Singularities and beginning of the universe

[sayak83]

Many of the classical solutions of Einstein's equations of space-time have universes that apparently had a beginning from a state of infinite density and zero space-time dimension. GR also predicts their occurrence inside collapsed massive stars that are called black holes. What makes singularities attractive for study is that they are straightforwardly the zones where GR theory fails and hence better insights into such regions provide physicists with clues of how a Quantum Gravity theory may look like.

But the first question is this. Does General Relativity truly predict singularities in our universe? This in itself was the major debate till 1980 when Penrose and Hawking clearly proved that if GR equations are applicable exactly to the universe there must be some past or future singularities in all physically relevant models of the universe.

When singularities first appeared, Einstein thought that they were artifices of simplifying assumptions made by the researchers in finding solutions to his equations. For example most early solutions excluded radiation pressure, and this, Einstein thought would stop any region of space-time to get to infinite density. Unfortunately pressure itself was a form of energy density and hence had a gravitational effect. Thus, as mass and radiation is squeezed further, this attractive gravitation effect of pressure overwhelms the repulsive effect of pressure and accelerates the collapse to infinity.

The next attempt was made to show that singularities are artifacts of the coordinate system. This was proposed by Lif****z, and was argued as follows. Just as the point of convergence of all longitudes at the north pole does not imply anything special about the North pole, so also the point of convergence of all time lines into a "singularity" is just an artifact of our coordinate system. Thus one can avoid singularities by a series of coordinate changes. However, careful analysis over time showed that the singular region continue to persist through such coordinate transformation and hence was a "real" feature of the model. At this point singularities also got a mathematically sound definition as any region of space-time where any event-line or light ray begins or end and cannot be continued any further. This is very similar to how magnetic field lines behave as they converge or diverge on a pole, but instead here we have event lines that converge or diverge on a gravitationally singular region that looks like a perforation or an edge of space-time surface. A universe without a singularity is an universe without a past or a future end point as all event lines can be traced back and forward indefinitely. Thus the reformulation of singularities as regions or points or lines where event lines end or begin creates a fruitful way to see if our universe is indeed finite or infinite in past or future. This also overturns another intuition. Just like magnetic field lines, it appears entirely possible for universes to exist where only some event lines have a beginning or an end while others do not. In such universes (and ours may be one such) the question of beginning and ends depends on which event line one is located at.

With the new definition of singularity above, it became possible for Hawking and Penrose to create their singularity theorem in 1970.

The Singularities of Gravitational Collapse and Cosmology | Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences

They showed that if:-
1)Space and time are sufficiently smooth

2)There are no closed time-like curves (no time travel)

3)There is enough matter and radiation in the universe so that overall gravitational force is large enough

4)Gravity is always attractive (ie cosmological constant is small)

5) Einstein's GR is always true

Then there necessarily exists one space-time event line that had a beginning.

The first three assumptions are true for our universe. The fourth was held to be true at that time but does not hold if inflation occured. That was the reason that the second singularity theorem by Borde, Guth, Velankin was needed.

The fifth assumption is the crux. GR is certainly violated at high energy densities as its incompatible with QM. What the singularity theorem shows is that a full quantum gravity theory will be needed after all and one cannot do cosmology at black holes and big bangs with just GR.

I will look at how the concept evolved after 1970 in later posts.

Much of the material comes from reading John Barrows "Book of universes" and associated papers.

 

[sayak83]

Why quantum gravity?

The problem with a gravitational singularity is that it compresses all matter with its positional, momenta, energy and other properties into smaller and smaller volumes. But as quantum uncertainty principle notes, this is simply not possible. Thus there will come a time before which quantum considerations will override the classical predictions of GR.
What is that point? Here is a brief scale analysis. Universe has a certain amount of mass-energy. Mass and energy has a quantum wavelength associated with it (just like an electron has a wavelength associated with it). When the dimensions of the universe was smaller than the dimension of this wavelength, quantum considerations necessarily overwhelm classical relativity. This corresponds to when the visible universe was just 10^-33 cm across. While quantum effects can exist at much larger scale, this is the minimum scale at which QG has to necessarily apply. The density of the universe at this point would be 10^94 gm/cc. Light takes about 10^-43 seconds to traverse a sphere 10^-33 cm across and this is conveniently called the Planck epoch time.

