【摘要】： 目前,通過對(duì)Ia型超新星觀測以及對(duì)源于Wilkinson Microwave AnisotropyProbe(WMAP)精確數(shù)據(jù)的分析表明我們的宇宙目前正處于加速膨脹的階段。這與以普通重子物質(zhì)為基礎(chǔ)的熱大爆炸宇宙學(xué)模型相矛盾。按照熱大爆炸宇宙學(xué)模型的觀點(diǎn),宇宙應(yīng)該是減速膨脹的。為了能夠在熱大爆炸宇宙學(xué)模型的框架下解釋宇宙當(dāng)前的加速膨脹,就要對(duì)其進(jìn)行修正。修正的方式主要有兩種,一是通過在宇宙組分中引入一種新的、具有負(fù)壓強(qiáng)的、且在大尺度結(jié)構(gòu)中是均勻分布的動(dòng)力學(xué)成分,即所謂的暗能量。這實(shí)際上是對(duì)Einstein引力場方程的右邊進(jìn)行了修正。這種修正的正確性是由Wilkinson Microwave AnisotropyProbe(WMAP)所支持。該探測顯示,暗能量占宇宙物質(zhì)總成分的73%。因此,有理由認(rèn)為它是當(dāng)前宇宙加速膨脹的誘因。二是通過對(duì)Einstein引力場方程的左邊,即時(shí)空幾何部分,進(jìn)行修正。這類修正通常被稱為引力修正理論,f(R)引力理論就是其中較具競爭力的一個(gè)。 本文分別從上述兩個(gè)途徑入手,對(duì)當(dāng)前加速膨脹宇宙中的若干物理問題進(jìn)行了研究。首先,對(duì)作為暗能量與暗物質(zhì)統(tǒng)一模型的新的廣義Chaplygin氣體進(jìn)行了討論。我們不僅分別討論了當(dāng)暗能量和暗物質(zhì)之間存在和不存在相互作用時(shí),能量密度隨紅移z的演化趨勢,而且還給出了暗能量和暗物質(zhì)間能量轉(zhuǎn)移的演化規(guī)律。同時(shí),標(biāo)記轉(zhuǎn)移強(qiáng)度常數(shù)的今天值也被給出。為了考察該模型對(duì)結(jié)構(gòu)形成的影響,我們給出了其增長因子的演化軌跡。并將其與廣義Chaplygin氣體和ΛCDM模型增長因子的演化軌跡進(jìn)行了比較。最后運(yùn)用Om診斷對(duì)新的廣義Chaplygin氣體,廣義Chaplygin氣體和ΛCDM模型進(jìn)行了區(qū)分。 其次,我們?cè)赗aychaudhuri方程的基礎(chǔ)上,導(dǎo)出了物質(zhì)與幾何間存在任意耦合時(shí)f(R)引力中的四種能量條件,即強(qiáng)能量條件,零能量條件,弱能量條件和主能量條件。同時(shí),我們還導(dǎo)出了在物質(zhì)與幾何間存在任意耦合的f(R)引力中使引力保持吸引的條件和Dolgov-Kawasaki不穩(wěn)定性判據(jù)。本文中得到的能量條件和Dolgov-Kawasaki不穩(wěn)定性判據(jù)具有普適性,它囊括了f(R)引力中當(dāng)物質(zhì)與幾何間存在非最小耦合時(shí),無耦合時(shí)以及廣義相對(duì)論的情況。為了看清四個(gè)能量條件和Dolgov-Kawasaki不穩(wěn)定性判據(jù)在具體模型中的含義,我們考慮了一類f(R)模型。 最后,我們討論了如何在物質(zhì)與幾何間存在非最小耦合的f(R)引力中實(shí)現(xiàn)當(dāng)前宇宙的加速膨脹。在冪律暴漲和態(tài)方程小于-1/3的條件下,我們給出了模型中參數(shù)間的關(guān)系以及在該模型中當(dāng)前宇宙加速膨脹的條件和物質(zhì)候選者。
[Abstract]:At present, the observation of Ia supernova and the analysis of precise data from Wilkinson Microwave AnisotropyProbe (WMAP) show that our universe is in the stage of accelerating expansion. This contradicts the thermal Big Bang cosmological model based on ordinary baryon matter. According to the thermal Big Bang cosmological model, the universe should be decelerating and expanding. In order to explain the current accelerating expansion of the universe within the framework of the thermal Big Bang cosmological model, it is necessary to modify it. There are two main ways of correction, one is by introducing a new kind of dynamic component with negative pressure and uniform distribution in large scale structure, that is, the so-called dark energy. This is actually a correction to the right side of the Einstein gravitational field equation. The correctness of this correction is supported by Wilkinson Microwave AnisotropyProbe (WMAP). The probe shows that dark energy accounts for 73 percent of the total composition of cosmic matter. Therefore, there is reason to think that it is the cause of the current accelerating expansion of the universe. The second is to modify the left side of the Einstein gravitational field equation, that is, the geometry of space-time. This kind of correction is usually called the gravitational correction theory / (R) 's gravitation theory is one of the more competitive. In this paper, some physical problems in the accelerating expansion universe are studied from the above two approaches. Firstly, a new generalized Chaplygin gas is discussed as a unified model of dark energy and dark matter. We not only discuss the evolution trend of energy density with redshift z when there is and no interaction between dark energy and dark matter, but also give the evolution law of dark energy and energy transfer between dark matter and dark matter. At the same time, the today's value of the label transfer intensity constant is also given. In order to investigate the influence of the model on the formation of the structure, we give the evolution trajectory of the growth factor. The evolution trajectories of the growth factors in the generalized Chaplygin gas model and the CDM model are compared. Finally, the new generalized Chaplygin gas, the generalized Chaplygin gas and the CDM model are distinguished by using the Om diagnosis. Secondly, on the basis of Raychaudhuri equation, we derive four kinds of energy conditions in f (R) gravitation, that is, strong energy condition, zero energy condition, weak energy condition and principal energy condition, when there is any coupling between material and geometry. At the same time, we also derive the conditions for the attraction of f (R) gravity in the case of arbitrary coupling between matter and geometry and the criterion of Dolgov-Kawasaki instability. The energy condition and the Dolgov-Kawasaki instability criterion obtained in this paper are universal, which covers the case of f (R) gravitation when there is a non-minimum coupling between matter and geometry, and when there is no coupling, as well as the general relativistic theory. In order to understand the meaning of the four energy conditions and the Dolgov-Kawasaki instability criterion in the concrete model, we consider a class of f (R) model. Finally, we discuss how to accelerate the expansion of the current universe in f (R) gravity, where there is a non-minimum coupling between matter and geometry. Under the condition that the power law surge and the equation of state are less than -1 / 3, we give the relations between the parameters in the model, the conditions for accelerating the expansion of the universe and the material candidates in this model.
【學(xué)位授予單位】：遼寧師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2010
【分類號(hào)】：P159.3

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本文編號(hào)：2230540