## The Early Radio Universe

As the expanding universe cooled, the first neutral1 hydrogen atoms formed about 380,000 years after the Big Bang (ABB), and most of the hydrogen in the universe remained neutral until the first stars began forming at least 65 million years ABB.

The period of time from 380,000 to 65 million years or so ABB is referred to as the “dark ages” since at the beginning of this period the cosmic background radiation from the Big Bang had redshifted from visible light to infrared so the universe was truly dark (in visible light) until the first stars began to form at the end of this period.

All the while, neutral hydrogen atoms occasionally undergo a “spin-flip” transition where the electron transitions from the higher-energy hyperfine level of the ground state to the lower-energy hyperfine level, and a microwave photon of wavelength 21.1061140542 cm and frequency 1420.4057517667 MHz is emitted.

Throughout the dark ages, the 21 cm emission line was being emitted by the abundant neutral hydrogen throughout the universe, but as the universe continued to expand the amount of cosmological redshift between the time of emission and the present day has been constantly changing. The longer ago the 21 cm emission occurred, the greater the redshift to longer wavelengths. We thus have a great way to map the universe during this entire epoch by looking at the “spectrum” of redshifts of this particular spectral line.

380,000 and 65 million years ABB correspond to a cosmological redshift (z) of 1,081 and 40, respectively. We can calculate what the observed wavelength and frequency of the 21 cm line would be for the beginning and end of the dark ages.

$\lambda _{obs} = (z+1)\cdot \lambda_{emit}$

The observed wavelength (λobs) for the 21 cm line (λemit) at redshift (z) of 1,081 using the above equation gives us 22,836.8 cm or 228.4 meters.

$\nu = \frac{c}{\lambda }$

That gives us a frequency (ν) of 1.3 MHz (using the equation above), where the speed of light c = 299,792,458 meters per second.

So a 21 cm line emitted 380,000 years ABB will be observed to have a wavelength of 228.4 m and a frequency of 1.3 MHz.

Using the same equations, we find that a 21 cm line emitted 65 Myr ABB will be observed to have a wavelength of 8.7 m and a frequency of 34.7 MHz.

We thus will be quite interested in taking a detailed look at radio waves in the entire frequency range 1.3 – 34.7 MHz, with corresponding wavelengths from 228.4 m down to 8.7 m.2

The interference from the Earth’s ionosphere and the ever-increasing cacophony of humanity’s radio transmissions makes observing these faint radio signals all but impossible from anywhere on or near the Earth. Radio astronomers and observational cosmologists are planning to locate radio telescopes on the far side of the Moon—both on the surface and in orbit above it—where the entire mass of the Moon will effectively block all terrestrial radio interference. There we will finally hear the radio whispers of matter before the first stars formed.

1 By “neutral” we mean hydrogen atoms where the electron has not been ionized and resides in the ground state—not an excited state.

2 Incidentally, the 2.7 K cosmic microwave background radiation which is the “afterglow” of the Big Bang itself at the beginning of the dark ages (380,000 years ABB), peaks at a frequency between 160 and 280 GHz and a wavelength around 1 – 2 mm. So this is a much higher frequency and shorter wavelength than the redshifted 21 cm emissions we are proposing to observe here.

References

Ananthaswamy, Anil, “The View from the Far Side of the Moon”, Scientific American, April 2021, pp. 60-63

Burns, Jack O., et al., “Global 21-cm Cosmology from the Farside of the Moon”, https://arxiv.org/ftp/arxiv/papers/2103/2103.05085.pdf

Koopmans, Léon, et al., “Peering into the Dark (Ages) with Low-Frequency Space Interferometers”, https://arxiv.org/ftp/arxiv/papers/1908/1908.04296.pdf

Ned Wright’s Javascript Cosmology Calculator, http://www.astro.ucla.edu/~wright/CosmoCalc.html

## Cold Matters

Our current best estimate for the age of the universe (as we know it) is 13.799 Gyr ± 21 Myr. The Great Flaring Forth (GFF) occurred 13.8 billion years ago, and the universe has been expanding and cooling ever since.

The background temperature of the universe is today 2.72548 ± 0.00057 K. “K” stands for Kelvin, a unit of temperature named after William Thomson, 1st Baron Kelvin (1824-1907) – Lord Kelvin – who championed the idea of an “absolute thermometric scale”. A temperature in Kelvin is equivalent to the number of Celsius degrees above absolute zero. Put into terms we may be more familiar with, the cosmic background temperature is -270.42452° C, or -454.764136° F. While in the absence of nearby stars or other energy sources, the universe is certainly cold, scientists have artificially produced temperatures as low as 100 pK (1 picoKelvin = 10-12 K).