The challenge for quantum gravity is to determine what physics holds under these extreme conditions.

 

[sayak83]

The simple expanding universe

In the early phases of the expansion of the universe, the universe was extremely hot. What this meant was that the universe was hot and dense enough to act as a nuclear fusion reactor, combining proton and neutrons and emitting radiation (I. e. photons) in the process. However at these early periods, the universe was too dense for the photons and they were rapidly reabsorbed by the excited atomic nuclei and electrons. It was only when the universe cooled down sufficiently that the atoms stopped absorbing photons, and the radiation was free to travel unimpeded through matter. This transition appears to us like an opaque wall of radiation (think of surface of the sun) that is all around in the sky but far far far away. It's the furthest object one can hope to see in the night sky. However since the space is expanding, the light waves that come through space also gets stretched along with it, thus their wavelengths get longer and the frequencies lower. Just like the sun or a coal fire, the temperature of this ancient radiating surface can be estimated from the frequency of light at arrives on earth. It is called the cosmic microwave background radiation (CMB).

In 1948, Gamow, Alpher and Herman predicted the presence of this radiation. Using simple measures of the then uncertain rates of expansion of the universe, they also predicted that the radiation should have a temperature of approximately 5 Kevins. The way this can be calculated is simple. The ratio of matter density of the universe and the cube of the temperature of this background radiation should be constant if the Universe is expanding everywhere at the same rate and identically in all directions. So one can use the temperature at which matter ceases to absorb photons and the mass density of the universe at that time to evaluate this constant. Then one can find the current mass density and hence take advantage of the constancy of the ratio to get the radiation temperature. They predicted it to be 5 K.

This radiation was finally discover in 1960 through radio antennas. Since then both the theory and the experiment has been refined extraordinarily. The radiation temperature was found to be 2.7K in accordance with more accurate theoretical results. Recent data from Planck safelite shows the amazing match between theory and the predictions of today's Big Bang models.

https://www.aanda.org/articles/aa/full_html/2016/10/aa27101-15/aa27101-15.html

The figure below shows the extremely small temperature fluctuations (less than 300 microKelvins) in the radiating surface demonstrating how smoothly expanding the universe actually was.

The match between the thermal power spectrum and theory is also excellent. The top figure shows the theoretical prediction and the data with the error bars. The bottom figure shows the scatter magnitude in blown up scale.

The power spectrum is a very sensitive guide to the validity of the current theory on inflationary expansion. The link below shows how it is generated and what it means.
Power Spectrum

By now it is clear that some sort of simple inflation must be the explanation for our universe. The predictions match the data extremely well. I will try to write my new posts regarding

1)what inflation is and how it happened
2)does it predict a multiverse
3)can it explain the alleged fine tuning
4)can it avoid a past singularity

 

[sayak83]

Breaking of symmetry

Once upon a time there was only the Force...


Today there are four forces and many types of elementary particles. They are given by the Standard Model.

At the top are the quarks, which make up protons and neutrons and act through the strong force. In the middle is the electron family that acts through the electromagnetic force. At the bottom are the neutrinos that act through the weak force. Yet to be discovered will be the particles of dark matter that act only via gravity.

Why four? Why not one? Well, in the very early universe, when it was very very hot, physicists think that at least the three atomic forces... electromagnetic, strong nuclear and weak nuclear forces were indeed one. What this means is that the electrons, quarks and neutrinos were indistinguishable from each other and so were the forces between them. But as the universe cooled, they lost this initial symmetry and became different. The key to this transition are the various scalar fields that permeate the universe and are well known as the Higgs fields.

