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Planck: "Big Bang Sound" in High Fidelity

by John G. Cramer

Alternate View Column AV-169
Keywords: cosmology, microwave, background, angular, structure, sound, frequencies, Planck, mission, simulation
Published in the October-2013 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 4/4/2013 and is copyrighted ©2013 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.

This column is about the improved understanding of the universe gained with the Planck satellite mission.  Let me begin by explaining the phenomenon being studied.  Almost 14 billion years ago the Big Bang occurred, creating our universe by at first inflating it at superluminal speed to smooth out irregularities and then slowing to a steady pace of expansion.  The Big Bang produced a slight excess of matter over antimatter, and in the dense initial medium all of the antimatter was annihilated, until only the small excess of normal matter was left.  Sound-like compression waves rang through the tiny self-enclosed space-time of that era, leaving behind an imprint of temperature variations in the expanding medium.  

About 379,000 years after the original explosion, the universe cooled enough that light was set free.  The population of free charged particles, positive protons and negative electrons, populating the expanding and cooling medium paired off to form electrically neutral hydrogen atoms, and the photons of light that had been trapped by bouncing between the charged particles were able to travel freely through the neutral hydrogen.  Most of these photons are still present in the universe and have been traveling ever since, constituting the cosmic microwave background (CMB) from the aftermath of the Big Bang.  The small temperature variations from the initial bell-like ringing of the early universe, the "sounds" of the Big Bang, are still imprinted on this radiation, carrying detailed information about the characteristics of the Big Bang.

The existence of this fundamental information, embedded in the cosmic microwave background radiation, was first realized in the 1990s (see AV-73 published in the August-1995 issue of Analog).  Specialized balloon flights and satellite experiments, particularly BOOMERaG (see AV-104), and WMAP (see AV-119), have been designed to measure the small-angle structure of the CMB with ever increasing precision, unfolding the "sound of the Big Bang" at ever-improving fidelity.

The Planck Collaboration, consisting of about 278 authors from 107 institutions, 17 of which are in the USA , working with the European Space Agency, has designed, constructed, launched, and operated the Planck satellite mission to study the CMB.  Planck was launched on May 14, 2009.  It masses 1900 kg, cost 0.7 billion Euros,  and has collected high-resolution data of the CMB over many months of operation.  Planck was placed at the L2 Largrange point 1.5 million kilometers from Earth on the side away from the Sun, so that Earth blocks the Sun's microwave emissions.  The mission includes two independent experiments, LFI and HFI, for investigation the structure of the CMB.  HFI is a high-frequency cryogenic instrument spanning frequencies of 83 to 1,000 GHz that operated from August 12, 2009 to January 13, 2012, when cryogenic liquids were used up.  LFI is a low-frequency instrument spanning 27 to 77 GHz that began operation in August 12, 2009 and is still operating.  The Planck satellite spins and precesses, scanning the sky and recording the strengths of preset microwave frequency bands in narrow angular regions.  These data are downloaded and stored for analysis.

The  Planck Collaboration has spent the last three years analyzing this data, and has just released the first results.  To get at the CMB itself, they had to carefully remove the contributions from other sources of microwave radiation, particularly from discrete radio sources, from the Milky Way, and from galactic dust.

The resulting data shows detailed temperature variations with angle of the CMB.   The angular variations were decomposed into "multipoles", mathematical functions of a frequency variable L that break up space directions into 2L positive and negative pieces.  The larger the L, the smaller the angular structure being characterized.  The 2013 Planck analysis has been able to go from L=2 to 2500, corresponding to an angular-structure sizes ranging from 90° to 0.07°.  The previous 2003 WMAP analysis only extended to L=853, missing considerable high frequency structure in the CMB.

The theory behind this analysis is based on the assumption that the early universe contained sound or compression waves that resonated and rang in the tiny universe at many frequencies, vibrating in many modes like a ringing bell.  The resonant modes are linked to the characteristics of the early universe and can be "decoded" in the analysis.   The Planck analysis shows significant resonant "bumps" in the frequency structure around L=237, 522, 829, 1134, 1409, 1716, and 1983.


Theoretical predictions link the strengths of these multipoles to the characteristics of the universe.  In particular, some of the parameters that describe our universe are: W0, WB, WD, WL, H0, and t0.  This table compares the WMAP and Planck results for these parameters.

Cosmological Parameter Comparison

Description

Symbol

WMAP (2003)

Planck (2013)

Units

Total density (flatness)

W0

1.037 ± 0.044

1.0096 ±0.009

number

Baryon fraction

WB

4.63%± 0.24%

4.81% ± 0.24%

percent

Dark Matter fraction

WD

23.3 %± 2.3%

25.82% ± 0.56%

percent

Dark Energy fraction

WL

72.1%± 2.5%

69.2%± 1.0%

percent

Hubble constant

H0

70.0 ± 2.2

67.80 ± 0.77

km/sec/Mpc

Age of the universe

t0

13.74 ± 0.11

13.798± 0.037

billion years

 

Here the "0" subscript indicates the present value of a time-dependent parameter.   The density parameter W0 describes the ratio of the present mass-energy-density of the universe to the "critical" mass density rc that would exactly "close" the universe (about 10-29 gm/cm3).  A value of 1.0 means that the universe is completely "flat", with the gravitational and kinetic energy in perfect balance.  If there were no dark energy, the value of W0 by itself would imply the ultimate fate of the universe, whether it will expand forever or will re-contract to a Big Crunch singularity.  However, with sufficient dark energy, the universe accelerates in its expansion for a wide range of W0 values including 1.0.  The baryon density parameter WB describes the fraction of W0 that is provided by ordinary matter (galaxies, stars, planets, gas clouds, atoms, protons, etc).  Similarly, the dark matter density parameter WD describes the fraction of W0 that is provided by cold dark matter, that mysterious non-luminous form of mass that surrounds galaxies and is observable mainly from the orbit speeds of outlying stars and from gravitational lensing.  The dark energy density parameter WL describes the fraction of W0 that is provided by dark energy, an even more mysterious form of mass-energy that has a net repulsive gravitational effect (antigravity) and that accounts for more than 2/3 of the mass-energy of the universe.

