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Mighty Oaks from Little Acorns Grow

Most cosmologists would like us to believe this; the mighty oaks being the stars and galaxies we see today, while the acorns are minute temperature fluctuations in the CMB. Yet, we know the composition of acorns and the mighty oaks they produce, we don't know what the acorns are in the CMB.

According to NASA,

"Tiny variations in the density of matter in the early universe leave an imprint on the CMBR in the form of temperature fluctuations from point to point across the sky."

But, in order to go from density fluctuations to temperature fluctuations we must know the equation of state linking density to temperature, which should be obeyed on the average.

Continuing, NASA claims:

"The temperature fluctuations are minute one part of the sky may have a temperature of 2.7251 K, while another point has a temperature of 2.7249. COBE has detected these tiny fluctuations on a large angular scale."

Temperature fluctuations in a black body can, and need to, be discussed independently of any matter present. Thermal fluctuations in a black cavity have been analyzed since the time of Einstein and can be found (with criticism) in my book Statistical Physics: A Probabilistic Approach.

NASA concedes that gravity is not the answer. In fact, "Cosmologists speculate about the new physics needed to produce the primordial fluctuations that formed galaxies."

So after going through a big spiel about the importance of temperature fluctuations in the development of cosmic structures, we are left holding the bag. NASA alludes to two speculate theories that would produce such fluctuations: inflation and topological defects. The former predicts that the largest temperature fluctuation should have an angular scale of 1 degree, while topological defects predict somewhat less. The WMAP tends to support the former.

"WMAP satellite measures these small [temperature] fluctuations which, in turn, reveal the early stages of structure formation." Pray tell how this is accomplished? No equation of state relating density to temperature and pressure leaves temperature fluctuations in a black body cavity devoid of matter at all. In other words, temperature fluctuations in a black body cavity don't imply anything other than the nature of the radiation. For instance, the variance in temperature should tend to zero as the heat capacity tends to infinity. No matter at all!

It is advisable to first discover the "new" physics and then try to find a place, if any, for the tiny minute temperature fluctuations that have been noticed in the CMB. But if this weren't enough, we are told that "For the first time in history, we now have a standard cosmological model that agrees with a large body of data about the past history of the universe to an unprecedented precision." (A. Loeb, How Did the First Stars and Galaxies Form?) This is mere wishful thinking than hard science.

The decomposition of the minute temperature fluctuations into spherical harmonics is like reading the future of someone in tea leaves. The story is that the early universe was made up of a relativistic fluid of photons that are hot enough to ionize hydrogen, which rather than propagating at the speed of light, propagate at the speed of sound because they form a "mixture" with matter. Transverse oscillations have given way to longitudinal ones.

Gravity attracts and compresses the fluid into potential wells while the radiation pressure opposes it thereby setting up acoustic oscillations in the fluid. (The other "pressure" stemming from a positive cosmological constant is negative and supposedly drives expansion!) Regions that have been compressed appear hotter and are supposedly visible as localized positive anisotropies in the CMB. The modes arrive at the maxima or minima of the oscillation at recombination allowing the photons to decouple and from then on travel unobstructedly till the present day. But, this would raise havoc with the black body photons that are required to maintain the CMB.

Unfortunately the liberated photons have no longer any information to tell us about the CMB. This role is reserved for dark matter (DM). The acoustic oscillations remain as imprints on the CMB in the form of hot and cold spots. These oscillations are decomposed into modes by developing the temperature fluctuation in a series of associated Legendre polynomials. The first peak represent the fundamental mode, while all other, smaller, peaks represent the harmonics. Supposedly, the fundamental mode represents a compression between when the big bang occurred and recombination began. The second peak represents the modes that have had time to compress and rarify before the photons were release by their captors, the baryon fluid. The temperature difference versus the Legendre polynomial index is shown in the figure.

Temperature variation decomposition into Legendre polynomials of index l. The boxes are related to the uncertainties. Taken from W Hu,

Again, supposedly, the third peak provides the "clearest" evidence for DM. It is the magnitude of the third peak that constrains the time of transition between a radiation and matter dominated universe. So DM, because it doesn't interact with matter, should contain the precious information of the early universe. In particular, if the second and third peaks were of equal magnitude, it would predict that DM dominate before recombination, and "this is a fundamental prediction of big bang cosmology." Moreover, the magnitude of the third peak is also of interest in estimating the amount of DM in the universe.

Instead of acorns producing mighty oaks, we have a contorted chain of predictions emanating from the attempt of rationalizing hot and cold spots superimposed on the CMB. It is like predicting the evolution of a cooking pan with hot and cold spots that have formed from unequal heating. According to Hoyle, it is like predicting the spectrum of black body radiation from the shape of the coals that stoke the furnace. It is a complete and utter waste of time.

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