Consider a magnetic field. It has a magnitude and a direction of attraction or repulsion. Such fields are called vector fields and fields associated with electrons, quarks etc. are all vector fields. A scalar field (like temperature) has only magnitude and Higgs fields have this feature. They permeate space, and like all fields, imbues space with energy density. However unlike ordinary fields, the lowest energy state of a Higgs field is a non-zero value. In fact the energy of Higgs field at zero magnitude is quite high. What this means is that a cold, low energy universe settles into non zero values of Higgs fields to get to minimum energy. Figure below shows how a Higgs field looks like. It's like a hat, with a energy peak at the center (zero value), a minimal at the periphery of the dome, with the energy rising again in the upturned rim.

When the universe is very hot, space is very hot and is vibrating vigorously with energy. Think of this as the hat jumping up and down very hard. So all particles in this hot vibrating space is also jumping up and down energetically (now think of the hat as a trampoline) and easily jumps over the small central peak. What this means is that in this hot state, to an energetic particle, the Higgs field looks almost flat and they do not interact with it. But as the energy drops, the Higgs particles find it harder to jump everywhere and keep the effective field value zero. Eventually, it tired rolls downhill and comes to rest at one location of the circular minima in the periphery of the dome.

But now the entire space has a set of nonzero Higgs field values. And this nonzero Higgs field now interacts with the electron, quark and neutrino fields. The interaction between the fields differ from each other, causing them now behave differently from each other. Thus now the symmetry between them is broken-electrons, quarks and neutrinos- resonating in a different way with the Higgs fields- now look very different and also gain different masses from one another (when originally they were massless).

Quantum Diaries

Apart from the importance of Higgs fields in giving us the forces we know, physicists believe that a higher energy Higgs field is responsible for starting the expansion of the universe in the first place. To this idea, called the inflation theory, we shall turn next.


May the force be with you till then

 

[Polymath257]

Nice presentation!

 

[sayak83]

The rise of Magneto (err.. Magnetic Monopole)
Here is our friendly heroic electron circling about an atom (real image)

It carries one unit of electric charge. We also know from Maxwell that electric and magnetic fields are two sides of each other. So where is the particle that has one unit of magnetic charge, which physicists call the magnetic Monopole?


That problem of the missing magnetic Monopole seems another asymmetry in need of an explanation. The problem got more acute when Dirac showed that not only Quantum theory allows the existence of magnetic Monopole, at least a few must exist in Nature in order to explain why electric charge is quantified, that is comes in discrete buckets like electrons. They need each other.

Calculations shown below
Dirac Monopoles

So far none have been found in nature. Cosmologists in 1970, using elementary particle physics, asked the question: Is there a reason in the early hot universe that suppressed the formation of magnetic monopoles even though electrons were created in their billions?

Note in the earlier post that particles (like electrons) gain their distinctive identity when they interact with the various low energy non-zero values of the Higgs fields into which regions of space settle into as the universe cools. A region of space, which is casually connected through information transfer by light rays, will choose one position in the valley.

But this only applies to regions that could communicate with each other by light. Since the universe at the point of this phase transition is still very hot and young, just 10^-39 seconds after the Big Bang, light has had 10^-39 seconds to travel, and it is only within this small spherical region of space that the Higgs fields will have a common set of values. Other, causally disconnected regions of the universe will settle into different regions of the low energy valley and will have different values for the Higgs Field.

What this shows is there will boundaries in the universe where the Higgs fields will change values. While electrons etc. are predicted to emerge in regions of uniform Higgs field within each zones, magnetic monopoles are predicted to emerge out of this boundaries where the field value changes, shown below.

So the number of expected monopoles boils down to the number of such boundaries between expanding light cones at the time of phase transition 10^-39 seconds after the Big Bang. When the interaction between Higgs fields and other fields are considered in the configuration shown above the magnetic strength of a monopole is found to be 69 times stronger than the electric charge. Thus the force between monopoles would be 5000 times stronger than force between electrons. Also the magnetic monopoles would be immensely heavy, 10^16 times heavier than a proton.

