Gravitational Lensing Exposes Further Discrepancy in Hubble Constant - Past 5 Standard Deviations

We know the standard model of Big Bang cosmology, known as ΛCDM, incorporates how the assorted cosmological components outwardly behave. Dark energy, the model presumes,

• Dark Energy - Evidence for a New Law of Physics?

 Takes the form of a cosmological constant Λ, or a constant energy density per unit volume of vacuum. And dark matter is cold—that is, nonrelativistic—and interacts only via gravity and possibly the weak force.

Now it turns out (Phys. Today, March, p. 14) discrepancies are showing up in the measurements of the Hubble constant H0 - based on gravitational lensing techniques.  To fix ideas, the ΛCDM model predicts that the universe today should be expanding at a rate of 67.4 ± 0.5 km/s/Mpc. But a direct measurement of H0 based on observations of standard candles—Cepheid variable stars  (e.g. Measuring Stellar and Celestial Distances )

 And type Ia supernovae—give a different value: 74.0 ± 1.4 km/s/Mpc.

Now we learn that new collaborative research led by Sherry Suyu, from H0LiCOW (H0 Lenses in COSMOGRAIL’s Wellspring)  uses gravitationally lensed quasars to independently measure H0. The group’s latest result, 73.3 + 1.7 − 1.8 km/s/Mpc, agrees well with the standard-candle value. Combining the H0LiCOW and standard-candle measurements gives an H0 of 73.8 ± 1.1 km/s/Mpc, which differs from the ΛCDM value by 5.3 standard deviations.

As I noted in a previous blog post e.g

Arriving at a More Refined Hubble Constant

There has been ongoing work on improving the value of   such as described in the link to an Astrophysical Journal preprint paper in the above blog post link.  In the current research related to the  H0LiCOW work, it is crucial to note the link to a theoretical basis called "time delay cosmography".   Reference to the graphic shown (compliment of Freddie Pagani, ibid.)  can be instructive in understanding how the gravitational lensing works.

Basically, when a quasar or other luminous distant object lies in the line of sight of massive object, i.e  foreground galaxy, its light is deflected so strongly that multiple images appear (see the extreme right frame of the graphic)

The challenge in any direct measurement of H0 is in gauging the distances to faraway astronomical objects; their velocities relative to Earth, in contrast, are readily inferred from the redshifting of their radiation. Standard candles are appealing because their luminosities are known, so their distances can be calculated from how bright they appear on Earth. In H0LiCOW’s complementary measurement, the researchers studied quasars whose light is so strongly deflected by foreground galaxies that they appear as multiple distinct images, as shown in the figure. Because the light in each image traverses a path of a different length, fluctuations in the quasar’s light show up in the lensed images at different times. 

Measuring those time differences, which are on the order of weeks, doesn’t directly yield Dd (the distance from Earth to the lens) or Dds (the distance from the lens to the quasar). But it does constrain their combination, which is enough information to calculate H0 from the objects’ known redshifts. In 2017 the collaboration published a first result based on three lensed quasars (see Physics Today, April 2017, page 24). The current work extends the analysis to six quasars.  Below are shown the light curves from four lensed images of the quasar shown in the top graphic.

These curves were collected over 13 years from the COSMOGRAIL collaboration.  Note that fluctuations in the quasar's intensity appear first in the curves A and C, then in light curve B. Finally, two weeks later in light curve D.   The key point is that sufficient information is obtained - using 1 to 2 m telescopes- to get H0.

Basically, given the two angles, q1  and  q2   are small, the difference in path lengths shown(top graphic)  will be proportional to:   (Dd  Ds )/ Dds  .   Here  the denominator refers to the distance from the galaxy to the quasar.  Now, the difference in light travel time, which includes the effects of general relativity and the cosmic expansion, is proportional to the same value.  Recall in the case of general relativity, we are looking at the deflection of light as a result of encountering a massive object along its path, e.g.

