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[{"key": "dc.contributor.advisor", "value": "Kainulainen, Kimmo", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.advisor", "value": "Schiappacasse, Enrico", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "V\u00e4is\u00e4nen, Olli", "language": "", "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2021-12-03T06:15:00Z", "language": null, "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2021-12-03T06:15:00Z", "language": null, "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2021", "language": "", "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/78878", "language": null, "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "Maailmankaikkeuden ep\u00e4homogeenisuuksien vaikutuksia sen laajenemiseen ja mittaustuloksiin on tutkittu kirjallisuudessa paljon. Koska Einsteinin yht\u00e4l\u00f6ille ei tunneta yleisi\u00e4 ratkaisuja, n\u00e4m\u00e4 tutkimukset ovat kuitenkin perustuneet h\u00e4iri\u00f6teoriaan ja hyvin symmetrisiin, yksinkertaistettuihin malleihin. T\u00e4ss\u00e4 tutkielmassa selvit\u00e4n, kuinka ep\u00e4homogeenisuuksien vaikutuksia olisi mahdollista tutkia k\u00e4ytt\u00e4m\u00e4ll\u00e4 t\u00e4ysin relativistisia numeerisia simulaatioita. T\u00e4t\u00e4 varten esittelen Arnowitt-Deser-Misner- ja Baumgarte-Shapiro-Shibata-Nakamura -formalismit (ADM- ja BSSN-formalismit) yleiselle suhteellisuusteorialle ja tutkin ADM-formalismin numeerista stabiiliutta\nerilaisilla alkuarvoilla aineen dominoimassa maailmankaikkeudessa. Saamieni tulosten stabiilius riippui vahvasti simulaatioille valitusta pituusskaalasta. Hyvin suurilla skaaloilla (\u223c 500 Mpc) tulokset olivat varsin luotettavia simulaation loppuhetki\u00e4 lukuun ottamatta, kun taas fysikaalisesti merkitt\u00e4vill\u00e4 pituusskaaloilla (\u223c 100 Mpc) yht\u00e4l\u00f6t olivat l\u00e4hes v\u00e4litt\u00f6m\u00e4sti ep\u00e4stabiilit. Jatkotutkimuksissa tulisi siirty\u00e4 ADM-formalismista luotettavampaan BSSN-formalismiin. T\u00e4m\u00e4n lis\u00e4ksi laadin simulaation havaittujen punasiirtymien laskemiseksi numeerisista aika-avaruuksista ja arvioin sen tuloksia kvalitatiivisesti. Alustavien tulosten mukaan n\u00e4enn\u00e4iset tiheysvaihtelut v\u00e4\u00e4ristyv\u00e4t gravitaatiolinssi-ilmi\u00f6n vuoksi.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.abstract", "value": "There is an extensive literature on the effects of inhomogeneities on the expansion of the universe and measurable quantities. However, as there is no known general solution to Einstein\u2019s field equations, much of the analysis relies on perturbation theory and very symmetric toy models. In this thesis, I will assess a method of studying the effects of inhomogeneities using fully relativistic simulations. To this end, I will introduce the Arnowitt-Deser-Misner- and Baumgarte-Shapiro-Shibata-Nakamura -formulations (ADM- and BSSN-formulations) for general relativity and discuss the numerical stability of the ADM-formalism with different initial conditions in a matter dominated universe. The stability of the results depends heavily on the chosen length scale. On very large scales (\u223c 500 Mpc) the results appear reliable until late in the evolution, whereas on more physically relevant scales (\u223c 100 Mpc) the equations are almost immediately unstable. Further research should move on to the more stable BSSN-formalism. In addition, I implemented a simulation for calculating observed redshifts in numerical spacetimes and assessed its results qualitatively. The preliminary results suggest an apparent deformation of density perturbations due to gravitational lensing.", "language": "en", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by Paivi Vuorio (paelvuor@jyu.fi) on 2021-12-03T06:15:00Z\nNo. of bitstreams: 0", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2021-12-03T06:15:00Z (GMT). No. of bitstreams: 0\n Previous issue date: 2021", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "99", "language": "", "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "eng", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "numerical relativity", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "ADM-formalism", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Simulating inhomogeneous spacetimes using the ADM-formalism", "language": "", "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-202112035876", "language": "", "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Fysiikan laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Physics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Teoreettinen fysiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Theoretical Physics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": null, "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4024", "language": "", "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "kosmologia", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "suhteellisuusteoria", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "numeeriset menetelm\u00e4t", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "cosmology", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "theory of relativity", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "numerical methods", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
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