At this point, the standard Big Bang model was the hot Big Bang. It was simple. Sometime in the past an extremely hot soup of elementary particles and radiation starting from a single point or a small Planck sized zone expanded outwards for some unknown reason at the rate given by Hubble's law, cooled, created elements, collapsed into various galaxies by gravity and became our universe.

Only one problem. Physicists found that under such conditions, the expected number of these heavy magnetic monopole particles in the universe would be equal to the number of protons and neutrons. Being so much more heavier than everything else, they would contribute immense gravitational mass to the universe and the universe would collapse back into a black hole before it even began. Even if by some miracle, the initial expansion rate was fantastically high to avoid this fate, today's matter would be dominated by this heavy highly magnetic monopoles and the history of the universe and its matter distribution would be utterly different from what is seen today. But one sees no monopoles and the universe looks like they are incredibly rare. So either the Higgs field theories are wrong or the Big Bang model is wrong. Magneto should have ruled the world, but something stops him and put him away safely from reality.

Here is the original paper on the topic
- Google Scholar

One final note. While elementary magnetic monopoles are yet to be found, they often arise under special conditions as an emergent system in condensed matter physics so that one could study its properties. Here is the latest results and images of such a monopole
https://phys.org/news/2015-04-physicists-quantum-mechanical-monopoles.html

An image of an experimentally created Bose-Einstein condensate containing the monopole (left) and the corresponding theoretical prediction (right). Brighter area has higher particle density and the different colors denote the internal spin state of the atoms. The monopole is located in the center of the condensate. Credit: monopole collaboration

 

[gnostic]

It would seem that you cover a lot of areas, quite thoroughly.

It is very good and informative, sayak.

 

[sayak83]

The cosmic telepathy problem (or the horizon problem)

As I showed in the last post, the standard Big Bang theory has a serious problem of predicting that the universe should have been overrun by massive and highly magnetic elementary particles of the magnetic field called the magnetic monopoles. But scientists see no sign of them. The universe is very nice and well behaved, as if the villainous Magnetos have been banished from reality.

But there is more. The universe is too well behaved. As scientists look to the cosmic microwave background radiation, the first light from the young universe just 300,000 years after the Big Bang, what they see is unbelievable uniformity, essential for the universe to be the way it is, but not explained by the Standard Big Bang theory.

How uniform was the universe back then? Consider the spectra of the cosmic background radiation.

As can be seen, the radiation signature is amazingly smooth. The temperature fluctuations are in the range of one part in 100,000! And this extreme smoothness is the puzzle, as it says that the entire early universe was in perfect thermal equilibrium with all its parts. And that should not have happened. Thermal uniformity comes through the flow of heat from hotter to colder regions. But heat flow cannot occur faster than the speed of light. So the speed of light sets the upper limit on how large a region of thermal equilibrium could be expected in a 300,000 old universe when the CMB was emitted. This is called the horizon distance and it was 900,000 light years according to the standard Big Bang model at the time of CMB emission. However the observed span of the young universe seen in the CMB itself is calculated to be far greater... 90 million light year across. Thus we have a perfect thermal equilibrium of regions of the universe that was 100 times the horizon distance, showing that regions that should have had no causal contact since the Big Bang were somehow highly correlated to each other. This is cosmological telepathy in a grand scale!

The Critical universe

But that is not the last strange fact. The universe it turns out has very nearly exact critical density to make it flat (instead of curved) with just 0.4% margin of error.
WMAP- Shape of the Universe

The problem is that a flat universe is very very very unlikely according to the standard Big Bang model. For it to happen, the attractive force of gravity and the initial expansion must exactly balance, and since the universe began as dense and hot, the balance has to be stupendous good.

Flatness Problem | COSMOS

To phrase it more scientifically, the flatness problem arises because we appear to live in a Universe that has an observed a density parameter (Ω_0) very close to 1. In other words, the Universe is very close to the critical density. The ‘problem’ is that for the Universe to be so close to critical density after ~ 14 billion years of expansion and evolution, it must have been even closer at earlier times. For instance, it requires the density at the Planck time (within 10^-43 seconds of the Big Bang) to be within 1 part in 10^57 of the critical density. i.e. Ω_0 initially must have been almost exactly:

There is no known reason for the density of the Universe to be so close to the critical density, and this appears to be an unacceptably strange coincidence in the view of most astronomers. Hence the flatness ‘problem’.