Here the light from a star at an actual position S2 is seen to deflect by some angle  a    thereby altering the image position to that seen at S1. This is a direct result of the effect of the gravitational field of the Sun on the light rays. The true direction is thus alone the ray ES2 while the deflected position is along the ray ES1.  By more formally arriving at the geometry below:

We can obtain for the deflection angle, :

 a   = - 4 GM/ b   or (in cgs units): 

 a       = - 4 GM/ b c²  

Finally, in obtaining H0  we note the importance of the lensing galaxy's mass distribution.   This is needed to calculate the deflection angles,   q1  and  q2 .These, again, are analogous to the angle  a  computed in the example above. 

 These results in tandem  lessen the likelihood that the H0 discrepancy is due to some unappreciated systematic uncertainty in the standard-candle measurement.  Taken at face value, they seem to point toward a need to revise the ΛCDM (Standard) model. 

For those interested in further details, see:  K. C. Wong et al., Mon. Not. R. Astron. Soc., in press, https://arxiv.org/abs/1907.04869.)

Selected Questions (And Answers) From All Experts Astronomy Forum (Big Bang, proper time, quantum cosmology etc.)

The following were culled from cosmology questions asked on the All Experts Astronomy forum over 2010--2012:


1-What is the evidence for the Big Bang and how was it discovered?

The evidence for the Big Bang is the 2.7 Kelvin degree, cosmic background radiation. The key aspect that makes it evidence is that it has the same intensity in all directions- wherever one observes in the sky. No ordinary radiative or local explosive source (e.g. supernova) would produce such a characteristic. The only feasible explanation to account for it would be a vast “explosion” occurring in the distant past and affecting the entire universe. Its entire volume.

The isotropic (all directions) radiation was discovered during a sky survey at the Bell Laboratories in 1965, by Arno Penzias and Robert Wilson. They had pointed their radio telescope in different directions in the sky and received the same “buzz” no matter where they observed. After rigorous data reduction (removal of data detritus and effects of bat guano), plus later confirmation of the “universal buzz” - it was later identified by Robert Dicke as the cosmic microwave background radiation (CMB), the radio remnant of the Big Bang, they realized they’d discovered the relic radiation left over from the Big Bang.

In 1978 the pair received the Nobel Prize in Physics for their discovery

2- If there was a Big Bang can we say the universe had a beginning, or not? What came before the Big Bang?

Asking ‘what came before the Big Bang’ is like asking ‘what’s north of the north pole?’ It’s the kind of question that at first glance seems logical, but really isn’t. The key thing here is that the time continuum we use to measure instants or epochs starts at the Big Bang, using the Hubble constant. Going to epochs before the Big Bang isn’t feasible because there is no temporal template to go by.

Though we can use the current Hubble constant to measure the proper time since the Big Bang as 13.7 billion years we can’t go any further than that. Or, into any “negative times” – as defined “before the Big Bang”. The reason is that so far there is no physically operational meaning to these.

3- You mentioned “proper time” – what’s that?

Proper time   τ   is defined in terms of the relativistic factor  (from special relativity):

g  =   [(1 - v  ²/c²)  ^-1/2]  

where v is a specific velocity- say of an observer’s frame, c is the speed of light.

Then the proper time is:   dτ   = dt/ g

Reversing the above, we can say that when the (relativistic) clock advances by increment dτ   then  the clock time that elapses on Earth is given by:

dt  =    g   dτ  

Why use proper time? Basically, because normal time measures are unreliable and subjective owing to relativity. For example, even saying or asserting the energy is greater or less at one time (t2) than time (t1) is impossible since energy (like mass, time, length) varies depending on the observer’s frame.

For example, consider the energy of an object moving at velocity v in the simple diagram below:


But, to the observer O moving in a reference frame with the same velocity, the object appears at rest so its kinetic energy = 0. In more technical consideration, on the basis of the Lorentz transformation (google!) the energy E’ in a new frame will depend on the energy E in an older frame according to:

E’ =  g _o (E –  v _o  p _x )

Where  v _o is the velocity and  p _x   the momentum in direction (x).

The factor  g _o   =   1  / [(1 - v _o ²/c²)^½]  


The point is that the energy in the new frame E'  depends on the momentum in the old frame, p _x . If this momentum is not conserved, then energy won’t be conserved in the new frame.

Note here that the relation of the new p' _x momentum  to the old,  p _x is:

p' _x    =  g _o (p _x   –  v _o  E/   c² )

Bottom line, unless one employs corrections using proper time to make energy estimates or statements, he will end up talking nonsense.

