Arriving at a More Refined Hubble Constant

The Hubble constant is amongst the most critical values used in modern cosmology. Although it is referred to as a "constant" it is, in fact, subject to change based on changed (i.e. more up to date) data. The above pictogram shows basically the three steps by which its value is currently arrived at.

According to a report out of the Space Telescope Science Institute by Donna Weaver and Ray Villard a team under the aegis of  Nobel Laureate Adam Riess (of the Space Telescope Science Institute and Johns Hopkins University) ,  has made a discovery leading to an updated value for the Hubble constant. This has been based on refining the universe’s current expansion rate to unprecedented accuracy, reducing the uncertainty to only 2.4 percent. The team made the refinements by developing innovative techniques that improved the precision of distance measurements to faraway galaxies.

The results will appear soon in an upcoming issue of The Astrophysical Journal but interested readers can access the basic details here:

http://science.nasa.gov/science-news/science-at-nasa/1999/ast25may99_2/
 

The Riess et al team looked for galaxies containing both Cepheid stars and Type Ia supernovae. Cepheid stars pulsate at rates that correspond to their true brightness, which can be compared with their apparent brightness as seen from Earth to accurately determine their distance. Type Ia supernovae, another commonly used cosmic yardstick, are exploding stars that flare with the same brightness and are brilliant enough to be seen from relatively longer distances.

By measuring about 2,400 Cepheid stars in 19 galaxies and comparing the observed brightness of both types of stars, see e.g.

http://brane-space.blogspot.com/2011/08/tackling-intermediate-astronomy.html


they accurately measured their true brightness and calculated distances to roughly 300 Type Ia supernovae in far-flung galaxies.

The team then compared those distances with the expansion of space as measured by the stretching of light from receding galaxies. They used these two values to calculate how fast the universe expands with time, or the Hubble constant.

The improved Hubble constant value 45.5 miles (72.8 km) per second per megaparsec. (A megaparsec equals 3.26 million light-years.) The new value means the distance between cosmic objects will double in another 9.8 billion years.

This refined calibration presents a puzzle, however, because it does not quite match the expansion rate predicted for the universe from its trajectory seen shortly after the Big Bang. Measurements of the afterglow from the Big Bang by NASA’s Wilkinson Microwave Anisotropy Probe (WMAP) and the European Space Agency’s Planck satellite mission yield predictions which are 5 percent and 9 percent smaller for the Hubble constant, respectively.

“If we know the initial amounts of stuff in the universe, such as dark energy and dark matter, and we have the physics correct, then you can go from a measurement at the time shortly after the big bang and use that understanding to predict how fast the universe should be expanding today,” said Riess. “However, if this discrepancy holds up, it appears we may not have the right understanding, and it changes how big the Hubble constant should be today.”

Comparing the universe’s expansion rate with WMAP, Planck, and Hubble is like building a bridge, Riess explained. On the distant shore are the cosmic microwave background observations of the early universe. On the nearby shore are the measurements made by Riess’ team using Hubble.

“You start at two ends, and you expect to meet in the middle if all of your drawings are right and your measurements are right,” Riess said. “But now the ends are not quite meeting in the middle and we want to know why.”

There are a few possible explanations for the universe’s excessive speed. One possibility is that dark energy, already known to be accelerating the universe, may be shoving galaxies away from each other with even greater — or growing — strength.

Another idea is that the cosmos contained a new subatomic particle in its early history that traveled close to the speed of light. Such speedy particles are collectively referred to as “dark radiation” and include previously known particles like neutrinos. More energy from additional dark radiation could be throwing off the best efforts to predict today’s expansion rate from its post-Big Bang trajectory.

The boost in acceleration could also mean that dark matter possesses some weird, unexpected characteristics. Dark matter is the backbone of the universe upon which galaxies built themselves up into the large-scale structures seen today.

And finally, the speedier universe may be telling astronomers that Einstein’s theory of gravity is incomplete.

“We know so little about the dark parts of the universe, it’s important to measure how they push and pull on space over cosmic history,” said Lucas Macri of Texas A&M University in College Station, a key collaborator on the study.

The Hubble observations were made with Hubble’s sharp-eyed Wide Field Camera 3 (WFC3), and were conducted by the Supernova H0 for the Equation of State (SH0ES) team, which works to refine the accuracy of the Hubble constant to a precision that allows for a better understanding of the universe’s behavior.

The SH0ES team is still using Hubble to reduce the uncertainty in the Hubble constant even more, with a goal to reach an accuracy of 1 percent. Current telescopes such as the European Space Agency’s Gaia satellite, and future telescopes such as the James Webb Space Telescope (JWST), an infrared observatory, and the Wide Field Infrared Survey Telescope (WFIRST), also could help astronomers make better measurements of the expansion rate.