There are many implications of the new measurements.  Planck has shown convincingly that the universe is completely flat (W0 =1) to an accuracy of less than a percent.  Its expansion rate is a bit slower, and it is a bit older than we had thought.  It contains more normal matter, more cold dark matter, and less dark energy than the WMAP analysis had implied.  However, perhaps the most interesting results of the Planck measurements are the appearance on new anomalies in the CMB structure.

If one divides the sky into two hemispheres north and south of the plane of the ecliptic (the plane that on the average contains the orbits of the planets), Planck finds that the average temperature of the CMB to be slightly higher in the south ecliptic hemisphere than in the north hemisphere.  There is no known reason for such an anomaly.

Further, the south ecliptic hemisphere contains a large "cold spot" first detected by WMAP.  As pointed out in a previous column (see AV-137 in the April-2008 issue of Analog) it may be that the Cold Spot is not a characteristic of the CMB itself, but instead it is a phenomenon that happens as the CMB photons pass through the universe on the way to our detectors. Perhaps  there is an enormous volume in that direction containing almost no stars, galaxies, or gas.  The integrated Sachs-Wolfe Effect, the gravitational wavelength shift of photons as they pass through varying gravitational fields in an expanding universe, may be responsible for the cold spot.  As photons of light fall into the gravity well of a massive object like a galactic cluster, they gain energy and are blue-shifted.  On emerging from the gravity well, the photons should lose the energy gained.  However, due to the repulsive effect of the large quantity of dark energy in the universe, it is a bit easier for the photons to get out of the gravity well, so that not all of the gained energy is removed.  The net result is that CMB photons that pass through regions containing significant mass arrive at our detectors with a bit more energy on the average than those passing through regions of the universe that are relatively empty.  Therefore, the CMB radiation should appear cooler along a line of sight passing through a large “empty” region.  In effect, the CMB radiation is weighing the universe along the various lines of sight and has found a low-weight spot.

About 10 years ago, when the WMAP multipole data became available, I did a Mathematica calculation to produce the "Sound of the Big Bang", I wrote an AV column about it (see AV-122 in the May-2003 issue of Analog), and I put it online, where it received a great deal of attention.  I have decided to do the same thing with the new multipole strengths from the Planck analysis, which I captured from two of their published graphs.

The simulation includes three important effects: (1) The multiply peaked frequency spectrum measured by Planck is made into a single sound wave (monaural, not stereo) by the process described above; (2) According to the Planck analysis, the emission profile of the cosmic background radiation peaked at 379,000 years and dropped to 60% intensity at 110,000 years before and after the peak emission time. The simulation represents the first 760,000 years of evolution of the universe, as the emitted CBR rises and falls in intensity following the Planck profile; (3) The universe was expanding and becoming more of a "bass instrument" while the cosmic background radiation was being emitted. To put it another way, the expanding universe "stretches" the sound wavelengths and thereby lowers their frequencies. To account for this effect, the program shifts the waves downward in frequency to follow the expansion in the first 760 thousand years of the universe. How fast the universe initially expanded depends on what cosmological model is used. I decided to follow the predictions of the flat-space Robertson-Walker metric with zero cosmological constant. That model predicts that the radius of the universe grows as time to the 2/3 power (R ~ t2/3). Therefore, instead of the component sine waves varying as (frequency ´ time), they vary as (frequency ´ time1/3) to implement the cosmological Doppler shift. The sound frequencies used in the simulation must be scaled upward by a huge factor (about 10 to the 26 power) to match the response of the human ear, because the actual Big Bang frequencies, which had wavelengths on the order of a fraction of the size of the universe, were far too low to be heard by humans (even had any been around).

If you would like to play the Sound of the Big Bang .wav file on your computer, it can be downloaded form one of the links at http://faculty.washington.edu/jcramer/BBSound.html .  There are .wav files lasting 20, 50, 100, 200, and 500 seconds, but the 100 second version is recommended.


References:

Planck Overview:

"Planck 2013 results. I. Overview of products and scientific results",  The Planck Collaboration: P. A. R. Ade, et al., Submitted to A&A. available on the Web at ArXiv.org as arXiv:1303.5062 [astro-ph.CO]

CMB Power Spectra:

"Planck 2013 results. XV. CMB power spectra and likelihood", The Planck Collaboration: P. A. R. Ade, et al., Submitted to A&A. available on the Web at ArXiv.org as arXiv:1303.5075 [astro-ph.CO]

Cosmological parameters:

" Planck 2013 results. XVI. Cosmological parameters", The Planck Collaboration: P. A. R. Ade,, et al., Submitted to A&A. available on the Web at ArXiv.org as arXiv:1303.5076 [astro-ph.CO]


SF Novels by John Cramer:  my two hard SF novels, Twistor and Einstein's Bridge, are newly released as eBooks and are available at : http://bookviewcafe.com/bookstore/?s=Cramer .

AV Columns Online: Electronic reprints of about 170 "The Alternate View" columns by John G. Cramer, previously published in Analog , are available online at: http://www.npl.washington.edu/av.


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