For example, let’s say you are looking at an object receding at a velocity of 0.5 c, and assert based on careful ordinary time measurements that it emerged 1 billion years after the Big Bang. Or – 12.7 billion year removed from your observation. But how does this compare to the proper time?

We have: dτ  = dt/ g

Where dt = 12.7 billion yrs.

g  = [1 – (0.5c/c) ²]  
 
 = 1/  Ö[1 – (0.25)] = 1/  Ö[0.75] = 1.155

Then the proper time interval dτ   is: (12.7 x x 10 ⁹  yr)/1.155 = 1.1 x x 10¹⁰  yr

Or 11 billion years not 12.7 billion.

This obviously also means that one cannot say or assert that from the Big Bang there has been “an infinite” amount of time, or instants. No, there hasn’t, and one can do the computation for the actual time interval using the proper time format.


4- What is meant by Quantum Cosmology and how does it work? Can it explain the Big Bang?

Quantum cosmology means that we use terms, conditions and parameters that are peculiar to the quantum level – for example quantum variables – in examining how they might work in explaining aspects of cosmology and yes, origins.

Quantum cosmology also is not for the faint of heart, or those who haven’t done a lot of physics – including taking quantum physics courses. In other words, one can’t simply approach its basis or claims using common sense or even ordinary logic. I believe it was Richard Feynman in one of the prefaces to his lectures who wrote: “Don’t even try to go down the rabbit hole of understanding quantum mechanics, or you will be lost forever.”

What he meant by that is that we don’t approach quantum formulations on the basis of trying to understand them, like one might wish to understand how an electronic amplifier works. We approach them from the mathematics we use, and let those math results lead the way.

At least one theory of the origin of the cosmos uses quantum cosmology in what we call “quantum bootstrapping”. This means, formulating a quantum fluctuation which could have incepted the cosmos via the Big Bang.

The starting point for these sorts of theories actually resides in a real world phenomenon. Particle production is one- wherein particles are created then quickly destroyed with energy release.

The typical pi meson (call it p ) lasts 10 ^-16 sec then vanishes yielding two gamma ray photons in its wake,viz.

 p    -> g   +   g

Thus, rest energy is real energy and is capable of doing work. In the case of the pion above, the total mass 2.4 x 10^-28 kg, is converted to electromagnetic energy.

The amount of the energy can be estimated using the Heisenberg Uncertainty Principle in the energy-time format:

D E D t   <  ħ  (where   ħ   is the  modified Planck constant: 

 h/ 2p =   1.05 x 10^-34 J-s

Thus,  if the time uncertainty for disappearance of the pi meson is:  D E = 10^-16 s

Then the energy available that comes off is:

   D E =    ħ  / D t   = 1.054 x 10 ^-18  J = 6.5 eV

In the same manner, a number of theoreticians (e.g. T. Padmanabhan) have speculated the universe could have emerged like the pi meson using the same basis for energy arising out of “nothing”.

Padmanabhan’s full paper: Universe Before Planck Time – A Quantum Gravity Model, can be found in Physical Review D, Vol. 28, No. 4, p. 756.

Is There Really A "Discrepancy" In The Hubble Constant? Is It Truly A Constant?

According to Dennis Overbye, writing recently in the NY Times "there is a crisis brewing in the cosmos, or perhaps in the community of cosmologists". He adds that some astronomers believe  the universe seems to be expanding too fast.   Further, recent measurements of the distances and velocities of faraway galaxies don’t agree with a hard-won “standard model” of the cosmos that has prevailed for the past two decades. The latest result shows a 9 percent discrepancy in the value of the Hubble constant, which describes how fast the universe is expanding.

First, a bit of background: thanks to astronomer Edwin Hubble cosmology was put on a more secure observational footing on the basis of his "Hubble law". It is encapsulated by the graph shown below:

This relation between distance D  to an extra-galactic object  e.g. quasar, galaxy cluster) and its recessional velocity (v), has since come to be known as Hubble's law and is  expressed:

v = cz = HD

where H is known as the Hubble constant, c is the speed of light and z is the red shift.

This quantity z measures the extent to which spectral lines, say L1 and L2,  are shifted to the red  (longer wavelengths) compared to the normal spectrum, say of an element like hydrogen. The greater this shift the higher the velocity of recession.

