Department of Mathematics

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Author: search.filters.author.Dr. Shamaila RaniSubject: search.filters.subject.MATHEMATICS

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    Inflationary Parameters and Swampland Conjectures in Various Scenarios of Gravity
    (Library Information Services COMSATS University Islamabad Lahore Campus, 2022) Shama Sadiq; FA20-RMT-019; LHR TP 7923; Dr. Shamaila Rani
    The purposeofthisthesisistoinvestigatethein°ationaryparameters and swamplandconjecturesinthepresenceofscalar¯eldandChaplygin gas models.Weinvestigatethein°ationaryparameterssuchasslowroll parameters, scalarpowerspectrum,tensorpowerspectrum,spectralin- dex, tensor-to-scalarratiointhepresenceofscalar¯eldandChaplygingas modelsandalsodiscusstherecentlyproposedswamplandconjectures.The in°ationary scenarioisassumedtobeworkingunderastandardscalar¯eld having¡asdecayratio.Thisdecayratiohasdependenceintheformof generic power-lawofscalar¯eld Á along withthermalbathtemperature T, that is,¡(Á; T) = CÁ Ta Áa¡1 , where CÁ is dimensionlessparameterand a is in°ation decayrate.Assumingthatourmodelbendsaccordingtostrong dissipativeregime(R À 1), westudythebackgroundandperturbativedy- namics aswellasin°ationaryobservableasthescalarpowerspectrum PR, scalar spectralindex ns, dissipativeratio R, thetensor-to-scalarratio r, run- ning ofthescalarspectralindex dns d ln k and generalizedratioofSwampland de-Sitter conjecture ¶ TV ¶ V T for threedi®erentpotentials V (Á) = 3H2inf 8¼ e 2Á p(Á+1) , V = M4µ Á Mp¶2µ1 + ¯ Á2 M2p ¶ and V = 3 4M2(1 ¡ ep 2 3Á)2 respectively.
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    Thermodynamics in Non-Zero Torsion Theory
    (Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Nageen Pervaiz; FA19-RMT-001; LHR TP 7419; Dr. Shamaila Rani
    In thisthesis,westudythecosmicevolutionoftheacceleratinguniverse in theEinstein-Cartan-Sciama-Kibbletheorybyusing°athomogeneous and isotropicmodel.Inthisregards,weconsidersomeparameterizations of theequationofstateparameter ! in termsofredshiftfunction.This parametrization maybeaTaylorseriesextensioninthescalefactor,a Taylorseriesextensionintheredshiftoranyothergeneralparametrization of !. Weusegraphicalbehaviortoexplorethecosmologicalparameters suchasdeceleration,Om-diagnostic,state¯nderandsquaredspeedofsound parameters. Also,weexaminethevalidityofthegeneralizedsecondlaw of thermodynamicsatapparenthorizontakingintoaccountBekenstein- Hawkingentropy.
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    Stability and Topological Thermodynamics of Specific Black Holes
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Hifza Riaz; FA23-RMT-012; Dr. Shamaila Rani; LHR TP 9760
    In this thesis, we explore the charged higher-dimensional black holes by employing the Sharma-Mittal entropy which is widely used in black hole thermodynamics due to the non extensive nature of black holes. We compute different thermodynamic quantities like tem perature, heat capacity, and Gibbs free energy to study the stability of higher-dimensional black holes in Einstein-Gauss-Bonnet gravity. We explicitly analyze the behavior for differ ent horizon topologies (parameterized by k) in Einstein-Gauss-Bonnet gravity and observe that these black holes exhibit both local and global instabilities. Furthermore, to support our analysis, we chose thermodynamical topology methods (specifically the temperature and on-shell Gibbs free energy) to observe the stability of aforementioned black hole so lutions. It is found that the total topological charge obtained from the free energy method leads to +1for specific values of k which also gives the confirmation of the stability of these black hole solution in Einstein-Gauss-Bonnet gravity for specific choice of other constant parameters. Additionally, we study the sparsity of Hawking radiation, noting that the spar sity parameter tends to zero as the horizon radius increases. It is also observed that emission of energy radiates most rapidly for larger black holes which exhibits the consistency with physical observations.