Any little deviation greater than one will be rapidly magnified and universe will collapse into a black hole within a second, and any deviation less than one will also rapidly magnified and the universe will be so dilute that no galaxy or stars will ever form.

Thus the universe started to expand with
1)All disastrous magnetic monopoles completely exiled for unknown reason
2)With mysterious telepathic correlation between vast regions of spacetime.
3)On a knife edge of stability between collapse and dilution.

A naive theist in 1970 would have (and did) immediately cried "fine tuning" and "divine hand" for such apparent extraordinary state of affairs. Instead, 1980 brought about amazing joint collaborative innovativeness from an American and a Soviet cosmologist to not only solve these problems but provide us with the reason the universe expanded in the first place. That would be the next post.

 

[sayak83]

Inflation theory... Or Making the Universe great again!

We have seen earlier how the standard Big Bang model, while successful in many ways, predicts lots of unenviable phenomenon which are not seen and would have severely affected the universe if they were true. The first problem the Alan Guth and Andrei Linde tackled was the problem of magnetic monopoles. Notice that monopoles were being created because different regions of space were settling to different low energy Higgs values on the trough at the bottom of the hat.

The cosmologists wondered what would happen if, instead of a dome at the center, the Higgs field at the center resembled a plateau? Perhaps it looked lie a proper British hat.

Now, suddenly things begin to look different. There is a large flat area of high energy density at the center and Higgs field may stay at this high energy plateau for much longer, lazily and slowly rolling this way and that before dropping off eventually into the low energy region in the outer circumference. This means that even after the universe has cooled enough such particles are not jumping energetically everywhere, there is a short but crucial period in the early universe where the Higgs field, and hence space-time is trapped in this high energy density plateau region. This delays the decay of the Higgs field to its nonzero low energy value and delays the emergence of normal matter and radiation from the interaction of nonzero Higgs values with quantum fields. This period is called the period of inflation and the nature of space during this period is called the false vacuum. A simpler figure of the process is shown below,

Let's see what happens as a result.

Today's empty space also has some energy associated with it, called the dark energy. But during the inflation era, the high energy density of the Higgs field contributed enormously to the energy density of space. Space, caught in false vacuum had an energy density of 10^80 gm/cc which is an astoundingly high number. When the Higgs field finally dropped to its current low levels, all this energy was transformed in radiation and elementary particles out of which the universe is made. Thus decay of the Higgs field created the hot dense Big Bang which we know, and the universe with it.

Higgs field is a constant scalar field that permeates space. Unlike ordinary matter and radiation, it's energy is not tied up in bundles of particles or quanta like photons. So unlike ordinary matter and radiation, whose energy density dilutes and falls as space expands... the energy density of Higgs field remains constant. More space there is, more energy the Higgs field has in total as the energy density remains steady.

This extra energy comes from the gravitational field, which also permeates space. The constant energy density property has the peculiar effect (based on Einstein's GR) of producing repulsive gravity. Gravitational force from this repulsive gravity exponentially increases the rate of expansion of the universe, increasing space, increasing the total energy of the Higgs field in space, all driven by a repulsive gravitational field that transfers gravitational potential energy into Higgs energy.

It's a runaway process. The inflation period lasts from 10^-37 to 10^-35 seconds from the beginning only. But the repulsive gravity causes the universe to double in size every 10^-37 second interval. Thus the universe goes through 100 doublings in the inflation era. The size of the universe increases by 2^100 times it's initial value within this very small period. The size of the universe increases by a factor of 10^30.
Figure below show this rapid phase of expansion. Note that the size values of the universe are in factors of 10. The blue line shows the inflation model while the red line shows the standard Big Bang model

We have effectively explained the expansion of the universe.

