Tesi sul tema "Expanding universe"

Kyoto University (京都大学)
0048
新制・課程博士
博士(人間・環境学)
甲第9663号
人博第147号
13||132(吉田南総合図書館)
新制||人||35(附属図書館)
UT51-2002-G421
京都大学大学院人間・環境学研究科人間・環境学専攻
(主査)教授 松田 哲, 助教授 阪上 雅昭, 助教授 早田 次郎
学位規則第4条第1項該当

Las ondas gravitatorias primordiales representan una ventana privilegiada para determinar la evolución del Universo, ya que a partir de su espectro seria posible reconstruir el factor de escala desde los instantes iniciales de expansión hasta el instante presente. En esta tesis, trabajando en aproximación de vacío adiabático, hemos revisado como la expansión del Universo amplifica las fluctuaciones del vacío cuántico. Hemos evaluado el espectro en un modelo de expansión del universo que considera una era inicial inflacionaria, una era dominada por agujeros negros primordiales y radiación, una era dominada por radiación y finalmente una era de la materia. Hemos demostrado como el espectro de este escenario es mucho menor que el del modelo habitual (inflación- era de radiación-era de materia), también hemos visto como las anisotropías observadas del CMB ponen limites a los parámetros libres del modelo de las cuatro eras. Hemos calculado el espectro en un modelo con un universo dominado por energía oscura en la era presente, concluyendo que pese a que este espectro coincide con el del escenario de las tres eras evoluciona de manera diferente. También hemos calculado el espectro en una hipotética segunda era de la materia, en el caso de que esta era de expansión acelerada sea sólo una etapa transitoria. Hemos estudiado como se cumple la segunda ley de la termodinámica durante la era de expansión acelerada, asignando una entropía a las ondas gravitatorias primordiales que debe cumplir una determinada condición. Finalmente, dejando de lado las ondas gravitatorias, hemos estudiado la segunda ley de la termodinámica en universos dominados por energía oscura fantasma, concluyendo que la entropía de estos fluidos es negativa y que la segunda ley es respetada.
Cosmology has for a long time been a rather speculative science. Hubble's discovery that the Universe is expanding, and -more recently- the realization that at present this expansion is accelerated, the measured abundance of light elements, the mass distribution of galaxies and clusters thereof, and the discovery and posterior measurements of the anisotropies of the CMB have changed this picture. Hopefully, measurements of GWs will soon be added to this short list. At any rate, now we can speak confidently of physical cosmology as a fully-fledged branch of Science. The relic GWs constitute a privileged window to determine the evolution of the Universe. Little is known from the early evolution of the Universe and the predictions for their spectrum depend on the model considered. According to these predictions, a spectrum of relic GWs is generated making feasible its detection with the technology currently being developed. In this thesis, using the adiabatic vacuum approximation, we have reviewed how the expansion of the Universe amplifies the quantum vacuum fluctuations, and how the relic GWs spectrum is related with the scale factor. We have later evaluated the spectrum in a four-stage model (which consist on a De Sitter stage, a stage dominated by a mixture of MBHs and radiation, a radiation dominated stage and finally a non-relativistic matter (dust) dominated stage). We have demonstrated that the spectrum in this scenario is much lower than the predicted by three-stage model (De Sitter-radiation era-dust era). We have also shown how the bound over the GWs spectrum from the measured CMB anisotropies places severe constraints over the free parameters of the four-stage model. We have also considered a scenario featuring an accelerated expanding era dominated by dark energy, right after the dust era of the three-stage model. We have found that the current power spectrum of this four-stage scenario exactly coincides with that of the three-stage, but it evolves in a different fashion. We have considered as well the possibility that the dark energy decays in non-relativistic matter leading to a second dust era in the far future and obtained the power spectrum of the GWs as well as the evolution of the density parameter. We have applied the generalized second law of thermodynamics to the four-stage model of above. Assuming the GWs entropy proportional to the number of GWs, we have found the GSL is fulfilled provided a certain proportionality constant does not exceed a given upper bound. Finally, we have extended the GSL study to a single stage universe model dominated by dark energy (either phantom or not), and found that the GSL is satisfied and that the entropy of the phantom fluid is negative. Likewise, we have found a transformation between phantom and non-phantom scenarios preserving the Einstein field equations that entails a "quasi" duality between the thermodynamics of both scenarios.

