# LOG#128. A chaosmic TSOR returns.

Dear followers and dear readers! Time has come!
I am back with the brand new TSOR and its new site. The wait is over. :).
Firstly, I have some interesting things to tell you:
1) I have not finished the changes and the metamorphosis of my site, but there are no too many left.
2) I recommend you not to use Internet Explorer. It seems that Explorer does not scale the images very well. Moreover, Explorer seems to be bad working with LaTeX code I use here. So, please, use any other web browser to read this site.
3) I am going to pause my Neutrinology thread in order to post some interesting stuff, I believe, that I want to share with you (after all, it is something I have learned recently) in the next (nor this one) post.
4) If you have some suggestions, you can post anywhere and anytime with you follow my rules as stated in the section “About”.
5) You can now contribute to my project in new ways.
Finally, I would add that I am expecting you will enjoy my new site as much as I will…
Today, due to the fact I am taking the Coursera course titled From The Big Bang to Dark Energy, by Hitoshi Murayama and Tokyo University, I decided to post some additional cosmological data and some about the future of the Universe (Multiverse?). Of course, the numbers are a bit old fashioned (most of them are from 2007 data), but there are also mathematical identities that you could likely enjoy.
Here you are, a summary some basic numbers and equations from Cosmology…

Einstein Eq.:

$H^2 =\left(\frac{\dot{a}}{a}\right)^2 = \frac{8 \pi G}{3}\rho- \frac{k}{a^2}; k=(+1,\,0,\, -1)= ({\rm closed},\,{\rm flat},\,{\rm open})$
Equation-of-state

$w \equiv p/\rho$
$\rho \sim a^{-3(1+w)}$
$a \sim t^{2/[3(1+w)]}$
Hubble constant
$H_0= 71.0 \pm 2.6$km/s/Mpc

or

$h=0.710 \pm 0.0026$

$1 km/s= 0.98pc/Myr\approx 10^{-12}Mpc/yr$

Hubble time

$T_H= H_0^{-1}= 3.086 \times 10^{17}\,h^{-1}\, {\rm sec}$
$T_H= 9.778 \,h^{-1}\, {\rm Gyr}= 4.35 \times 10^{17} \,{\rm sec}$

Hubble distance

$c H_0^{-1} = 2997.9 \, h^{-1}$Mpc
$c H_0^{-1}= 9.2503 \times 10^{27}h^{-1}$
$c H_0^{-1}= 9.2503 \times 10^{27}h^{-1}$cm

Age of the Universe

$T_U= 13.77 \pm 0.15 {\rm Gyr}$
$\Omega_b=0.044$
$\Omega_{DM} = 0.221$
$\Omega_m=0.265$
$\Omega_{\Lambda}=0.735\pm 0.030$
$\Omega_b h^2 = 0.0223 \pm 0.0007$
$\Omega_m h^2 = 0.133 \pm 0.006$
$\rho_{DM}=1.17 \times 10^{-6}GeV/cm^3$(but =$0.4GeV/cm^3$ near sun)
$q_0 = - \frac{\ddot{a} a}{\dot{a}^2} = \frac{\Omega_m}{2} - \Omega_{\Lambda} + \frac{1}{2}(1+3 \gamma) \Omega_{\gamma}$

Luminosity distance:

$d= H_0^{-1} [ z + \frac{1}{2}(1-q_0) z^2 + \ldots]$

Angular distance = (Luminosity distance)$/(1+z)^2$

$T_{BH}=2 \times 10^{67}(M/ M_{\rm solar})^3$$=2 \times 10^{67}(M/ M_{\rm solar})^3$
Critical Density

$\Omega_m=1$

$8.0992 h^2 \times 10^{-47}GeV^{-4} =1.8791 h^2 \times 10^{-29} =1.8791 h^2 \times 10^{-29}g cm^{-3}$

Fluct. amp.