We have also explained why the universe is flat and is so close to the critical density. Whatever the initial curvature of the universe, inflation has expanded space so much that it looks flat. As shown in the figure below. Universe did not begin with a fine tuned critical density, but was driven towards it by inflation

Inflation also explains why monopoles do not exist and the universe is so smooth and correlated in the large scale. As the curve shows, the repulsive gravity of the Higgs field expanded an extremely small patch of the universe, which was less than 10^-60 meters across into our visible universe of 100 billion light years. This initially small region is well within the region that light can travel and equilibrate and less than one or two magnetic monopoles are expected in a size of the early universe this small.

Thus inflation theory, based on only one assumption about the structure of the Higgs field, at a stroke solves all the problems of the Standard Big Bang and provides the mechanism of expansion of the universe.

Inflation


Excellent articles about the inflationary universe can be found here
A BALLOON PRODUCING BALLOONS, PRODUCING BALLOONS:A BIG FRACTAL | Edge.org
Articles

 

[Polymath257]

That problem of the missing magnetic Monopole seems another asymmetry in need of an explanation. The problem got more acute when Dirac showed that not only Quantum theory allows the existence of magnetic Monopole, at least a few must exist in Nature in order to explain why electric charge is quantified, that is comes in discrete buckets like electrons. They need each other.

A slight quibble. Dirac showed that if there is even one magnetic monopole, then charge would be quantized. The other direction is not necessary, however. The fact that charge is quantized does NOT imply the existence of monopoles. That said, most theories on fundamental particles *do* imply the existence of a monopole.

 

[Polymath257]

Now, suddenly things begin to look different. There is a large flat area of high energy density at the center and Higgs field may stay at this high energy plateau for much longer, lazily and slowly rolling this way and that before dropping off eventually into the low energy region in the outer circumference. This means that even after the universe has cooled enough such particles are not jumping energetically everywhere, there is a short but crucial period in the early universe where the Higgs field, and hence space-time is trapped in this high energy density plateau region. This delays the decay of the Higgs field to its nonzero low energy value and delays the emergence of normal matter and radiation from the interaction of nonzero Higgs values with quantum fields. This period is called the period of inflation and the nature of space during this period is called the false vacuum. A simpler figure of the process is shown below,

Another quibble: Since we now know the mass and some other properties of the Higgs boson, we can exclude it as the inflaton (the spinless particle required for inflation). In particular, the inflaton has to be a *low* mass particle to work.

 

[sayak83]

A slight quibble. Dirac showed that if there is even one magnetic monopole, then charge would be quantized. The other direction is not necessary, however. The fact that charge is quantized does NOT imply the existence of monopoles. That said, most theories on fundamental particles *do* imply the existence of a monopole.

Yes correct.

 

[sayak83]

Another quibble: Since we now know the mass and some other properties of the Higgs boson, we can exclude it as the inflaton (the spinless particle required for inflation). In particular, the inflaton has to be a *low* mass particle to work.

The inflation field could be a high energy variant of the Standard Model Higgs field. They are also called Higgs fields however (for example one of the GUT models has 24 Higgs fields according to Alan Guth).

However, recently the Higgs field itself has been proposed as the inflation field itself and the theory is consistent with both LHC and Planck data. So, given all this, I have gone on to say that the inflation field is probably a kind of Higgs field.
Higgs and cosmology | Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences

 

[Polymath257]

The inflation field could be a high energy variant of the Standard Model Higgs field. They are also called Higgs fields however (for example one of the GUT models has 24 Higgs fields according to Alan Guth).

However, recently the Higgs field itself has been proposed as the inflation field itself and the theory is consistent with both LHC and Planck data. So, given all this, I have gone on to say that the inflation field is probably a kind of Higgs field.
Higgs and cosmology | Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences

While Shaposhnikov's ideas are very interesting, they do require an extension of the Standard Model. In particular, they require a very large coupling of th HIggs field to spacetime curvature. This would require additional particles (in the original article, three Majorana fermions). At this point, the Higgs particle alone isn't enough to drive inflation.

