Cosmology inflationary

If we now include the issue of inflation, the situation becomes somewhat more complex. During the inflationary period of expansion the radius of the cosmology expands exponentially... 

We shall first review the (well-known) problems of the hot Big-Bang scenario in the next section. The we shall do a presentation of the inflationary mechanism, where we shall also introduce some important quantities the slow roll parameters (Section 7.3). In order to understand properly how inflation can seed density perturbations in the Universe, we shall then make an introduction to the problem of density perturbation in cosmology (Section 7.4). We shall then adapt this formalism to the inflationary situation where the Universe experiences a quasi-exponential expansion under the influence of a single scalar field (Section 7.5). The seeds for the cosmological perturbations (i.e. what we have to take as initial conditions when solving the perturbation equations are in fact the quantum fluctuations of this scalar field. We shall make a very brief introduction to this subject in Section 7.6. With all these tools we shall then compute the final spectrum (i.e., long after inflation) of the cosmological perturbations in Section 7.7. 

Before continuing the study of the dynamics of the inflationary phase, let us focus on one specific example of inflationary scenario chaotic inflation. Historically, this was not the first model that was proposed but we think it was the first to provide a satisfactory scenario. The main difficulty with inflation is to have the slow roll conditions to be satisfied at some epoch. Indeed, as we saw, one need to put the field away from the minimum of its potential for the inflaton to behave like a cosmological constant. The first inflationary model ( Guth 1981) supposed a potential like that of Eq. (7.28) where the field slowly moved away from its minimum because of a phase transition. However, this led to a number of difficulties, see for example Ref. (Liddle Lyth). Fortunately, it was soon realized that it was not necessary to have a time dependent potential for inflation to proceed. Linde (Linde 1985) noticed that inflation could start as soon as the Universe would exit the Planck era. The idea was that it is reasonable to suppose that at the end of the Planck era (when p > ), no large-scale correlation could be expected in the scalar field, so that one could expect very irregular (hence, chaotic) initial condition with... 

A.D. Linde, Particle Physics and Inflationary Cosmology 1990, Harwood, Chur, Switzerland... 

As we have seen during the course on inflation, a scalar field can behave as a cosmological constant when its kinetic term becomes negligible in front of its potential term. However, the features of the scalar field we are interested in differ significantly from an inflationary scalar field in the former case, we want a field that is negligible at early times and which dominates afterwards, whereas in the latter case, it is the contrary. Historically, the first scalar field dark energy model was aimed to address the possibility to have some components with a constant equation of state parameter w other than 0 (matter), 1/3 (radiation), —1/3 (curvature) and —1 (cosmological constant) (Ratra Peebles 1988). 

Measurements of the CMB anisotropy made in the last 5 years have moved cosmology into a new era of precise parameter determination and the ability to probe the conditions during the inflationary epoch. These results depend on the study of perturbations that are still in the linear, small amplitude regime, and thus are not confounded by non-linearities and the difficulties associated with hydrodynamics. 

Low-entropy Planck-power (or other [21-25,33-35]) input such as hydrogen in nonoscillating cosmologies, or two-time low-entropy boundary conditions in oscillating ones [61,62,101-105], would enable our Universe — and likewise any Universe in the Multiverse — to forever thwart the heat death predicted by the Second Law of Thermodynamics. It should be noted that there also are other ways that the heat death can be thwarted see, for example, Ref. [127], Hopefully, one way or another, the heat death is thwarted in the real Universe, whether within an inflationary Multiverse [89-94,105] or otherwise [88,89,101-105,127]. 

Tegmark M. How unitary cosmology generalizes thermodynamics and solves the inflationary entropy problem. Phys. Rev. D. 2012 85 123517, 19 pages. DOI 10.1103 / PhysRevD. 85.123517... 

Fundamental relationship between cosmology and particle physics originates from the well established links between microscopic and macroscopic descriptions in theoretical physics. Remind the links between statistical physics and thermodynamics, or between electrodynamics and theory of electron. To the end of the XX Century the new level of this relationship was realized. It followed both from the cosmological necessity to go beyond the world of known elementary particles in the physical grounds for inflationary cosmology with... 

Linde, A. D. (1990a). Inflation and Quantum Cosmology. Boston, MA Academic Press. Linde, A. D. (1990b). Particle Physics and Inflationary Cosmology. New York, NY ... 

An important idea in the theory of the early universe is that of inflation - the idea that the nature of the vacuum state gave rise, after the big bang, to an exponential expansion of the universe. The hypothesis of the inflationary universe solves several long-standing problems in cosmology, such as the flatness and homogeneity of the universe. In particular, it is thought that quantum fluctuations in the early universe... 

An important prediction of the inflationary scenario for the origin of CMBR anisotropy is a sequence of maxima in the multipole spectrum (Hu 2001). The latest results (see Fig. 12.1) confirm the existence of at least two further maxima, in addition to the main maximum known before. The new satellite-based CMBR observations by the European satellite PLANCK launched in May 2009 will improve the accuracy of the deduced cosmological parameters to 0.5% and determine the multipole projection of the anisotropy up to angular momentum I 2,500. 

Unfortunately, such a universe that inflated sufficiently never made a smooth transition to a radiation-dominated, early Friedmann cosmology. In the new inflationary models (1982), the vacuum energy density dominates while the relevant region of the universe inflates and... 

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