A New Analytic Approximation of Luminosity Distance in Cosmology Using the Parker–Sochacki Method
The luminosity distance <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>d</mi><mi>L</mi></msub></semantics></math></inline-formula> is possibly the most...
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MDPI AG
2022-05-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/8/6/300 |
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| author | Joseph Sultana |
| author_facet | Joseph Sultana |
| author_sort | Joseph Sultana |
| collection | DOAJ |
| description | The luminosity distance <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>d</mi><mi>L</mi></msub></semantics></math></inline-formula> is possibly the most important distance scale in cosmology and therefore accurate and efficient methods for its computation is paramount in modern precision cosmology. Yet in most cosmological models the luminosity distance cannot be expressed by a simple analytic function in terms of the redshift <i>z</i> and the cosmological parameters, and is instead represented in terms of an integral. Although one can revert to numerical integration techniques utilizing quadrature algorithms to evaluate such an integral, the high accuracy required in modern cosmology makes this a computationally demanding process. In this paper, we use the Parker–Sochacki method (PSM) to generate a series approximate solution for the luminosity distance in spatially flat <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>CDM cosmology by solving a polynomial system of nonlinear differential equations. When compared with other techniques proposed recently, which are mainly based on the Padé approximant, the expression for the luminosity distance obtained via the PSM leads to a significant improvement in the accuracy in the redshift range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo>≤</mo><mi>z</mi><mo>≤</mo><mn>2.5</mn></mrow></semantics></math></inline-formula>. Moreover, we show that this technique can be easily applied to other more complicated cosmological models, and its multistage approach can be used to generate analytic approximations that are valid on a wider redshift range. |
| first_indexed | 2024-03-09T22:18:07Z |
| format | Article |
| id | doaj.art-4e98ec0804994d5b9c9c51c42536db8e |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T22:18:07Z |
| publishDate | 2022-05-01 |
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| series | Universe |
| spelling | doaj.art-4e98ec0804994d5b9c9c51c42536db8e2023-11-23T19:18:56ZengMDPI AGUniverse2218-19972022-05-018630010.3390/universe8060300A New Analytic Approximation of Luminosity Distance in Cosmology Using the Parker–Sochacki MethodJoseph Sultana0Department of Mathematics, Faculty of Science, University of Malta, MSD2080 Msida, MaltaThe luminosity distance <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>d</mi><mi>L</mi></msub></semantics></math></inline-formula> is possibly the most important distance scale in cosmology and therefore accurate and efficient methods for its computation is paramount in modern precision cosmology. Yet in most cosmological models the luminosity distance cannot be expressed by a simple analytic function in terms of the redshift <i>z</i> and the cosmological parameters, and is instead represented in terms of an integral. Although one can revert to numerical integration techniques utilizing quadrature algorithms to evaluate such an integral, the high accuracy required in modern cosmology makes this a computationally demanding process. In this paper, we use the Parker–Sochacki method (PSM) to generate a series approximate solution for the luminosity distance in spatially flat <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>CDM cosmology by solving a polynomial system of nonlinear differential equations. When compared with other techniques proposed recently, which are mainly based on the Padé approximant, the expression for the luminosity distance obtained via the PSM leads to a significant improvement in the accuracy in the redshift range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo>≤</mo><mi>z</mi><mo>≤</mo><mn>2.5</mn></mrow></semantics></math></inline-formula>. Moreover, we show that this technique can be easily applied to other more complicated cosmological models, and its multistage approach can be used to generate analytic approximations that are valid on a wider redshift range.https://www.mdpi.com/2218-1997/8/6/300FLRW cosmologyluminosity distanceParker–Sochacki method |
| spellingShingle | Joseph Sultana A New Analytic Approximation of Luminosity Distance in Cosmology Using the Parker–Sochacki Method Universe FLRW cosmology luminosity distance Parker–Sochacki method |
| title | A New Analytic Approximation of Luminosity Distance in Cosmology Using the Parker–Sochacki Method |
| title_full | A New Analytic Approximation of Luminosity Distance in Cosmology Using the Parker–Sochacki Method |
| title_fullStr | A New Analytic Approximation of Luminosity Distance in Cosmology Using the Parker–Sochacki Method |
| title_full_unstemmed | A New Analytic Approximation of Luminosity Distance in Cosmology Using the Parker–Sochacki Method |
| title_short | A New Analytic Approximation of Luminosity Distance in Cosmology Using the Parker–Sochacki Method |
| title_sort | new analytic approximation of luminosity distance in cosmology using the parker sochacki method |
| topic | FLRW cosmology luminosity distance Parker–Sochacki method |
| url | https://www.mdpi.com/2218-1997/8/6/300 |
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