$\Delta_{\cal R}^2$ ( k=0.002 /Mpc)$= 24.1 \pm 1.3 \times 10^{-10}$
Cosmic Microwave Background:
$T= 2.725 \pm 0.002$K

Cosmic Neutrino Background:

$T_\nu (C\nu B)= 1.945 \pm .003$ K

$a_{eq}=4.1707 \times 10^{-5} \, (\Omega_m h^2)^{-1} a_0$
$T_{eq} = 5.6362\, (\Omega_m h^2)eV$

Planck Mass(=”$M_P$“)

$M_P=(1/G)^{1/2} = 1.2211 \times 10^{19}$GeV or “reduced” $\overline{M_p}$$=2.4 \times 10^{18}$GeV

Megaparsec

1 Mpc$= 3.085 \times 10^{24}cm=1.5637 \times 10^{38}GeV^{-1}=3.2615 \times 10^6lyr$

The GeV

$1 GeV=1.1605 \times 10^{13}K$ $=1.6022 \times 10^{-3}erg$

$1GeV= 5.0676 \times 10^{13}cm^{-1}$ $=1.5192\times 10^{24}s^{-1}$

$1 GeV^{3}$= $1.3014 \times 10^{41}$$cm^{-3}$

$1 GeV^{4}=2.3201 \times 10^{17}g cm^{-3}$

$M_{\rm solar} = 1.99 \cdot 10^{33}g=1.116 \times 10^{57}$GeV
After these numbers, I want to finish this post discussing some possible cosmic destinies/fates of our Universe.

## Cosmic destiny

Einstein believed in a closed Universe (or that our Universe was a big bubble) and that either it was ethernal and static, so he introduced the cosmological constant, the vacuum energy (now, sometimes referred as dark energy but this name is more general that a mere cosmological constant). A closed universe could be ethernal but also expands forever or collapse into a spacetime singularity called the Big Crunch. In other words, if there is enough matter in the Universe eventually gravitational forces will stop its expansion. At the point of maximum expansion, gravity will cause the universe to reverse its direction and it will begin to collapse under its own weight. This phase of the Universe’s life is known as the “Big Crunch”. The alternative is that the Universe, without new creation of matter, will freeze to something close to the absolute zero. This scenario is called the Big Freeze/the Big Chill or the thermal death of the Universe.
Eventually, according to Einstein’s theory of gravity, all of the matter in the Universe will collapse into a hyperdense state and possibly something similar to a supermassive black hole. Some people theorize that the Universe could collapse into the same state that it began as and then blow up in another Big Bang. This idea is called the cyclic cosmology or the Phoenix Universe (even sometimes you know it as oscillating cosmology, but this name is something that does not imply a total collapse or a permanent positively accelerate Univers).  In this way the Universe would last forever but would continually go through these phases of expansion and contraction, Big Bang and Big Crunch and so on…
Therefore, we have 3 classical destinies/dooms for our Universe:
A) The Universe collapses into a future singularity, similar to a supermassive black hole. It is the Big Crunch.
B) The Universe expands forever, it freezes or cools until a temperature close to the absolute zero. It is the Big Freeze/Big Chill/thermal death of the Universe.
C) The Universe is “ethernal” after succesive aeons/cycles of collapse/expansion. This is the cyclic cosmology scenario or the Phoenix Universe. It begins with a Big Bang, it recollapses with a Big Crunch, then another Big Bang reignites a new Universe, it follows another Big Crunch, and so on…
This 3 classical scenarios are standard if you neglect the existence of dark energy/the cosmological constant and/or its relatives (quintessence, phantom energy,…), and they are provided by the geometry of space. Mathematically, if Ω > 1, then the geometry of space is closed like the surface of a sphere. The sum of the angles of a triangle exceeds 180 degrees and there are no parallel lines, therefore all lines eventually meet. The geometry of the universe is, at least on a very large scale, elliptic. By the other hand,  in a closed universe lacking the repulsive effect of dark energy, gravity will theoretically halt the expansion of the universe, after which it starts to contract until all matter in the universe collapses to a point, a final singularity termed the “Big Crunch,” by analogy with Big Bang. However, if the universe has a large amount of dark energy (as suggested by recent findings), then the expansion of the universe can continue forever – even if Ω > 1! This is a really awesome discovery!
The universe DOES have a large amount of Dark Energy(DE). WMAP and PLANCK show it.  Gravity as a force is far too weak to pull all the mass back in, much less stop the accelerating at large scales! Remember, we are not moving forward at the same terminal velocity, we have yet to reach terminal velocity. We are still accelerating away from the Big Bang event horizon. But, if the universe does not contain enough matter to stop its expansion it will continue to expand forever.
Using the currently known and understood laws of physics it is possible to project into the
future what the Universe may look like in very distant eras.
The current Era is known as the stelliferous or Star-Filled era. The state of the Universe is filled with stars and galaxies and planets. This era ends when all the stars have exhausted their fuel and have died leaving behind only remnants of their brilliance.
The next era is known as the Degenerate era. The universe will be composed of dead planets, brown dwarfs, white dwarfs, neutron stars, black holes, and some theoretical forms of dark matter in that time. This era ends with the disintegration of all protons (supposing the GUT idea is right), which compose the nuclei of all atoms. Then the universe will enter then into the Black Hole era. Black holes will be the only gravitationally important objects remaining in the universe. Black holes do not last forever if our understanding of them is right. They will eventually evaporate, radiating away into nothingness. After that all that will remain is radiation and particles which have an infinite lifetime such as electrons, positrons, and neutrinos. From this point on it is impossible to fathom what will happen as we have reached the limits of our knowledge.

