Cosmology initial conditions

The prediction of cosmological initial conditions is a different business, however, from the validation of causal theories. Initial conditions by assumption have no cause that can be varied to check their dependence, and the cosmos is by assumption a single instance of these values, which we cannot compare experimentally to anything else to test for repeatability. Weak anthropic principles are a conservative response to this dilemma, in which the issue of boundary conditions is put off to a larger theory determining a distribution of pseudo-initial conditions for the universe we see [2, 3]. A radical response is to propose that only one universe exists and to make predictions for its initial conditions on some criterion other than causality, such as a form of mathematical consistency [92]. 

The difference between the conservative and radical interpretations of anthropic arguments for cosmological initial conditions corresponds roughly to the difference between frequentist and Bayesian interpretations of the distribution N) we have... 

In a sense, all these problems had to do with some choice of initial conditions for the Universe. In particular, the Universe had to be supposed initially homogeneous and isotropic. These features had to be put by hand in order the cosmological scenario to work properly, a situation which was of course very uncomfortable. 

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... 

So far, we have been able to compute the large scale amplitude of the cosmological perturbations as a function of some quantity C which now has to be fixed by the initial conditions, which in our context are given by quantum held theory. 

The only factor of some chemical importance that features prominently in the theories of cosmology is the synthesis of small nuclides such as deuterium and helium. Unfortunately, the initial conditions that are considered to be crucial in these models are purely conjectural. There is little hope of a meaningful test against chemical reality and, in the present climate, no chance for the growth of a mathematically based alternative cosmology. However, the simple qualitative model of a non-orientable universe provides interesting insight into the nature of matter, non-local interaction and quantum theory. 

Or, as Barrow and Tipler put it The appeal of this type of explanation [chaotic cosmology] is obvious it makes knowledge of the (unknowable ) initial conditions at the origin of the Universe largely superfluous to our present understanding of its large-scale character (1986, p. 422 see also McMullin, 1993). 

Hoyle s [1] successful prediction of the 7.6 MeV resonance of the carbon-12 nucleus, based on observation of his own carbon-based existence, established the scientific usefulness of anthropic principles. These principles have become common, if not yet standard, tools in cosmology, where theories of initial conditions may not yet exist - or, if they do exist, may admit a range of values [2, 3, 4, 5, 6]. At the same time, anthropic principles have retained a traditional role in religion and philosophy, where sensitive dependence of human existence on laws of nature that could imaginably have been otherwise is interpreted as evidence for human significance in the creation of the universe. 

The constructive model P(A(M) SC C )xN) acts as before, as a filter on the prior P(S( -C)x I A) output from the cosmological theory. In this respect, the anthropic bias is indistinguishable from the pruning rule generated by Hoyle but as it is driven by incomplete theoretical specification rather than mere intractability, the posterior distribution is not provisional and cannot act as a constraint on reductionist refinements of N or X It is not a substitute for a theory of particular initial conditions, because it adds nothing axiomatic to the structure of the causal theories represented by... 

The posterior evidence variable A(M) has three distinguishable roles in the three anthropic interpretations we have presented. It is chosen for predictive specificity in the generation of a pruning rule for appropriateness as a constraint on the observable ensemble in multiverse cosmology arrd for selectivity of those aspects of initial conditions we regard as relevant to modification of beliefs in the Bayesian cosmological interpretation. 

Symmetry breaking is a universal phenomenon, from cosmology to the microscopic world, a perfectly familiar and daily experience which should not generate the reluctance that it induces in some domains of Physics, and especially in Quantum Chemistry. In classical physics, the symmetry breaking of an a-priori symmetrical problem is sometimes refered to as the lack of symme of the initial conditions. But it may be a deeper phenomenon, the symmetry-broken solutions being more stable than the symmetrical one. 

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