17. Beginning inflation: problem of initial conditions in cosmology (Inflationary perturbations 4)
DmitryThis is the next post in the series based on my lectures on inflationary perturbations and large scale structure given at the University of Helsinki. Today we will finally start to discuss the physics of inflation.
To get a theoretical prediction for the correlation functions of 
at observable scales as well as their dependence on the redshift 
, it is not enough to know the general solution of equations governing the dynamics of cosmological perturbations; one also has to know the initial conditions for them - namely, the distribution of matter at some moment of time in the early Universe as well as the distribution of velocities of the matter particles. Initial conditions should be defined at a time scale not earler than the Planckian time 
sec, since quantum corrections to GR become important at 
. From the observations we are able to conclude that the initial distributions of matter density and velocity field had very special, in a sense unnatural forms. What was so unnatural about them?
As we know, the Universe at scales larger than a hundred of MPcs is extremely homogeneous - namely, the average amplitude of the density fluctuation 
is of the order of 
. Since large scales correspond to earlier moments of time in the history of the Universe, the distribution of matter in the early Universe was homogeneous to the same extremely fine-tuned degree as well. To understand how exactly large is the fine-tuning, let us do a quick estimation.
The current size of homogeneous isotropic region in the Universe is at least of the same order as the horizon scale
,
where 
is the age of the Universe. Since any physical length in the expanding universe grows as a, in the very beginning of the evolution of the Universe the homogeneity scale was much lower:
(we took into account the fact the temperature 
drops as 
in the expanding universe and used notation 
for the present value of scale factor). If we suppose that the temperature of primordial plasma was 
at the Planckian time, we find that 
, so the initial size of the homogeneous patch in the Universe was of the order of 
, where 
is the Planckian length scale determining the size of the causal patch at the Planckian time.
Naively, it is impossible to have strong correlations in the matter distribution at scales larger than the size of a causally connected region; however, it looks like that in the beginning of its evolution the Universe consisted of 
causally disconnected regions, and the matter distribution was highly correlated between them - indeed, it was homogeneous everywhere in the region with the size 
. Estimating 
, we find
.
Thus, it looks like the ratio 
is incredibly fine-tuned. What we have just described is the essence of horizon and homogeneity problems of the standard Big Bang cosmology.
Similar issues to be explained are why the present Universe is extremely isotropic at horizon scale 
and why it was so close to be absolutely spatially flat in the beginning of its evolution. Let us discuss the second issue a bit more. The question can be reformulated as follows: why the average energy density in the Univere is so extremely close to the critical value
?
Rewriting the Friedmann equation as
,
where 
is the spatial flatness parameter, we see that
in the early Universe. Why the spatial flatness of the early Universe was so extremely fine-tuned to be close to 0? This problem as known as the spatial flatness problem of the standard Big Bang cosmology.
Finally, we notice that the total present entropy of the observable part of the Universe is of the order of 
. Why it is so huge? One has to explain this number, and the explanation should be based on the initial conditions we introduce.
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16. Eye on ArXiv: 10 Apr 2008 - NG in ekpyrotic models, quantum noise as entanglement meter
DmitryAs you may remember, ekpyrotic scenario predicts much higher level of primordial non-gaussianity than single field inflationary scenarios. The technical reason for this is more or less that the level of nongaussianity
for a single field inflation is proportional to the slow roll parameter 
, while for a elpyrotic scenario it is inversely proportional to . This feature of the ekpyrotic scenario seems especially attractive in light of recent Yadav-Wandelt estimation of primordial nongaussianity
at the 95% CL
(let me remind that for a single field inflation 
, and this is model independent prediction).
In the present paper, the authors show that there is typically a contribution to 
determined by geometric mean of the effective equation of state (EOS) during the ekpyrotic phase and during the phase when curvature perturbations are generated, which is the source of the largeness of in ekpyrotic scenarios. Basically, one can say that nongaussianity is large 
during the ekpyrotic phase, and self interactions of the scalar field are strong (compare it to inflationary stage, where self interactions of the scalar field are suppressed by the slow roll parameter).
2. Israel Klich, Leonid Levitov, “Quantum Noise as an Entanglement Meter”
This is a cond-mat preprint and I excuse my writing about it by the fact that 1) I have learned diagrammatic methods by working through Levitov’s great book and 2) the paper is about entanglement entropy :-) I don’t need to expain to you how the notion entanglement entropy is important in, say, black hole physics or inflation.
In the paper, authors actually identify a condensed matter system where entanglement entropy can be measured experimentally (!!)
The system is a quantum point contact (QPC), serving as a door between two electron reservoirs, which can be opened and closed when necessary. As authors show, fluctuations of electric current through the QPC can be used to quantify the entanglement generated by the connection, i.e., to measure the entanglement entropy directly.
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