The image below illustrates this for two extragalactic objects:



In fact 'H' is more technically the Hubble "scale factor".  The REAL Hubble constant (H o ) is the scale factor (a) divided by the distance in megaparsecs  MPC (km) where 1 parsec = 3.26 light years.

If then currently MPC (km)   =   3.08 x 10  ¹⁹     km/ Mpc  then:

H o =   a / MPC(km)   =  2.26 x 10 ^-18  s ^-1

Then the age of the cosmos can be obtained from:  t o =  1 / H o =

 (1 /   2.26 x 10 ^-18  s ^-1 )   =   4.4 x 10 ¹⁷  s   = 1.3 x 10 ¹⁰  yrs. or 13 billion years in age

The scale factor a, called the "Hubble constant",  is currently a »  70 km/ sec/Mpc. But as I reported last summer, e.g.

http://brane-space.blogspot.com/2016/06/arriving-at-hubble-constant.html

has since been refined to a = 72.8  km/ sec/Mpc.

Clearly then what we call the Hubble constant depends on the accuracy of a, and this in turn depends on the latest techniques to attain more exact values.  As I noted in the preceding link the newer,  more exact value has been based on refining the universe’s current expansion rate to unprecedented accuracy, reducing the uncertainty to only 2.4 percent.

However, an uncertainty of even just 2.4 percent means we cannot be talking about a real physical constant, but only an approximate factor that determines the proportionality value H in the Hubble law.  This is important to process before continuing.  My point is that the "discrepancy" with the standard model is a separate issue, because the standard model itself is still under scrutiny, although it's gained much more traction with the discovery of the Higgs boson.

This elicits the question of whether this small "mismatch" (Overbye's term)  is truly an indicator of  how well we know the cosmos. According to  Wendy Freedman of the University of Chicago, who has spent most of her career charting the size and growth of the universe:

“If it is real, we will learn new physics,”

Perhaps. But I don't think the 'new physics' will enter until we also are able to incorporate the role of dark energy, which has been identified as the primary agent responsible for the accelerated expansion. Relevant to this we invoke what can be called a cosmological "equation of state" (think of something like the equation of state for an ideal gas, e.g. P = nkT) for the vacuum energy presumed to underlie most theories of  dark energy . This is:

w = (Pressure/ energy density) = -1

One advantage is that this equation of state is consistent with Einstein's general theory of relativity - which one could say approaches the status of a 'basic law of physics'. 

In this case, the existence of a negative pressure is consistent with general relativity's allowance for a "repulsive gravity" - since any negative pressure has associated with it gravity that repels rather than attracts. (See, e.g. 'Supernovae, Dark Energy and the Accelerating Universe', by Saul Perlmutter, in Physics Today, April, 2003, p. 53.) Of course, simple algebra applied to the above also shows that the energy density would have to be negative, e.g. energy density =  - (pressure).

Specifically the term (r + 3p) acts as a source of gravity in general relativity, (where r = energy density).

 Set:  0 = (r + 3p),   then the pressure :

 p =  -r /3   (or  r  = - 3p)

 and if:  p <  (r /3) we have gravity that repels.

To ascertain the proportions of dark matter and dark energy one uses graphs derived from supernova  data with corrected apparent visual magnitude m v , redshift (z),   to give different combinations of  W _dark to W _matter over the range. However, only one of the graph combination bests fits the data. Currently this yields:

Wd_ark = 0.68 and  W_matter = 0.27


As a result,  astronomers have accepted that the universe consists of roughly 5 percent atomic matter by weight, 27 percent dark matter and 68 percent dark energy . The last is what's speeding up the cosmic expansion.

Back to the link above for my earlier post last summer citing a team led by Adam Riess of Johns Hopkins University and the Space Telescope Science Institute, using the Hubble Space Telescope and the giant Keck Telescope on Mauna Kea in Hawaii . They obtained a value with  only 2.4 percent uncertainty - but as I pointed out-   this is still nowhere near acceptable constant territory. Check any table of physical constants - actual ones, like the Newtonian G, or speed of light c - for comparison.