If Ω<1, the geometry of space is open, or negatively curved like the surface of a saddle. The angles of a triangle sum to less than 180 degrees, and lines that do not meet are never equidistant; they have a point of least distance and otherwise grow apart. The geometry of such a universe is hyperbolic. But even in the absence of dark energy, a negatively curved universe expands forever, with gravity having little effect in slowing the rate of expansion. With dark energy, the expansion not only continues but accelerates, which seems to be our current condition after some 13.6 billion years of existence.

The ultimate fate of an open universe as proposed is either universal heat death, the “Big Freeze”, or something called the Big Rip, in which the dark energy inspired acceleration eventually becomes so strong that it completely overwhelms the effects of the gravitational, electromagnetic and weak binding forces. On the other hand, a negative cosmological constant, which would correspond to a negative energy density and positive pressure, would cause even an open universe to recollapse to a Big Crunch. This has been ruled out by recent observations. But there are aspects of all of this that remain problematic.
The last classical option is the flat universe (a contemporary update of the flat Earth idea extended to the whole Universe!)…If the average density of the universe equals the critical density so that Ω=1, then the geometry of the universe is flat: as in Euclidean geometry, the sum of the angles of a triangle is 180 degrees and parallel lines continuously maintain the same distance. Absent of dark energy, a flat universe expands forever but at a continually decelerating rate, with expansion asymptotically approaching a fixed rate. With dark energy, the expansion rate of the universe initially slows down, due to the effect of gravity, but eventually increases. The ultimate fate of the universe is the same as an open universe. That is, there is a Big Rip in the future of the Universe or the Universe becomes disconnected from every place. In a dark energy dominated future of the Universe, we will not see clusters, galaxies or even stars, they will be taken away beyond our horizon. Astronomy will become boring in some Gyrs!!!
There are actually many theories about the end of universe, and that fate will be determined by the total density of the universe and the dominating fluid. The preponderance of evidence to date, based on measurements of the rate of expansion and the mass density, favors a universe that will continue to expand indefinitely, resulting in the “big freeze” scenario.

## The Big Freeze, The Big Chill or Heat Death

The Big Freeze is a scenario under which continued expansion results in a universe that asymptotically approaches absolute zero temperature. It could, in the absence of dark energy, occur only under a flat or hyperbolic geometry. With a positive cosmological constant, it could also occur in a closed universe. This scenario is currently the most commonly accepted theory within the scientific community. A related scenario is Heat death, which states that the universe goes to a state of maximum entropy in which everything is evenly distributed, and there are no gradients — which are needed to sustain information processing, one form of which is life. The Heat Death scenario is compatible with any of the three spatial models, but requires that the universe reach an eventual temperature minimum.

## The Big Rip: Finite Lifespan

In the special case of phantom dark energy (a relative of the cosmological constant with dynamical exotic features), which has even more negative pressure than a simple cosmological constant, the density of dark energy increases with time, causing the rate of acceleration to increase, leading to a steady increase in the Hubble constant. As a result, all material objects in the Universe, starting with galaxies and eventually (in a finite time) all forms, no matter how small, will disintegrate into unbound elementary particles and radiation, ripped apart by the phantom energy force and shooting apart from each other. The end state of the universe is a future singularity, as the dark energy density and expansion rate becomes infinite. While on the surface this makes sense, it too is problematic. But the Big Rip, or some variants dubbed as Little Rips or even no Big Rip at all are possible cases with a phantom energy future.

