Universe inflation

Infiation theory continues to be important in describing the evolution of our universe. Inflation theory suggests that the universe expanded like a drunken balloon-blower s balloon while the universe was in its first second of life. 

Huterer D, Starkman GD, Trodden M (2002) Is the universe inflating Dark energy and the future of the universe. Phys Rev D 66 043511 Hyde WT, Crowley TJ, Baum SK, Peltier WR (2000) Neoproterozoic snowball Earth simulations with a coupled climate/ice-sheet model. Nature... 

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... 

The universe initially went through a phase of rapid expansion, the so-called inflation. Fail Elegant theory, but still no evidence requires huge extension of the laws of physics. 

By comparing calculated values with the actual content of these various elements in the oldest astronomical objects, we deduce that the density of nuclear matter cannot exceed 5% of the critical density. Now it so happens that the best cosmological theory to date, the theory of cosmological inflation, predicts that the Universe has exactly the critical density. This conclusion is supported by recent observations of remote supernovas and the relic background radiation. 

On the other hand, we must somehow close the Universe, or more precisely, find some way of giving it the critical density, since this is what inflation demands. Indeed, it is required not only by inflationary theory, but also by close scrutiny of the leopard skin p attern that constitutes the microwave background, radiative relic from the B ig B ang. We... 

Obstacles remained as PTCA was not universally available and often associated with considerable time delay, especially in off peak hours. In the National Registry of Myocardial Infarction-2 (NRMI-2 >27,000 patients), total ischemia time (symptom onset to balloon inflation) was 3.9 h with onset to hospital arrival 1.6 h [45]. Unadjusted in-hospital mortality was higher in patients treated later. Door to balloon time > 2 h was related to in-hospital death (41-62% adjusted odds increase) and centers who treat >3 STEMIs/month had improved in-hospital mortality compared to less experienced facilities (Figs. 5.4 and 5.5). Lastly, similar to trials of unstable angina, PTCA was plagued by high restenosis rates... 

Clawson, J. M. (2007). Feasibility of a Mars surface inflatable greenhouse Availability of photosynthetic irradi-ance and durability of transparent polymer films. Dissertation, University of Colorado, Aerospace Engineering Dept.(191 pages). 

It is apparent that the numbers and masses of the flavor and quark-lepton transforming gauge bosons are larger than those of the SU(5) minimal model. This means that the value of a is lower, and assuming that the duration of the inflationary period is fixed, the scale for the expansion of the universe is reduced. This means that there is the enhanced prospect for deviations from flatness. So one may presume that the universe started as a small 3-sphere with a large curvature, where the inflationary period flattened out the universe, but maybe not completely. This leaves open the prospect that if before inflation that if the universe were open or closed, k = 1, that the universe today still contains this structure on a sufficiently large scale. The closer to flatness the universe is, the tighter are the constraints on the masses of particles in the early universe. 

Considering the inflation, we assume a universe with a critical density Qo = 1, k = 0 and qo = The universe is assumed to be matter dominated during all the epoch of interest. Then the scale factor Rit) of the universe expands as ... 

If you want to be sure something is left when you die, here s a plan that will work for you. Harvard University s endowment fund developed a spending guideline in 1973 to ensure a person wouldn t prematurely run out of money. The rule assumes a balanced portfolio allocated half to stocks and half to bonds and cash equivalents. It limits the first-year withdrawal to four percent of the portfolio s total value. Then, in each following year, increase this amount by the previous year s rate of inflation. Continue in this manner from year to year. For example, if you have a 500,000 portfolio, you could withdraw 20,000 in the first year. If the rate of inflation were 3.5 percent that year, you could withdraw 20,700 the second year. 

Academic institutions are facing difficult fiscal times as are many other areas of our society. The research universities are often being asked to do more with less. Even in these days of reduced inflation, research support is a precious commodity. Equipment costs rise, personnel costs rise, and the general cost of doing business increases with the net result that less research is accomplished. Unreasonable increases in paperwork reduce actual productivity. 

C. T. Pillinger (Open University, U.K.). People have talked about inflating C60, but what happens when you compress I have heard reports that diamonds are produced. What are your thoughts on the subject ... 

In its original formulation, inflation provided an explanation for the homogeneity and isotropy of the Universe (Guth 1981). It also explained why no heavy relics were observed in the Universe. Moreover, it was soon realized that for some unexpected reason, it could seed the density perturbations which gave birth to all the structures we observe in the Universe (Vilenkin 1982 Linde... 

So far, inflation represent the simplest (and maybe the most natural) way to solve all above mentioned problems. More importantly, it also proposes a framework which allows to address them and is at present the most widely accepted scenario for the history of the early Universe. Of course, this does not mean that this represents the ultimate step toward our description of the early universe, but most of the alternative to inflation fit in a similar framework even though some alternative scenarios rely on very different physical processes, in practice, the techniques one uses to compute the predictions from all these scenarios do not differ much from each others. Therefore, the following sections must be seen as a general overview of the current framework as well as a set of recipes which are extremely useful to address some issues about the early Universe, rather than an unambiguously well-established presentation about how things really happened. 

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. 

Maybe the most annoying problem of the hot Big-Bang scenario is that it does not provide any explanation for the existence of structures in the Universe. It is well-known that structures can form through the Jeans instability only in a matter dominated era. However since the matter domination occurred quite recently in the history of the universe (around z 104, see Eq. (7.29)), one is forced to suppose that small density fluctuations already existed before that epoch. Since no efficient process is known to form density perturbations in a radiation-dominated universe, so one has to suppose that the seeds for the astrophysical objects we observe were part of the initial condition of the whole scenario. As we shall now see, the biggest success of inflation is to provide a simple explanation for the presence of such density perturbations, in addition to solving quite naturally the other problems. 

There is very simple form of matter which can exhibit such an equation of state parameter a scalar field. The idea of inflation is based on the hypothesis that the Universe has been dominated at some early epoch by a scalar field whose equation of state parameter remained close to —1 for a while. 

What is the necessary number of e-folds to solve the horizon and flatness problems For the horizon problem, we want that the observable universe today was inside the Hubble radius at the beginning of inflation. Let us assume for definiteness than the Universe was matter dominated since zeq 104 till now then radiation dominated before. The relation between the comoving horizon today rjo and the comoving horizon rjf at some early epoch deep in the radiation era is given by Eq. (7.24) ... 

During inflation, the physical size of the observable universe is almost constant, dirji (i f rjf. However, between the beginning and the end of inflation, the physical distance of two comoving objects has grown of a factor o//ai. Therefore the size of a region which was causally connected at the beginning of inflation is VifF- In order to solve the horizon problem, one therefore need to impose that... 

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... 

Since one has initially > Mpi, one expects the number of e-folds to be very large. This means that in chaotic inflation there is absolutely no difficulty to reach the minimum number of e-fold of 60. This also mean that there is probably no hope to see the very large scale structure of the universe in typical models, N can easily reach 105 or 106 the size of the inflationary region we are in is something like e10 ore10 times larger than the size of our observable universe. 

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