The claim of Overbye  in his piece is that this "made waves because it meant that, if true, the Hubble constant as observed today was now clearly incompatible with a result of the lower slower value of 67 inferred from data obtained in 2013 by the European Planck spacecraft of relic radiation from the Big Bang."

But how big were these "waves",  really? Those  Planck mission observations revealed the universe when it was only 380,000 years old  and these are considered "the gold standard of cosmology."  But how reliable and trustworthy is this gold standard?  Interestingly, whether the standard cosmic recipe might now need to be modified  depends on whom you talk to.

Personally, I side with the higher  H values because I place more confidence in the supernova data and observations, redshifts derived therefrom, than the Big Bang Plank observations. Heresy? Maybe, but there it is. Also, Prof.  Riess has admitted that the Planck mission measured the Hubble constant only indirectly as one of several parameters, i.e. in the standard model of the universe. So why would you place more faith in those measures than the supernovae data?

Bolstering this POV, another group called H0LiCOW (short for H0 Lenses in COSMOGRAIL’s Wellspring),  from the Max Planck Institute for Astrophysics in Garching, Germany, reported its own value of 72 km/ sec/Mpc , also inconsistent with the lower value from the Planck space mission’s analysis.  This interjects the question of whether the "Big Bang' results might themselves be spurious and based on as yet undetected systematic or other errors. Or, perhaps the Standard Model itself needs revision. (See addendum).

Stay tuned, because the issue isn't resolved yet, but for my money, the high z supernova data hold the key. Until I see much more consistency in the results from the "Big Bang"- Standard model teams.
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Addendum on the Standard Model- Higgs boson discovery:

The so-called 'Standard Model' is generally defined as the symmetry:

SU(3) x SU(2) X U(1)

where each of the above denotes a specific matrix, or more exactly a group. See, e.g.

http://brane-space.blogspot.com/2010/04/looking-at-groups.html

In the case of SU(2) we describe it as the "special unitary group" which has the form:

S =

(a.........-b*)
(b..........a*)

where a*, b* are complex conjugates and we have (aa* + b*b) = 1. Thus the elements of SU(2) are the unitary 2 x 2 matrices with DET (determinant) = 1. These groups thus define the behavior of a specific class of subatomic particles. Spontaneous symmetry breaking would therefore resolve this combination into constituent parts, e.g.: SU(3) associated with the 'color force' of quarks:

 SU(2) x U(1)

associated with the electro-weak force.

One possible symmetry breaking (quark -boson format) is:

SU(3) x SU(2) X U(1) -> SU(3) + SU(2) x U(1)

which would occur at a particular ambient temperature (T_qb) for the universe at some epoch (E_qb) in the past. In the foregoing, the synthesis of SU(2) and U(1) into the locally gauge invariant electro-weak theory requires a mechanism which confers mass to three vector bosons while leaving the photon massless. This 'mass-giving' mechanism is called the Higgs Field or Higgs mechanism, and it demands the existence of one or more massive, spin-0 bosons otherwise called Higgs bosons.

Enter now the putative discovery of the Higgs, thanks to the large hadron collider, which  was announced at CERN. Dr. Rolf Heuer, director general of CERN, while referring to the new discovery as "a historic milestone"  nevertheless cautioned that it was too soon to know for sure if the new particle (coming in at 125 billion electron volts) is actually the long sought particle.

The problem? The culmination of analyses of over 800 trillion proton-proton collisions over the 2 years leading up to the announcement generated a quandary. When buttonholed,  the physicists admitted they  actually knew little. The CERN results were mostly based on measurements of two or three of the dozen different ways, or “channels,” by which a Higgs boson could be produced and then decay. Worse, there were hints that some of the channels were overproducing the Higgs while others might have been underproducing. In either case, false positives or false negatives, one had to look askance at the initial results.

The upshot? There may not have been a real Higgs discovered but a spurious 'mirage' imitating some of its properties but more a confection of the data than based in reality. Also, assuming a genuine signal or find, it may not have been unique but only ONE of two or three different Higgs bosons. Much like the case of the neutrino, which was once believed to be one entity only, but we now know is THREE: the electron neutrino, the tau neutrino and the muon neutrino, see e.g. http://brane-space.blogspot.com/2012/06/solving-neutrino-puzzleand-matter.html