examine modified gravity theories to explain this transition and to get a better understanding of dark energy. In this work, dark energy in modified <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><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity is investigated, where <i>R</i> is the Ricci scalar and <i>T</i> is the trace of the energy momentum tensor. Normally, the simplest form 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><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> is used, viz., <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><mo>=</mo><mi>R</mi><mo>+</mo><mi>λ</mi><mi>T</mi></mrow></semantics></math></inline-formula>. In this work, the more complicated form <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><mi>T</mi><mo>)</mo><mo>=</mo><mi>R</mi><mo>+</mo><mi>R</mi><mi>T</mi></mrow></semantics></math></inline-formula> is investigated in Friedmann–Lemaître–Robertson–Walker spacetime. This form has not been well studied. Since the jerk parameter in general relativity is constant and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, in order to have as small a departure from general relativity as possible, the jerk parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> is also assumed here. This enables the complete solution for the scale factor to be found. One of these forms is used for a complete analysis and is compared with the usually studied form <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><mi>T</mi><mo>)</mo><mo>=</mo><mi>R</mi><mo>+</mo><mi>R</mi><mi>T</mi></mrow></semantics></math></inline-formula>. The solution can also be broken down into a power-law form at early times (deceleration) and an exponential form at late times (acceleration), which makes the analysis simpler. Surprisingly, each of these forms is also a solution to the differential equation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> (though they are not solutions to the general solution). The energy conditions are also studied, and plots are provided. It is shown that viable models can be obtained without the need for the introduction of a cosmological constant, which reduces to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Λ</mi></semantics></math></inline-formula>CDM at late times. |
| first_indexed | 2024-03-10T20:50:45Z |
| format | Article |
| id | doaj.art-f1a4d31c093b49c1b5bc64d6743bc721 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-10T20:50:45Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-f1a4d31c093b49c1b5bc64d6743bc7212023-11-19T18:23:19ZengMDPI AGUniverse2218-19972023-09-0191043010.3390/universe9100430Jerk Parameter and Modified TheoryDeğer Sofuoğlu0Aroonkumar Beesham1Department of Physics, Istanbul University, Vezneciler, Fatih, Istanbul 34134, TurkeyDepartment of Mathematical Sciences, University of Zululand, Kwa-Dlangezwa 3886, South AfricaThe accelerated expansion of the universe during recent times is well known in cosmology, whereas during early times, there was decelerated expansion. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Λ</mi></semantics></math></inline-formula>CDM model is consistent with most observations, but there are some issues with it. In addition, the transition from early deceleration to late-time acceleration cannot be explained by general relativity. Hence, it is worthwhile to examine modified gravity theories to explain this transition and to get a better understanding of dark energy. In this work, dark energy in modified <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><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity is investigated, where <i>R</i> is the Ricci scalar and <i>T</i> is the trace of the energy momentum tensor. Normally, the simplest form 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><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> is used, viz., <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><mo>=</mo><mi>R</mi><mo>+</mo><mi>λ</mi><mi>T</mi></mrow></semantics></math></inline-formula>. In this work, the more complicated form <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><mi>T</mi><mo>)</mo><mo>=</mo><mi>R</mi><mo>+</mo><mi>R</mi><mi>T</mi></mrow></semantics></math></inline-formula> is investigated in Friedmann–Lemaître–Robertson–Walker spacetime. This form has not been well studied. Since the jerk parameter in general relativity is constant and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, in order to have as small a departure from general relativity as possible, the jerk parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> is also assumed here. This enables the complete solution for the scale factor to be found. One of these forms is used for a complete analysis and is compared with the usually studied form <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><mi>T</mi><mo>)</mo><mo>=</mo><mi>R</mi><mo>+</mo><mi>R</mi><mi>T</mi></mrow></semantics></math></inline-formula>. The solution can also be broken down into a power-law form at early times (deceleration) and an exponential form at late times (acceleration), which makes the analysis simpler. Surprisingly, each of these forms is also a solution to the differential equation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> (though they are not solutions to the general solution). The energy conditions are also studied, and plots are provided. It is shown that viable models can be obtained without the need for the introduction of a cosmological constant, which reduces to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Λ</mi></semantics></math></inline-formula>CDM at late times.https://www.mdpi.com/2218-1997/9/10/430<i>f</i>(<i>R</i>,<i>T</i>) gravityjerk parameternon-minimal couplingdark energy |
| spellingShingle | Değer Sofuoğlu Aroonkumar Beesham Jerk Parameter and Modified Theory Universe <i>f</i>(<i>R</i>,<i>T</i>) gravity jerk parameter non-minimal coupling dark energy |
| title | Jerk Parameter and Modified Theory |
| title_full | Jerk Parameter and Modified Theory |
| title_fullStr | Jerk Parameter and Modified Theory |
| title_full_unstemmed | Jerk Parameter and Modified Theory |
| title_short | Jerk Parameter and Modified Theory |
| title_sort | jerk parameter and modified theory |
| topic | <i>f</i>(<i>R</i>,<i>T</i>) gravity jerk parameter non-minimal coupling dark energy |
| url | https://www.mdpi.com/2218-1997/9/10/430 |
| work_keys_str_mv | AT degersofuoglu jerkparameterandmodifiedtheory AT aroonkumarbeesham jerkparameterandmodifiedtheory |