Before Hubble was launched in 1990, the estimates of the Hubble constant varied by a factor of two. In the late 1990s the Hubble Space Telescope Key Project on the Extragalactic Distance Scale refined the value of the Hubble constant to within an error of only 10 percent, accomplishing one of the telescope’s key goals. The SH0ES team has reduced the uncertainty in the Hubble constant value by 76 percent since beginning its quest in 2005.

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Source: Donna Weaver and Ray Villard, Space Telescope Science Institute
 

Initial Conditions of the Big Bang?

In a recent issue (Oct.-Nov.) of the Intertel journal, INTEGRA, Ken Wear asks:

“Supposing the Big Bang theory is correct, what were the initial conditions that produced it?”

This can be approached in a more or less practical way by treating the ‘Big Bang’ as a solution to Einstein’s tensor (field) equations. (See, e.g. ‘Quantum Field Theory – A Modern Introduction’, by Michio Kaku, p. 643):

As per the 2.7K isotropic, microwave background radiation, we assume radial symmetry for the metric tensor – for which we adopt a Robertson-Walker form. This omits all angular dependence and leaves a function of form R(t) which sets the scale and defines an ‘effective radius’ of the universe.

We have:

ds^2 = dx^u g_uv dx^u = dt^2 – R^2(t) [ (dr^2/ 1 – kr^2) + r^2 d (S)^2]

where d(S)^2 is the solid angle differential and k = const.

Associate with this a fluid of average density rho(t) and internal pressure p(t)

The energy-momentum tensor becomes: T_o^0 = rho, T_I^I = -p

with all other components zero.

After inserting these into the Einstein field eqns.

(dR/dt /R)^2 = (8 pi)/ 3 (G_N rho) – k / R^2

whence:

(d^2R/ dt^2 )/ R = - 4 pi G_N (p + rho/3) + LAMBDA/ 3

After setting the cosmological constant (LAMBDA) = 0 and eliminating rho, one obtains as a solution for R (radius of universe as power law function).

R= (9/ 2GM)^1/3 [t ^2/3]

One can deduce from this (ibid, p. 645) that at the Planck energy of 10^19 GeV (giga -electron volts) of energy, the symmetries of gauge theory were still united in a single force. This is at a cosmic age of 10^-44 s.

This represents the closest approach of physics to the cosmic singularity (t = 0) but still defines the ‘Big Bang’ since the explosion is already underway and forces are still unified.

This continues as other symmetries ’break’ one by one, leading to the radiation dominated era. (Described by the Bose-Einstein distribution function, which perfectly applies to the expanding pure photon gas).

The fact that the ‘Big Bang’ can be obtained as a solution to one version of Einstein’s tensor equations, discloses that QM and GR equations certainly don’t ‘blow up’ and are impossible to use.

Mr. Wear then makes the assertion that it “would certainly be a violation of our concepts of cause and effect to say that suddenly, out of nothing….came this cataclysmic explosion”


But again, as I noted earlier, cause and effect notions are of little use. What we need instead are necessary and sufficient conditions for the event to occur - which by the way, is not an ‘explosion”! I refer Mr. Wear to ASTRONOMY magazine, May, 2007, ‘5 Things You Need To Know’, p. 31:

“The Big Bang wasn’t any kind of explosion. It was closer to an unfolding or creation of matter, energy, time and space itself. What would actually have been a much better name is ‘expanding universe theory’.”

As to how spontaneous cosmic inception can occur, this was referenced by T. Padmanabhan, 1983, ‘Universe Before Planck Time – A Quantum Gravity Model', in Physical Review D, Vol. 28, No. 4, p. 756.

To fix ideas, we are interested in first determining the gravitational action, and from this whether acausal determinism is more or less likely to apply. For any action S(g) if

S(g) < < h (the Planck constant)

where h = 6256 x 10^-34 J/s

we may be sure that classical causality is out the window and we are dealing with acausal determinism

If S(g) > > h

the converse holds.

To evaluate S(g) as Padmanabhan shows (op. cit.) , we need V the 4-volume of the space-time manifold for which we choose a de Sitter space, in the first approximation.

We have

S(g) = c^3/ (16 pi G) INT_V R(-g)^1/2 d^4x


where G is the gravitational constant, c is the speed of light, the integral (INT) is over the 4-volume V with the differential (d^4x) to match.

In the big bang model one takes V as the spatial volume enclosed by the particle horizon, and bounded by the time span (t) of the universe. Thus, at any epoch t for k = 0,

S(g) ~ t^1/2

The particle horizon is defined by

rS(g) = 2 ct

Einstein's gravitational equations (with cosmological term, for the sake of generality) are

R ( i k ) - (1 / 2) g ( i k ) R = T ( i k ) + lambda g ( i k )

where the ‘lambda’ denotes the cosmological constant. For de Sitter space it is equal to:

(n – 1)(n – 2)/ [2 a^2]

where a is a scale factor, and n denoted the dimension (4) of the volume under consideration. R(ik) is the Ricci tensor.

