暗能量與f（T）引力相關(guān)問(wèn)題研究
發(fā)布時(shí)間：2018-12-06 11:51
【摘要】：本文對(duì)暗能量的巧合問(wèn)題以及與暗能量相關(guān)的修改引力理論,f(T)引力,進(jìn)行了研究。 首先是對(duì)三重巧合問(wèn)題的研究。我們指出了目前比較流行的兩種三重相互作用暗能量模型之間的等價(jià)性。根據(jù)穩(wěn)態(tài)假設(shè),我們求出了各能量分量之間的轉(zhuǎn)化項(xiàng)的具體形式,并發(fā)現(xiàn),符合穩(wěn)態(tài)假設(shè)的能在數(shù)學(xué)層面解決三重巧合問(wèn)題的解有三組,但只有一組解是符合實(shí)際觀測(cè)的,這組解表明。在宇宙膨脹過(guò)程中,暗能量轉(zhuǎn)化為物質(zhì),物質(zhì)又轉(zhuǎn)化成輻射,即：隨著宇宙膨脹,密度減小慢的能量密度向著密度減小快的能量密度轉(zhuǎn)化,以此來(lái)解決巧合問(wèn)題。我們還對(duì)三重相互作用暗能量模型的穩(wěn)定性進(jìn)行了全面研究,分析了所有的不同形式的相互轉(zhuǎn)化項(xiàng)及其組合,發(fā)現(xiàn)只有當(dāng)物質(zhì)和暗能量之間的轉(zhuǎn)化項(xiàng)正比于臨界密度,或者暗能量密度、且物質(zhì)和輻射之間的轉(zhuǎn)化項(xiàng)不是正比于輻射密度時(shí),對(duì)應(yīng)的模型在微擾下才是穩(wěn)定的,這個(gè)結(jié)果對(duì)相關(guān)的模型構(gòu)建給出了限制。 其次是在全息能量模型的基礎(chǔ)上,對(duì)f(T)引力理論重新構(gòu)建的研究。由于f(T)是修改引力理論,它所修改的是引力理論中的幾何部分的內(nèi)容,而全息能量模型中的能量又是通過(guò)時(shí)空流形的幾何量來(lái)定義的,這種與時(shí)空幾何的共同聯(lián)系使我們可以將兩者結(jié)合起來(lái),以全息能量模型作為對(duì)f(T)引力理論的約束,從而確定f(T)引力理論的作用量形式,使得最終得到的f(T)理論自動(dòng)包含一個(gè)加速膨脹的宇宙學(xué)解。不同的全息能量模型會(huì)導(dǎo)致不同的f(T)引力理論。在本文中,我們對(duì)目前影響比較大的三種全息暗能量模型,HDE、NADE和RDE,分別進(jìn)行了相應(yīng)的f(T)引力理論的重新構(gòu)建；我們也在我們自己建立的全息ρKMR模型的基礎(chǔ)上,進(jìn)行了相應(yīng)的f(T)引力理論的重新構(gòu)建。在構(gòu)建過(guò)程中,我們發(fā)現(xiàn),目前普遍采用的邊界條件可以在微分方程的通解中選出符合厄米性要求的解,在這個(gè)意義上來(lái)說(shuō),這些邊界條件是有一定合理性的,但是,它們會(huì)導(dǎo)致一些重要信息的丟失,比如在RDE的物質(zhì)占主導(dǎo)時(shí)期,采用這些邊界調(diào)節(jié)得到的結(jié)果沒(méi)有展現(xiàn)出預(yù)期應(yīng)該有rescaling行為,這是由于邊界條件過(guò)于粗糙造成的。我們提出了新的邊界調(diào)節(jié),并利用它們給出更加合理的結(jié)果。
[Abstract]:In this paper, the coincidence problem of dark energy and the modified gravitational theory, f (T) gravitation related to dark energy are studied. The first is the study of triple coincidences. We point out the equivalence between two kinds of triple interaction dark energy models which are popular at present. According to the steady-state hypothesis, we have worked out the specific form of the transformation terms between the energy components, and found that there are three groups of solutions which accord with the steady-state hypothesis to solve the triple coincidence problem at the mathematical level, but only one set of solutions is in accordance with the actual observation. This set of solutions shows that. In the process of cosmic expansion, dark energy is transformed into matter and matter is transformed into radiation. That is, with the expansion of the universe, the energy density decreases slowly and the energy density decreases quickly, thus solving the coincidental problem. We also study the stability of the triple interaction dark energy model and analyze all the different forms of transformation terms and their combinations. It is found that only when the transformation term between matter and dark energy is proportional to the critical density, Or the dark energy density, and the transformation term between matter and radiation is not directly proportional to the radiation density, the corresponding model is stable under perturbation, which limits the relevant model construction. Secondly, on the basis of holographic energy model, the reconstruction of f (T) gravity theory is studied. Since f (T) is a modified gravity theory, what it modifies is the geometric part of the gravity theory, and the energy in the holographic energy model is defined by the geometric quantities of the space-time manifold. This joint relationship with space-time geometry allows us to combine the two and take the holographic energy model as a constraint on f (T) 's gravitational theory, thus determining the form of the f (T) 's gravitational theory. The resulting f (T) theory automatically contains a cosmological solution that accelerates expansion. Different holographic energy models lead to different f (T) gravitational theory. In this paper, we reconstruct the three holographic dark energy models, HDE,NADE and RDE, respectively. On the basis of the holographic 蟻 KMR model, we have reconstructed