We use standard general relativity to clarify common misconceptions about fundamental aspects of the expansion of the Universe. In the context of the new standard Lambda-CDM cosmology we resolve conflicts in the literature regarding cosmic horizons and the Hubble sphere (distance at which recession velocity equals c) and we link these concepts to observational tests. We derive the dynamics of a non-comoving galaxy and generalize previous analyses to arbitrary FRW universes. We also derive the counter-intuitive result that objects at constant proper distance have a non-zero redshift. Receding galaxies can be blueshifted and approaching galaxies can be redshifted, even in an empty universe for which one might expect special relativity to apply. Using the empty universe model we demonstrate the relationship between special relativity and Friedmann-Robertson-Walker cosmology. We test the generalized second law of thermodynamics (GSL) and its extension to incorporate cosmological event horizons. In spite of the fact that cosmological horizons do not generally have well-defined thermal properties, we find that the GSL is satisfied for a wide range of models. We explore in particular the relative entropic "eworth"e of black hole versus cosmological horizon area. An intriguing set of models show an apparent entropy decrease but we anticipate this apparent violation of the GSL will disappear when solutions are available for black holes embedded in arbitrary backgrounds. Recent evidence suggests a slow increase in the fine structure constant over cosmological time scales. This raises the question of which fundamental quantities are truly constant and which might vary. We show that black hole thermodynamics may provide a means to discriminate between alternative theories invoking varying constants, because some variations in the fundamental "econstants"e could lead to a violation of the generalized second law of thermodynamics.

碩士
國立臺灣師範大學
物理學系
96
The big-bang theory is arguably one of the most fascinating and significant theories in modern physics. However, an expanding space－the major notion of the big-bang cosmology－is also one of the most confusing concepts in modern physics. In this thesis, we first explore various models of expanding universe by virtue of three cosmological horizons, i.e. the particle horizon, the event horizon, and the Hubble radius. We then discuss some of the most perplexing features of the big-bang cosmology, such as cosmological redshifts and the receding velocity of distant galaxies. Finally, based on the gedanken experiment of the “tethered galaxy” proposed by Harrison in 1995, we investigate the very nature of space expansion and its consequences in different cosmological models.

碩士
國立臺灣大學
物理學研究所
88
In this M.S. thesis, we investigate the behavior of a hydrogen atom in the expanding universe making use of the appropriate Dirac equation in the Robertson-Walker (RW) metric. The equation is obtained by incorporating the electromagnetic potential of a static point-like charge, via gauge principle, into the Dirac equation phrased in the curved spacetime. The solutions to such equation are obtained by the perturbation method. The results are presented and briefly discussed.