Now for S(g) ~ t^1/2, R (the scalar curvature of de Sitter space) = 0, so S(g) = 0

However, the above happens because the Einstein tensor (T_ik) has trace = 0 in the early universe. The ‘trace’ is the sum of the diagonal elements of a tensor, e.g.

Tr(M) = 0

where M =

[0 1 0 ]
[0 -1 0 ]
[0 0 1 ]


This means the limits must definitely be for acausal determinism, NOT classical – including classical causality.

Wear also alludes to a “sequence of oscillations” (ibid.) but this is egregious, since there will be no oscillations, as the universe is not only forever expanding but accelerating in its expansion.

Universes that re-collapse (decelerate), expand forever with zero limiting velocity (e.g. v uniform) or expand forever with positive limiting velocity (accelerate) are called in turn: 'closed' (can have curvature k = +1); 'critical' (k =0) or 'open' (can be k = -1), respectively

Now, to determine whether any F-R-W (Friedmann-Robertson-Walker) cosmological template leads to deceleration or not, we need to find the cosmic density parameter:

OMEGA = rho / rho_c

where the denominator refers to the critical density. Thus if:

rho > rho_ c

(c = critical)

then the cosmic density is able to reverse the expansion (e.g. decelerate it) and conceivably usher in a new cycle. (New Big bang etc.) The observations that help determine how large OMEGA is, come mainly from observing galaxy clusters in different directions in space and obtaining a density estimate from them.

Current data, e.g. from Boomerang and other satellite detectors shows that OMEGA ~ 0.3 or that:

rho = 0.3 (rho_c)

I.e. that rho < rho_ c, so there is no danger of the cosmos decelerating.

Precision measurements of the cosmic microwave background (CMB), including data from the Wilkinson Microwave Anisotropy Probe (WMAP), have recently provided further evidence for dark energy. The same is true of data from two extensive projects charting the large-scale distribution of galaxies - the Two-Degree Field (2DF) and Sloan Digital Sky Survey (SDSS).

The curves from other data with corrected apparent magnitude v. redshift (z) give different combinations of OMEAG_dark to OMEGA_matter over the range. However, only one of the graph combinations bests fits the data:

OMEGA_dark = 0.65 and OMEGA_matter = 0.35

Corresponding to an expansion accelerating for the last 6 million years- with much more dark energy involved (~ 0.65) than ordinary matter.

When the predictions of the different theoretical models are combined with the best measurements of the cosmic microwave background, galaxy clustering and supernova distances, we find that:

0.62 < OMEGA_dark < 0.76,

where OMEGA_dark = rho_dark/ rho_c, and -1.3 < w < -0.9.

In tandem, the numbers show unequivocally that dark energy is the acceleration agent, and in addition that dark energy comprises the lion’s share of what constitutes the cosmos (~ 73%).

In addition, all of this data is firmly backed up by earlier Boomerang (balloon) data that – when plotted on a power spectrum- discloses two adjacent ‘humps’ one a bit higher than the other. The “first acoustic peak” and the “second acoustic peak” fit uncannily to the sort of spherical harmonic function that describes a particular plasma condition. In this case, one that conforms to the supernova-derived values of OMEGA (d, m). (See: ‘Balloon Measurements of the Cosmic Microwave Background Strongly Favor a Flat Cosmos’, in Physics Today, July 2000, p. 7 and 'Supernovae, Dark Energy and the Accelerating Universe', by Saul Perlmutter, in Physics Today, April, 2003, p. 53)


Lastly, astronomers make no “claim” that galaxies are moving apart with increasing velocities. We have actual data that this is so, and it’s based on the basic physics of the Doppler effect.



-----------------------! L1 -------! L2----

---!----------!------------------
L1(o) L2(o)

Thus, in the above pictograph, lines L1(o) and L2(o) are the observed, redshifted (by some number of nanometers) spectral lines for some distant object such that:

v = cz

Where V denotes the velocity of recession, c is the speed of light, and z is the red shift

z = {L2(o)/ L2} - 1

Note again that L2 is the (lab-emission) standard line and L2(o) the observed line wavelength. If z > 0 we say the line is Doppler-effect redshift and receding.

To illustrate, say the hydrogen alpha line (emitted at 656.3 nm, e.g. L2 = 656.3 nm) is redshifted in some distant object to 666 nm (L2(o)). Then we have:

z = 1.015 – 1.000 = 0.015

This translates to a recessional velocity: v = (3 x 10 8 m/s) (0.015) = 4.5 x 10^6 m/s

As to Wear’s claim that it “may be difficult to place credence in such observations over a comparatively brief interval of time”, perhaps, but this “brief interval” is all we have to work with. What, will he dismiss all our painstakingly obtained date (including from the new CERN large hadron collider) because they were obtained over brief intervals? This isn’t the way a Realist works, but it is certainly the modus operandi for an Idealist.