The Higgs and the inflation of the Universe - CERN Bulletin

One caution: this is a rapidly changing field right now. Articles from even a few years ago can be out of date because of the results of LHC and new Planck data.

 

[sayak83]

While Shaposhnikov's ideas are very interesting, they do require an extension of the Standard Model. In particular, they require a very large coupling of th HIggs field to spacetime curvature. This would require additional particles (in the original article, three Majorana fermions). At this point, the Higgs particle alone isn't enough to drive inflation.

The Higgs and the inflation of the Universe - CERN Bulletin

One caution: this is a rapidly changing field right now. Articles from even a few years ago can be out of date because of the results of LHC and new Planck data.

I agree. Please feel free to add comments and corrections in the thread. I am trying to make this thread a source that one can link to for science and religion discussion about cosmology. So all additions and corrections are welcome.

 

[sayak83]

While Shaposhnikov's ideas are very interesting, they do require an extension of the Standard Model. In particular, they require a very large coupling of th HIggs field to spacetime curvature. This would require additional particles (in the original article, three Majorana fermions). At this point, the Higgs particle alone isn't enough to drive inflation.

The Higgs and the inflation of the Universe - CERN Bulletin

One caution: this is a rapidly changing field right now. Articles from even a few years ago can be out of date because of the results of LHC and new Planck data.

Hi. I was wondering about how the latest CMB data constrains the various inflation models. I am having difficulty deciphering the Planck paper on the topic. Which types of inflation and inflaton field is being favored? Any insight appreciated.
https://www.aanda.org/articles/aa/full_html/2014/11/aa21569-13/aa21569-13.html

 

[Polymath257]

Hi. I was wondering about how the latest CMB data constrains the various inflation models. I am having difficulty deciphering the Planck paper on the topic. Which types of inflation and inflaton field is being favored? Any insight appreciated.
https://www.aanda.org/articles/aa/full_html/2014/11/aa21569-13/aa21569-13.html

OK, there are several different inflationary scenarios considered in this paper (as is to be expected).

it appears that the Shopshnikov proposal for the standard model Higgs being the inflaton is consistent with this data.

Also consistent are two models based on axions. Axions are particles that have been proposed to explain what is known as CP violation and are also candidates for dark matter. Axions tend to decay into two photons, and have been proposed as the cause of a 'glow' around the core of our galaxy. However, this glow is more likely to be from pulsars according to a recent study. In any case, this scenario is also quite interesting.

Inverse power law potentials (like inverse square) are strongly disfavored.

Quadratic potentials are strongly disfavored.

Certain 'natural inflation' potentials are disfavored.

One problem is that ALL inflationary scenarios predict 'gravitational waves' (not the same was what was detected at LIGO) and at this point the data is consistent with NO such waves. This leads to the following statement (r represents the percentage of gravitational waves):

"None of the inflationary models tested here fit the data as well as the ΛCDM model. This mostly reflects that there is no evidence in the data for r different from zero."

 

[Polymath257]

A treatment of more recent data from Planck is given in
https://arxiv.org/pdf/1502.02114.pdf

This is the 2015 data set. The previous was the 2013 data set.

One thing pointed out here is that the Higgs version of inflation and the R^2 version are observationally identical for CMB. That makes distinguishing between them impossible with this data.

The axion monodromy model is still allowed. The R^2 /Higgs model is still very much allowed. A quartic hilltop model is still allowed.

One big controversy was the BICEPII claim for observing gravitational waves (the r value in my previous post). This suggested a value of r=.20 which was larger than the r<.12 given by the Planck 2013 data. It was determined that the BiCEP data was probably from polarization due to galactic dust, so the current r<.12 is more robust that the 2013 value.

So, at this point, inflation has NOT been definitively detected. Everything seen so far is consistent with the Lambda-CDM model that is considered to be 'standard'. Some versions of inflation have been ruled out and some are between 68% and 95% confidence levels. Higgs inflation and R^2 are the 'best' with axions and hilltop close behind.