Cheung Kai Chung Mars = 宇宙學中的題目 / 張啓聰.
Thesis submitted in: September 2005.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2006.
Includes bibliographical references (leaves 93-95).
Text in English; abstracts in English and Chinese.
Cheung Kai Chung Mars = Yu zhou xue zhong de ti mu / Zhang Qicong.
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- "Hubble's Law, the cosmic scale factor and redshift" --- p.1
Chapter 1.2 --- The Big Bang Model and Cosmic Microwave Background --- p.3
Chapter 1.3 --- An overview of the universe --- p.4
Chapter 1.4 --- Current Observation Results and Motivation --- p.6
Chapter 1.5 --- Review of CMB calculation --- p.7
Chapter 1.5.1 --- Friedmann Cosmologies --- p.8
Chapter 1.5.2 --- The Perturbed Robertson-Walker Metric --- p.10
Chapter 1.5.3 --- Boltzmann Equations --- p.13
Chapter 1.5.4 --- Perturbative Einstein Equations --- p.16
Chapter 2 --- Ionization History of The Universe --- p.18
Chapter 2.1 --- Saha equation --- p.18
Chapter 2.2 --- Peebles recombination --- p.19
Chapter 2.3 --- RECFAST --- p.20
Chapter 3 --- CMB Anisotropics --- p.22
Chapter 3.1 --- The CMBA spectra --- p.23
Chapter 3.1.1 --- Tight Coupling Limit --- p.23
Chapter 3.1.2 --- Free Streaming --- p.25
Chapter 3.1.3 --- The Anisotropy Spectrum --- p.27
Chapter 3.1.4 --- CMBFAST --- p.28
Chapter 4 --- Variation of Fundamental Constant and CMBA spectra --- p.30
Chapter 4.1 --- The problem of units --- p.31
Chapter 4.2 --- Modification of CMBFAST and conversion of units --- p.32
Chapter 4.3 --- The constraints of varying constants using CMBA spectra --- p.35
Chapter 4.4 --- Physics involved and variation of the spectra --- p.36
Chapter 4.4.1 --- Effect of Recombination --- p.36
Chapter 4.4.2 --- Variation of hP --- p.38
Chapter 4.4.3 --- Variations of e and me --- p.41
Chapter 4.4.4 --- Variations of g and c --- p.48
Chapter 4.4.5 --- Constraints on the constants --- p.57
Chapter 5 --- MCMC and CMBA Spectra --- p.59
Chapter 5.1 --- Method --- p.60
Chapter 5.1.1 --- Algorithm --- p.60
Chapter 5.1.2 --- Check of Convergency --- p.61
Chapter 5.2 --- Likelihood function --- p.62
Chapter 5.3 --- Results --- p.66
Chapter 5.3.1 --- MCMC investigation of varying α in the temperature spectrum --- p.67
Chapter 5.3.2 --- MCMC investigation of varying α in the polarization spectrum --- p.69
Chapter 5.3.3 --- MCMC investigation of varying α and cosmological parameters --- p.71
Chapter 5.3.4 --- Summary --- p.73
Chapter 6 --- Extra Dimensions and Cosmology --- p.74
Chapter 6.1 --- A review of KK cosmology --- p.74
Chapter 6.2 --- Non-flat extra dimension universe --- p.80
Chapter 6.2.1 --- Close Extra Dimensions and Flat Usual Dimensions --- p.83
Chapter 6.2.2 --- Open Extra Dimensions and Flat Usual Dimensions --- p.87
Chapter 6.2.3 --- Summary: Possibility of Extra Dimension(s) --- p.91
Bibliography --- p.93