the corresponding f (T) gravity theory. In the process of construction, we find that the commonly used boundary conditions can be selected from the general solutions of differential equations to meet Hermitian requirements. In this sense, these boundary conditions are reasonable, but, They can lead to the loss of important information, such as when RDE is dominated by substances, the results of these boundary adjustments do not show that there should be expected rescaling behavior, because the boundary conditions are too rough. We propose new boundary adjustments and use them to give more reasonable results.
【學(xué)位授予單位】：北京工業(yè)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2013
【分類號(hào)】：P159
[Abstract]:In this paper, the coincidence problem of dark energy and the modified gravitational theory, f (T) gravitation related to dark energy are studied. The first is the study of triple coincidences. We point out the equivalence between two kinds of triple interaction dark energy models which are popular at present. According to the steady-state hypothesis, we have worked out the specific form of the transformation terms between the energy components, and found that there are three groups of solutions which accord with the steady-state hypothesis to solve the triple coincidence problem at the mathematical level, but only one set of solutions is in accordance with the actual observation. This set of solutions shows that. In the process of cosmic expansion, dark energy is transformed into matter and matter is transformed into radiation. That is, with the expansion of the universe, the energy density decreases slowly and the energy density decreases quickly, thus solving the coincidental problem. We also study the stability of the triple interaction dark energy model and analyze all the different forms of transformation terms and their combinations. It is found that only when the transformation term between matter and dark energy is proportional to the critical density, Or the dark energy density, and the transformation term between matter and radiation is not directly proportional to the radiation density, the corresponding model is stable under perturbation, which limits the relevant model construction. Secondly, on the basis of holographic energy model, the reconstruction of f (T) gravity theory is studied. Since f (T) is a modified gravity theory, what it modifies is the geometric part of the gravity theory, and the energy in the holographic energy model is defined by the geometric quantities of the space-time manifold. This joint relationship with space-time geometry allows us to combine the two and take the holographic energy model as a constraint on f (T) 's gravitational theory, thus determining the form of the f (T) 's gravitational theory. The resulting f (T) theory automatically contains a cosmological solution that accelerates expansion. Different holographic energy models lead to different f (T) gravitational theory. In this paper, we reconstruct the three holographic dark energy models, HDE,NADE and RDE, respectively. On the basis of the holographic 蟻 KMR model, we have reconstructed the corresponding f (T) gravity theory. In the process of construction, we find that the commonly used boundary conditions can be selected from the general solutions of differential equations to meet Hermitian requirements. In this sense, these boundary conditions are reasonable, but, They can lead to the loss of important information, such as when RDE is dominated by substances, the results of these boundary adjustments do not show that there should be expected rescaling behavior, because the boundary conditions are too rough. We propose new boundary adjustments and use them to give more reasonable results.
【學(xué)位授予單位】：北京工業(yè)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2013
【分類號(hào)】：P159
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