 

[sayak83]

A treatment of more recent data from Planck is given in
https://arxiv.org/pdf/1502.02114.pdf

This is the 2015 data set. The previous was the 2013 data set.

One thing pointed out here is that the Higgs version of inflation and the R^2 version are observationally identical for CMB. That makes distinguishing between them impossible with this data.

The axion monodromy model is still allowed. The R^2 /Higgs model is still very much allowed. A quartic hilltop model is still allowed.

One big controversy was the BICEPII claim for observing gravitational waves (the r value in my previous post). This suggested a value of r=.20 which was larger than the r<.12 given by the Planck 2013 data. It was determined that the BiCEP data was probably from polarization due to galactic dust, so the current r<.12 is more robust that the 2013 value.

So, at this point, inflation has NOT been definitively detected. Everything seen so far is consistent with the Lambda-CDM model that is considered to be 'standard'. Some versions of inflation have been ruled out and some are between 68% and 95% confidence levels. Higgs inflation and R^2 are the 'best' with axions and hilltop close behind.

Thanks a lot. I am not entirely sure what the various R2 or flat top models are. Are they all various versions of slow roll inflation. I do not think R2 model is though as it modifies GR laws correct.
Can Lambda cdm model account for isotrpopy, flatness, horizon, lack of magnetic monopole and nature of the scale invariant density or power spectra of the CMB? I thought inflation predicts these things? Can you get these things without inflation? Or does it just assumes that these things exist as brute fact? Is it not the case that lambda CDM is a bit like an emperical rical model like Keplers laws of planetary motion or the periodic table rather than theory?

By the way, you should find this paper interesting
Distinguishing between R2-inflation and Higgs-inflation - ScienceDirect

 

[Polymath257]

Thanks a lot. I am not entirely sure what the various R2 or flat top models are. Are they all various versions of slow roll inflation. I do not think R2 model is though as it modifies GR laws correct.

Edited:
Yes, R^2 modifies GR laws. Technically, though, so does dark energy: it is essentially adding a cosmological constant to the original GR laws. This is a minimal extension because it modifies gravity in a very minimal way and it gives both inflation and reheating (when inflation cuts out).

Higgs inflation has to work harder for reheating, but mostly in determining the coupling of Higgs to other fields.

Yes, ALL of the versions still on the table are slow roll inflation except a version of 'open' inflation that happens in local 'bubbles'.

Can Lambda cdm model account for isotrpopy, flatness, horizon, lack of magnetic monopole and nature of the scale invariant density or power spectra of the CMB?

No. What inflation does is provide the initial conditions for the LCDM description: flat, fluctuations, etc. The goal of inflation is to explain those initial conditions. But they can also be taken as brute facts and LCDM works perfectly well. It should be noted that we are dealing *solely* with the CBR data--we have not found the telltale signs of inflation from the background radiation.

I thought inflation predicts these things? Can you get these things without inflation? Or does it just assumes that these things exist as brute fact? Is it not the case that lambda CDM is a bit like an empericalrical model like Keplers laws of planetary motion or the periodic table rather than theory?

No, it is much more detailed than that. LCDM is based on GR, thermodynamics, and adds in initial fluctuations. It assumes a cosmological constant (equivalently, dark energy), which is what the lambda is for. It also assumes cold dark matter. In other words, non-relativistic dark matter (neutrinos, for example, do not qualify). These are on top of the standard BB cosmology provided by thermodynamics and GR.

There are six unspecified parameters in LCDM (age of the universe, baryon density, dark matter density, scalar spectral index, curvature fluctuation amplitude, and reionization optical depth) and some fixed parameters (equation of state for dark energy, flatness Omega=1, etc) that can be used to calculate things like the Hubble constant, age of decoupling (when the CBR was formed), etc. These parameters are fit to the CBR data.

By the way, you should find this paper interesting
Distinguishing between R2-inflation and Higgs-inflation - ScienceDirect

That was a good article to know about. It looks like we are getting close to being able to distinguish these two from the value of n_s. Of course, the *real* goal is to find those tensor mode fluctuations, which are the common to all inflation models.