Li Baojiu = 宇宙学和新物理学的交叉领域 / 李宝九.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2006.
Includes bibliographical references (leaves 93-99).
Text in English; abstracts in English and Chinese.
Li Baojiu = Yu zhou xue he xin wu li xue de jiao cha ling yu / Li Baojiu.
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Some Basic Conceptions in Cosmology --- p.2
Chapter 1.1.1 --- "The Big Bang, Hubble's Law" --- p.2
Chapter 1.1.2 --- The Cosmological Principle and Robertson-Walker Metric --- p.3
Chapter 1.1.3 --- The Cosmological Redshift --- p.4
Chapter 1.1.4 --- The Friedmann Equations --- p.4
Chapter 1.2 --- Big Bang Nucleosynthesis --- p.5
Chapter 1.3 --- Dark Energy --- p.9
Chapter 2 --- "Branes, Varying Constants and BBN" --- p.16
Chapter 2.1 --- A Brief Introduction to Theories Involving Extra Dimensions --- p.17
Chapter 2.1.1 --- The Kaluza-Klein Theory --- p.18
Chapter 2.1.2 --- Large Extra Dimensions --- p.19
Chapter 2.1.3 --- Warped Extra Dimensions --- p.22
Chapter 2.1.4 --- Universal Extra Dimensions --- p.24
Chapter 2.1.5 --- Cosmology in a Brane World --- p.27
Chapter 2.2 --- BBN and Varying Constants in Brane Models --- p.29
Chapter 2.2.1 --- The Low Energy Effective Action in Brane Models --- p.30
Chapter 2.2.2 --- BBN with a Varying Higgs VEV --- p.34
Chapter 2.3 --- Numerical Results --- p.38
Chapter 2.4 --- Discussion and Conclusions --- p.47
Chapter 3 --- "Universal Extra Dimensions, Varying Constants and BBN" --- p.49
Chapter 3.1 --- Introduction --- p.50
Chapter 3.2 --- The Low Energy 4-Dimensional Effective Actions --- p.50
Chapter 3.3 --- Radion Dependence of Fundamental Constants --- p.54
Chapter 3.4 --- Variations of Quantities Relevant For BBN Calculation --- p.57
Chapter 3.4.1 --- Neutron-proton Mass Difference --- p.57
Chapter 3.4.2 --- Weak Interaction Rates --- p.58
Chapter 3.4.3 --- Expansion Rate of the Universe --- p.58
Chapter 3.4.4 --- Nuclear Reaction Rates --- p.59
Chapter 3.5 --- Numerical Results --- p.64
Chapter 3.6 --- Discussion and Conclusions --- p.70
Chapter 4 --- Dark Energy as a Signature of Extra Dimensions --- p.74
Chapter 4.1 --- Introduction --- p.75
Chapter 4.2 --- The Underlying Higher Dimensional Theory --- p.75
Chapter 4.3 --- The Cosmic Evolution in Different Eras --- p.79
Chapter 4.3.1 --- The Blazing Era --- p.79
Chapter 4.3.2 --- The Radiation Dominated Era --- p.83
Chapter 4.3.3 --- The Matter Dominated Era --- p.84
Chapter 4.4 --- A Realistic Cosmology --- p.85
Chapter 4.5 --- Discussions and Conclusions --- p.92
Bibliography --- p.93

博士
國立交通大學
物理研究所
104
The main task of this Ph.D. thesis is seeking Bianchi type I metrics, which are homogeneous but anisotropic space, and studying their stability in some interesting cosmological models/theories to see whether they respect the well-known cosmic no-hair conjecture proposed by Hawking and his colleagues. In particular, chapters 2 and 3 of this thesis include results in some extended scenarios of a supergravity motivated model proposed by Kanno, Soda, and Watanabe recently, which includes a coupling between the scalar field $ hi$ and the $U(1)$ field $A_\mu$ such as $f^2( hi) F_{\mu\nu}F^{\mu\nu}$. As a result, this coupling causes stable spatial anisotropies in all the studied scenarios, in which the scalar field $ hi$ can be either canonical or non-canonical forms like the Dirac-Born-Infeld (DBI) or supersymmetric Dirac-Born-Infeld (SDBI) form. In other word, the existence of this coupling always leads to counterexamples to the cosmic no-hair conjecture. In order to make this conjecture alive, we introduce a phantom field $ si$, whose kinetic energy is negative definite, to these models. As a result, the inclusion of the phantom field $ si$ makes the following spatial hairs unstable during the inflationary phase, no matter the form of the scalar field $ hi$. In chapter 4, we study the cosmological implications of a non-linear massive gravity theory proposed by de Rham, Gabadadze, and Tolley (dRGT) recently, which has been shown to be free of the Boulware-Deser ghost. In particular, we are able to find a simple stable anisotropic cosmological solution to the dRGT theory. More interestingly, we are also able to show the cosmological constant-like behavior of massive graviton terms in the dRGT theory. This result might give us a hint in order to investigate the nature of cosmological constant $\Lambda$. Similar to the previous chapters, we introduce the phantom field into the system and see that this extra field does lead the anisotropic cosmological solution to unstable state in general. According to the study presented in this Ph.D. thesis, we might come to a conclusion that the phantom field is closely associated with the validity of the cosmic no-hair conjecture by causing, at least, one unstable mode to anisotropic metric(s).