## The Big Crunch

The Big Crunch theory is a symmetric view of the ultimate fate of the universe. Just as the Big Bang started a cosmological expansion, this theory postulates that the average density of the universe is enough to stop its expansion and begin contracting. The end result is unknown; a simple extrapolation would have all the matter and space-time in the universe collapse into a dimensionless singularity, but at these scales unknown quantum effects need to be considered such as Quantum Gravity. This scenario allows the Big Bang to have been immediately preceded by the Big Crunch of a preceding universe. If this occurs repeatedly, we have an oscillatory universe. Let me point out the oscillatory universe can be understood as well as a Universe in which there are several phases of positive acceleration (“inflation like” bounces) and negative acceleration (crunch like in which there is no total collapse into a future singularity). Anyway, the terminology is a bit fuzzy with respect to the name oscillatory universe, cyclic universe or Phoenix Universe. The universe could then consist of an infinite sequence of finite universes, each finite universe ending with a Big Crunch that is also the Big Bang of the next universe (after some timeless periods sometimes called aeons). Theoretically, the oscillating universe could not be reconciled with the second law of thermodynamics: entropy would build up from oscillation to oscillation and cause heat death.
Other measurements suggest that the universe is not closed. These arguments caused cosmologists to abandon the oscillating universe model. A somewhat similar idea is embraced by the cyclic model, but this idea evades heat death, because of an expansion of the different “branes” that dilutes entropy accumulated in the previous cycle. While people don’t believe the Universe is oscillating, some scientist believe in the multiverse idea. The multiverse oscilates and the universes are small subcarriers floating on the quantum wave, like the
static surfboard.

## Big Bounce

The Big Bounce is a theorized scientific model related to the beginning of the known Universe. It derives from the oscillatory universe or cyclic repetition interpretation of the Big Bang where the first cosmological event was the result of the collapse of a previous universe. According to one version of the Big Bang theory of cosmology, in the beginning the universe had infinite density. Such a description seems to be at odds with everything else in physics, and especially quantum mechanics and its uncertainty principle. It is not surprising, therefore, that quantum mechanics has given rise to an alternative version of the Big Bang theory. Also, if the universe is closed, this theory would predict that once this universe collapses it will spawn another universe in an event similar to the Big Bang after a universal singularity is reached or a repulsive quantum force causes re-expansion. While this has merit, it is still incomplete.

## The False vacuum and the Big Decay scenario

If the vacuum, our vacuum, is not in its lowest energy state it is a state we call  false vacuum, it could tunnel into a lower energy state. This is called the vacuum metastability event. This has the potential to fundamentally alter our universe; in more audacious scenarios even the various physical constants could have different values, severely affecting the foundations of matter, energy, and spacetime. Our current knowledge of the Standard Model seems to point out that we live in a false vacuum, a long-lived metastable phase of matter and energy. Only further studies of the Higgs sector and the hidden (dark) sector of the Standard Model will tell if it is so or there are new particles that stabilize the vacuum.
It is also possible that all structures will be destroyed instantaneously, without any forewarning,when we approach the true vacuum.  Many people and scientist  have issues with this as well.

## and our Great Destiny/Cosmic Doom

Each possibility described so far is based on a very simple form for the dark energy equation of state. But as the name is meant to imply, we know almost nothing of the real physics of the dark energy. If the theory of inflation is true, the universe went through an episode dominated by a different form of dark energy in the first moments of the Big Bang; but inflation ended, indicating an equation of state much more complicated than those assumed so far for present-day dark energy. It is possible that the dark energy equation of state could change again resulting in an event that would have consequences which are extremely difficult to parametrize or predict. It is also possible the universe may never have an end and continue in its present state forever.
Choosing among these rival scenarios is done by ‘weighing’ the universe, and it is not easy at all. For example, measuring the relative contributions of matter, radiation, dark matter and dark energy to the critical density. More concretely, competing scenarios are evaluated against data on galaxy clustering and distant supernovae, and on the anisotropies in the Cosmic Microwave Background.
So what do you believe?
Classical options: Big Crunch, ethernal expansion with or without Big Freeze, Phoenix Universe, each of them depending on the geometry and the total density omega.
Modern options: Big Crunch, Big Freeze, Thermal Death, Big Rip, Little Rip, oscillating universes, bouncing universes, the false vacuum scenario with a Big Decay (quantum tunneling through a massive desintegration event), and the Multiverse/Polyverse scenario.
Note: Scenarios with dark energy/cosmological constant, can make the Big Crunch to happen even in a open universe! Some non-classical options arise in the case of phantom energy and subtle variations of the dark energy field. For instante, in the case of a phantom dominated Big Rip (remarkly, the Big Rip could or not happen with a phantom dominated universe) we have the following cosmic doom:
The  multiverse hypothesis states that our universe is merely one Big Bang among an infinite number of simultaneously expanding Big Bangs or local vacuum bubbles  that are spread out over endless distances beyond our horizon. Each universe may be either matter or antimatter, with an equal number in existence at any given time. As the universes each expand away from their individual event horizons they collide and matter and antimatter annihilate, releasing energy.
Heat death of a finite universe would be predicted as entropy increases; however, the infinite size of the multiverse and its oscillation coupled with the infinite number of universes could mean that new ones would be formed as old ones were annihilated. Think of it as a chain reaction multiverse, much like the finale at a fireworks display with each explosion being symbolic of a Big Bang. It begins in one neighborhood and is followed by fireworks displays in surrounding neighborhoods and then in neighborhoods further out. The chain reaction of Big Bangs would continue to expand as Big Bang fuel is consumed. If the multiverse is open and the fuel is infinite then the chain reaction would expand forever. Of course, it is not known what the “fuel” is, but it is logical to assume that matter and energy are the product of a transformation from a real reactant, possibly related to the Higgs boson/field somehow. The multiverse as a whole will never end completely. But this is just a part of the equation. We have to add in the many-worlds interpretation of quantum mechanics. As such, each time a quantum event happens that causes the universe to decay from a false vacuum to a true vacuum state, the universe splits into several new worlds. In some of the new worlds the universe decays; in some others the universe continues as before. I believe that both of these theories are part of the same theory. One is entangled with the other creating many reactions relating to the whole.

