Hamiltonian analysis of covariant teleparallel theories of gravity
Date
2021-07-12
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Abstract
Möödunud sajandil valitses maailmapilt et gravitatsiooni kirjeldab jõuteooria asemel Üldrelatiivsusteooria, mille raames mateeria mõjub aegruumi geomeetriat milles me elame. Eelmainitud kirjeldus on tõestanud oma sobivust paljudes eksperimentaalsetes ja vaatuslikes testides alates Albert Einsteini gravitatsiooniteooria püstitamisest. Lisaks on ta oma edukust näidanud kosmoloogilise standardmudeli lahendamatu osana.
Sellest hoolimata on kaasaegsed vaatlused avaldanud statistiliselt märkamisväärseid pingeid kosmoloogilises standardmudelis. Lisaks koosneb 95% universumi mateeriasisust seni selgitamatuks jäänud tumeainest ja tumeenergiast. Nende probleemide käsitlemiseks on võimalik uurida modifitseeritud gravitatsiooniteooriaid.
Selles väitekirjas on uuritud modifitseeritud teleparalleelsed gravitatsiooniteooriad. Need teooriad lähtuvad arusaamast et Üldrelatiivsusteooriat on võimalik kirjeldada füüsikaliiselt ekvivalentsel viisil. Siiski näitab teleparalleelne kirjeldus ette uusi võimalusi gravitatsiooniteooria modifitseerida. Väitekirjas on lähemalt uuritud f (TNGR ) gravitatsiooniteooria ja käsitletud küsimus kas f (TNGR ) on teoreetilise vaatenurga alt kooskõlaline gravitatsiooniteooria.
Selle küsimusele vastamiseks rakendati teooriale esmakordselt kovariantset Hamiltoni formalismi. See käsitlus on fundamentaalsel perspektiivil asjakohasem ja üldisem ning annab võimalust jõuda erinevate järeldusteni võrreldes kirjanduses levinud käsitlusega. f (TNGR ) teooria Hamiltoni analüüsi esimene osa on konkreetselt tuletatud. Käsitletud lähenemine avab teed kõige populaarsemate teleparalleelsete gravitatsiooniteooriate kanoonilisele Hamiltoni analüüsile.
Väitekirja peamine järeldus näitab et f (TNGR ) teooria on tõsiselt kahtlustav, kuid on veel mõned aspektid mis on väärt uurida enne kui f (TNGR ) teooria on täielikult välistatud kui kooskõlaline gravitatsiooniteooria.
For over a century, it has been known that gravity should be described by the theory of general relativity, in which matter is affecting the spacetime geometry we live in, rather than as a force theory. This description has been proven to pass much experimental and observational tests since Albert Einstein formulated this theory of gravity. Furthermore, it has been proven successful as incorporated in the standard model of cosmology. However, recently it has become evident from observation that there are statistically significant tensions in observations within the standard model of cosmology. Furthermore, 95% of our universe consists of dark matter and dark energy, which is still not understood. In order to address these issues one may look into modified theories of gravity. In this thesis teleparallel modified theories of gravity are examined. They make use of the fact that there are alternative physically equivalent descriptions of general relativity. However, the teleparallel formulation admits new ways to modify gravity. In particular a theory called f (TNGR )-gravity is examined. The question this thesis address is if f (TNGR )-gravity is viable as a theory from a theoretical point of view. In order to answer this question the so-called covariant Hamiltonian analysis of the theory is considered for the first time. This theory is more correct and general from a fundamental perspective and it might lead to different conclusions than for those found in the literature. The first part in the Hamiltonian analysis for f (TNGR )-gravity is explicitly derived. This paves the way for a canonical Hamiltonian analysis for the most popular theories of teleparallel gravity. The main conclusion of the thesis is that the viability of f (TNGR )-gravity is in serious doubt. Though, there are still a few points that need to be examined before ruling out f (TNGR ) as a viable theory of gravity.
For over a century, it has been known that gravity should be described by the theory of general relativity, in which matter is affecting the spacetime geometry we live in, rather than as a force theory. This description has been proven to pass much experimental and observational tests since Albert Einstein formulated this theory of gravity. Furthermore, it has been proven successful as incorporated in the standard model of cosmology. However, recently it has become evident from observation that there are statistically significant tensions in observations within the standard model of cosmology. Furthermore, 95% of our universe consists of dark matter and dark energy, which is still not understood. In order to address these issues one may look into modified theories of gravity. In this thesis teleparallel modified theories of gravity are examined. They make use of the fact that there are alternative physically equivalent descriptions of general relativity. However, the teleparallel formulation admits new ways to modify gravity. In particular a theory called f (TNGR )-gravity is examined. The question this thesis address is if f (TNGR )-gravity is viable as a theory from a theoretical point of view. In order to answer this question the so-called covariant Hamiltonian analysis of the theory is considered for the first time. This theory is more correct and general from a fundamental perspective and it might lead to different conclusions than for those found in the literature. The first part in the Hamiltonian analysis for f (TNGR )-gravity is explicitly derived. This paves the way for a canonical Hamiltonian analysis for the most popular theories of teleparallel gravity. The main conclusion of the thesis is that the viability of f (TNGR )-gravity is in serious doubt. Though, there are still a few points that need to be examined before ruling out f (TNGR ) as a viable theory of gravity.
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Keywords
gravitation, quantum gravitation, theoretical physics