Sunday, February 28, 2016

Higgs inflation

The case for inflation is extremely strong. If you don't already understand how strong the case is, then I suggest watching the following lecture at MIT by Alan Guth. Alan Guth is the originator of the concept of inflation, and now he provides a fairly unbiased judge of the theory, since his original model for inflation has been effectively disproven (i.e. quantum tunneling from the false vacuum through a barrier to the real vacuum.)
The main evidence for inflation are the following:
(1) Horizon problem:  the universe that we see is extremely similar even though there was no way for parts of the universe that we see today to have been in contact...unless the universe we see today came ultimately from a small region that had been in contact, and then got inflated to a much larger size.
 (2) Flatness problem:  Overall, there is virtually no curvature (k) in the universe. In a matter dominated universe, the overall curvature grows with time, so this means that the curvature when the temperature was >TeV must have been extremely small. The smallness of the curvature can be explained if our universe went through a period of inflation before the temperature dropped to ~TeV.
(3) Small, Adiabatic, Gaussian fluctuations in curvature: While the overall curvature of the universe is small or zero, there are local fluctuations in the curvature that end up canceling overall, i.e. while the curvature might be negative in some locations, it is positive in other locations so that the overall curvature is near zero. (Imagine living on a fixed point in Sahara desert and imagine that the farthest that you can see is 100 km in any direction. You would see local variations in the curvature, due to dune piles scattered throughout the desert. However, the overall curvature would be virtually zero. In other words, you would be forced to conclude that, if you did live on the surface of a sphere, then the radius of the sphere is much, much greater than 100 km.) In this analogy, the dune piles are the remnants of the initial fluctuations before inflation. The primordial fluctuations are random, uncorrelated, adiabatic and overall add-up to near-zero curvature.

These are the three main sources of evidence for inflation.
What's interesting is that the standard model of physics provides a natural candidate for the inflation field: the Higgs field. Like the inflation field, the Higgs field is a scalar field, in the sense that at every point in 4-D space-time, there is a value (a quaternion) for the Higgs field. Examples of day-to-day scalar fields are pressure/temperature/electric potential. These should be contrasted with a vector field, which has at every point in space-time both a magnitude and a direction. Examples of day-to-day vector fields are electric field, magnetic field, and wind velocity. At every point, the vector field has both a magnitude and a direction.

The Higgs field is a fundamental scalar field. Scientists are still working out the shape of the Higgs energy density as a function of the value of the Higgs fields. We /they know that the shape of the energy density vs. field value when the value of the field is close to the value of the field (v = 246 GeV) which is a local (and perhaps global) minimum in the energy density. (see inset in the figure below from the paper by Bezrukov and Shaposhnikov.) What is still uncertain is the shape of the curve far from v = 246 GeV. It is well known that the coupling of the Higgs field to particles (such as the top quark) causes the shape of the curve to look somewhat like the curve below. Depending on the coupling to the top quark and the self-coupling of the Higgs field, the potential can look like the one below, which goes to an asymptote. The potential below is also nearly exactly the shape of the potential needed to explain slow-roll inflation. It is called slow-roll because of the small gradient in the field at large values of the Higgs field.

 Figure#1: Higgs energy density versus field value from the paper by Bezrukov and Shaposhnikov
 titled " The Standard Model Higgs boson as a the inflaton."
 Interestingly, the shape of the Higgs field in the case listed above is nearly the same as the primordial potential field that is measured experimentally. (By experimentally, I mean when combining data from WMAP/Planck/ACT/SPT/WeakLensing/LymanAlphaForest.) The primordial potential field was estimated by Hunt and Sarkar using the data list above and can be seen below:

Figure#2: Primordial potential of the inflaton field as estimated by Hunt and Sarkar

 Below, I show the data from Hunt and Sarkar, but with the Higgs potential field imposed on top.

 Figure#3: Primordial potential of the inflaton field as estimated by Hunt and Sarkar
with the Higgs field estimated by Bezrukov and Shaposhnikov imposed on top as a black line. (In the case that the Higgs self-coupling and the coupling between the Higgs field and the top quark produce an asymptotic value for the potential field.)

What one can see in Figure#3 is that the experimental data for the primordial inflaton field can be well described so far by a Higgs-like scalar field. Also interesting is that the potential field takes a nose-dive at smaller and smaller scales. This nose-dive in power help to explain why there appears to be a lack of fluctuations at the scale of galaxies (i.e. 1-100 kpc.) (Perhaps, we don't need warm dark matter as a complete explanation for the lack of fluctuations at small scale???)

