{"title":"Form Invariance of Raychaudhuri Equation in the Presence of Inflaton-Type Fields","authors":"Arijit Panda, Debashis Gangopadhyay, Goutam Manna","doi":"10.1002/prop.202400134","DOIUrl":null,"url":null,"abstract":"<p>We show that the Raychaudhuri equation (RE) remains form invariant for certain solutions of scalar fields <span></span><math>\n <semantics>\n <mi>ϕ</mi>\n <annotation>$\\phi$</annotation>\n </semantics></math> whose Lagrangian is non-canonical and of the form <span></span><math>\n <semantics>\n <mrow>\n <mi>L</mi>\n <mo>(</mo>\n <mi>X</mi>\n <mo>,</mo>\n <mi>ϕ</mi>\n <mo>)</mo>\n <mo>=</mo>\n <mo>−</mo>\n <mi>V</mi>\n <mo>(</mo>\n <mi>ϕ</mi>\n <mo>)</mo>\n <mi>F</mi>\n <mo>(</mo>\n <mi>X</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$\\mathcal {L}(X,\\phi)=-V(\\phi)F(X)$</annotation>\n </semantics></math>, with <span></span><math>\n <semantics>\n <mrow>\n <mi>X</mi>\n <mo>=</mo>\n <mfrac>\n <mn>1</mn>\n <mn>2</mn>\n </mfrac>\n <msub>\n <mi>g</mi>\n <mrow>\n <mi>μ</mi>\n <mi>ν</mi>\n </mrow>\n </msub>\n <msup>\n <mo>∇</mo>\n <mi>μ</mi>\n </msup>\n <mi>ϕ</mi>\n <msup>\n <mo>∇</mo>\n <mi>ν</mi>\n </msup>\n <mi>ϕ</mi>\n </mrow>\n <annotation>$X=\\frac{1}{2} g_{\\mu \\nu } \\nabla ^{\\mu }\\phi \\nabla ^{\\nu } \\phi$</annotation>\n </semantics></math> and <span></span><math>\n <semantics>\n <mrow>\n <mi>V</mi>\n <mo>(</mo>\n <mi>ϕ</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$V(\\phi)$</annotation>\n </semantics></math> the potential. Solutions exist for both homogeneous and inhomogeneous fields that are like inflatons. Certain recent observations indicate that the cosmos is inhomogeneous and thus their results are in sync with latest observations. So the RE can accommodate primordial inhomogeneities as well as cosmologically relevant scenarios.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":null,"pages":null},"PeriodicalIF":5.6000,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fortschritte Der Physik-Progress of Physics","FirstCategoryId":"101","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/prop.202400134","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
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Abstract
We show that the Raychaudhuri equation (RE) remains form invariant for certain solutions of scalar fields whose Lagrangian is non-canonical and of the form , with and the potential. Solutions exist for both homogeneous and inhomogeneous fields that are like inflatons. Certain recent observations indicate that the cosmos is inhomogeneous and thus their results are in sync with latest observations. So the RE can accommodate primordial inhomogeneities as well as cosmologically relevant scenarios.
期刊介绍：
The journal Fortschritte der Physik - Progress of Physics is a pure online Journal (since 2013).
Fortschritte der Physik - Progress of Physics is devoted to the theoretical and experimental studies of fundamental constituents of matter and their interactions e. g. elementary particle physics, classical and quantum field theory, the theory of gravitation and cosmology, quantum information, thermodynamics and statistics, laser physics and nonlinear dynamics, including chaos and quantum chaos. Generally the papers are review articles with a detailed survey on relevant publications, but original papers of general interest are also published.
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