## More ideas: inflation, holography, string theory and all that

Recent work in inflationary cosmology, string theory, and quantum mechanics has moved the discussion of the ultimate fate of the universe in directions distinct from the scenarios set out by some of the other theories. Theoretical work by Eric Chaisson and David Layzer suggest that an expanding spacetime gives rise to an increasing “entropy gap”, casting further doubt on the heat death hypothesis. Invoking Ilya Prigogine’s work on far-from-equilibrium thermodynamics, their analysis suggests that this entropy gap may contribute to information, and hence to the formation of structure. Hence the Information Theory may be a part of the TOE, or Theory of Everything. Add to this aspects of the Holographic Principle (HP). The holographic principle is a conjectured property of quantum gravity and string theories which states that the description of a volume of space can be thought of as encoded on a boundary to the region, preferably a light-like boundary like a gravitational horizon. First proposed by Gerard ‘t Hooft, it was given a precise string-theory interpretation by Leonard Susskind and Bousso.
In a larger and more speculative sense, the theory suggests that the entire universe can be seen as a two-dimensional information structure “painted” on the cosmological horizon, such that the three dimensions we observe are only an effective description at macroscopic scales and at low energies.
Cosmological holography has not been made mathematically precise, partly because the
cosmological horizon has a finite area and grows with time. However, there are some interesting proposals by Padmanabhan.
The holographic principle was inspired by black hole thermodynamics, which implies that the maximal entropy in any region scales with the radius squared, and not cubed as might be expected. In the case of a black hole, the insight was that the description of all the objects which have fallen in can be entirely contained in surface fluctuations of the event horizon. The holographic principle resolved the black hole information paradox within the framework of string theory until the recent work about Black Hole Firewalls. It is not clear (yet), what the firewall gedanken experiment is pointing out, but certainly it is a challenge for gravitational theories and QFT itself.

Meanwhile, back at the ranch, Andrei Linde, Alan Guth, Ted Harrison, and Ernest Sternglass argued that inflationary cosmology strongly suggests the presence of a Multiverse, and that it would be practical even with today’s knowledge for intelligent beings to generate and transmit de novo information into a distinct universe. Alan Guth has speculated that a civilization at the top of the Kardashev scale might create fine-tuned universes in a continuation of the evolutionary drive to exist, grow, and multiply.

This idea has been further developed by the Selfish Biocosm Hypothesis, and by the proposal that the existence of the fundamental physical constants may be subject to a Darwinian evolution of Universes.
Moreover, recent theoretical work on the unresolved quantum gravity problem and the Holographic Principle suggests that traditional physical quantities may possibly themselves be describable in terms of exchanges of information, which in turn raises questions about the applicability of older cosmological models. Of course, the holographic idea could be an illusion telling us that there is a new thermodynamics and statistical mechanics (based on non-extensive entropy) in which we should study these issues. But it is a current area of research. :).
This may just hold the secret to paranormal activity and the X-files (just joking a little bit)… Most of this text is my update of the following classical text: “Endings” with an initial commentary to go with Alex Reynolds’ “Origin” By David Rountree, that you can find in the internet. I have updated it and removed the author personal views to include mine.
People use to ask why Science matters…Is there something more important than knowing what is the destiny of the Universe (or Multiverse) where we live live in?
See you in my next chaosmic post!
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