Because the shape and size of the Higgs scalar field is so nearly the same as the shape and size of the inflaton field required to create primordial fluctuation, it is my opinion the Higgs field is the inflaton field. To prove this conjecture will require further research by theorists into the exact shape of the Higgs field and further experimental data on the mass of the top quark and Higgs boson as well as experimental data on the primordial fluctuations at both large and small scales (the middle scale seems pretty much nailed down.) Theorists will need to calculate the running of the Higgs field at large energy scales by including more than 5 loops of self-coupling and coupling to bosons/fermions.

All-in-all, it appears that the Higgs field is the inflaton field and there is no need to have supersymemtric particles to save the Higgs from going unstable.(Hence, another reason why I think that Supersymemtry is dead!)

Friday, February 12, 2016

Gravity Waves from Inflation???

Congrats to the LIGO team for the (likely) detection of gravity waves. It looks like they will be presenting us with many more candidates in the near future. I look forward to see the results.

But that leaves us with the question:  can we detect the tensor gravity waves from inflation?
The problem right now is that the data of B-polarized modes from the CMB has some large error bars and/or contamination from non-primordial sources.

For example, below is a plot of those experiments that have released data on the auto-correlation and/or self-cross-correlation between frequencies.
Yellow =  Planck 2015 low l
Light Blue = WMAP 9year
Light Green = Planck 2015 Mid-range l with foreground removed (see prior blog post)
Light Grey = SPTPol 100 day  95GHz x 150GHz
Orange = BICEP2 x KECK   95GHz x 150GHz
Black = Polar Bear1
Brown = Output from CAMB using BestFit Planck2015 TT+TE+EE+lowP+lensing+ext plus r =1
Blue = Output from CAMB using BestFit Planck2015 TT+TE+EE+lowP+lensing+ext plus r =0.1
Grey = Output from CAMB using BestFit Planck2015 TT+TE+EE+lowP+lensing+ext plus r =0.0
where r = initial tensor-to-scalar ratio (which is an input for CAMB)

I think that we can safely say that r = 1 is ruled out. But, from this graph alone, it's hard to rule out r=0.1 or r = 0. So, below is a ZoomIn around the region in which BICEP2/KECK are focused. This time, I plot CAMB output for r = 0.1, r = 0.01, and r = 0. The data points are almost always above the lines, which means that there is likely contamination from foreground or sources of B-modes other than primordial + lensing of E-polarized modes. Also note in the graph below that, if there is no lower error bar, then this means that the error bar goes into negative values. (This didn't happen in the Linear scale plot above.)

Note that the CAMB Output has no foreground added to it. The Planck Mid Range data supposedly has dust removed, but it seems to suffer from erroneous data near l = 225. The BICEP2/KECK data has some dust contamination because there is some dust contamination even at 95 GHz.

All of this just means that we'll have to wait a little bit longer before we can say definitively that we have detected primordial gravitational waves. We should be getting results some time this year from BICEP3+KECK at 95GHz. If this data plus the BICEP2/KECK data at 150GHz is cross-correlated with a B-lensing map and a foreground map to remove lensing+foreground, then one should be able to make some meaningful constraints on the tensor-to-scalar ratio, r. Also, the Planck collaboration is expected to make another release of their data this year (and a final release in 2017.) This data should have BB modes vs. l (for all l), which is something that they have not yet published.
I'm excited to see the results when they are announced.
In the somewhat near future, we should be expecting results from PolarBear2, SPT-3G, and CLASS. This is an exciting time for studying gravity waves produced during inflation.

Friday, February 5, 2016

Quick Update on BB Modes in CMB

This is just a quick update.
I found an arxiv manuscript by a researcher who was one of the many co-authors on that joint BICEP/Planck paper last year. (H.U. Nørgaard - Nielsen)
He has taken the Planck 2015 Polarization maps (U&Q) and he has tried to remove the dust foreground in order to obtain EE and BB power spectra. Note that the Planck Collaboration has yet to publish yet official BB power spectra (except between l =2 and l= 30.)

The plot below from his manuscript is a plot of his determination of the CMB's BB Power spectra (red) and models for the lensing B-modes plus primordial B-modes (blue) as a function of the tensor-to-scalar ratio (r =T/S.)

What we can see is (a) there is large error in the data, which is due to the low sensitivity of Planck to BB modes, and (b) there is likely a spike around l = 225, which corresponds to the location of the first peak in the TT data. As such, it would be interesting to see what H.U. Nørgaard - Nielsen obtains for the correlation spectra for TB. (The TB power spectra is not in the manuscript.)

(c) There's no way (using only these results) to make a meaningful constrain on the tensor-to-scalar ratio, or even the lensing B-modes.

As such, we will have to wait for BICEP3 and CLASS results before we can make any real constraints on the tensor-to-scalar ratio. (Luckily, BICEP3 and CLASS will be able to improve their constraints on r =T/S by using Planck estimates for dust and for lensing B-modes.)