Using Wien’s displacement law, we can calculate the wavelength of electromagnetic radiation where the background universe is brightest.

$\lambda _{max}=\frac{2.8977729\ \pm \ 0.0000017\ mm\cdot K}{T_{K}}=\frac{2.8977729\ \pm \ 0.0000017\ mm\cdot K}{2.72548\ \pm\ 0.00057 K}=\\1.0632\pm0.0002\ mm$

So, we see here that the background universe is “brightest” in the microwave part of the radio spectrum, at a peak wavelength around 1 mm. Using the relationship between frequency and wavelength, c = νλ, we can determine the microwave frequency where the background universe is brightest.

$\nu =\frac{c}{\lambda }=\frac{299,792,458\ m/s}{1.0632\times 10^{-3}\ m}=281.97\pm 0.05\ GHz$

Microwaves at this frequency are in the extremely high frequency (EHF) radio band, above all our allocated communications bands (275-3000 GHz is unallocated).

Of course, a significant amount of emission occurs either side of the peak, particularly at longer wavelengths and lower frequencies. (The background universe radiates with an almost perfect blackbody spectrum.)

There are several ways to define the wavelength/frequency of maximum brightness. The above is one. Depending on the method we choose, the peak wavelength lies between 1.0623 and 3.313 mm, and the peak frequency between 90.5 and 282.0 GHz.

## Emergence of Complexity

We continue our series of excerpts (and discussion) from the outstanding survey paper by George F. R. Ellis, Issues in the Philosophy of Cosmology.

7.3 Emergence of complexity
As the universe evolves an increase of complexity takes place in local systems as new kinds of objects come into being that did not exist before—nuclei, atoms, stars and galaxies, planets, life, consciousness, and products of the mind such as books and computers.  New kinds of physical states come into being at late times such as Bose-Einstein condensates, that plausibly cannot exist without the intervention of intelligent beings.

The first atoms formed about 400 thousand years after the Big Bang.  The first stars, at about 100 million years.  The emergence of atoms, stars, planets, life, intelligence, humans, morality, a Brahms symphony, etc. are a natural consequence of all the physical laws that existed at the moment of the Big Bang, 13.8 billion years ago.  There is nothing supernatural about the unfolding of the universe, remarkable as it is.  It is a completely natural process.  The only possibility of anything supernatural, I believe, is the cause of the Big Bang itself.  And, without scientific evidence…

We may never know or be able to understand the Big Bang, but the parturient possibilities contained in that creative moment are truly mind boggling: all that we see around us, all that was and is yet to be, existed then in a nascent state.  The universe as it evolves is not merely moving the furniture around, but it is creating entirely new structures and entities that never existed before.

Through the emergence of intelligence across billions of years, the universe has, at last, become self-aware.  Our consciousness is its consciousness.

References
Ellis, G. F. R. 2006, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

## The Beginning

We continue our series of excerpts (and discussion) from the outstanding survey paper by George F. R. Ellis, Issues in the Philosophy of Cosmology.

Thesis D1: An initial singularity may or may not have occurred.
A start to the universe may have occurred a finite time ago, but a variety of alternatives are conceivable: eternal universes, or universes where time as we know it came into existence in one or another way.  We do not know which actually happened, although quantum gravity ideas suggest a singularity might be avoided.

If we imagine, for a moment, running the clock of the universe backwards to earlier and earlier times, its size gets smaller and its density gets larger until we reach a moment—even earlier than the putative inflationary era—when classical physics at the macroscopic level no longer applies and some (as yet unknown) quantum physics must apply to everything—even gravity.  Therein lies the problem, because if you run the clock backwards just 5.39 x 10-44 second from this time, you reach the purported moment of the Big Bang—the initial singularity.  But whoa (or perhaps woe)!  How can we say anything about the Big Bang—or even if it occurred at all—since the laws of known physics completely break down 5.39 x 10-44 second (the Planck time) after the Big Bang!  See the problem?

Perhaps the universe came into existence through a process analogous to radioactive decay where an alpha particle leaves a nucleus through quantum tunneling.  Perhaps our universe “tunneled” into existence from somewhere else, and thus our beginning isn’t really the beginning.  This is just one of many possibilities.

This is a key issue in terms of the nature of the universe: a space-time singularity is a dramatic affair, where the universe (space, time, matter) has a beginning and all of physics breaks down and so the ability to understand what happens on a scientific basis comes to an end. However eternal existence is also problematic, leading for instance to the idea of Poincaré’s eternal return: everything that ever happened will recur an infinite number of times in the future and has already occurred an infinite number of times in the past.  This is typical of the problems associated with the idea of infinity.  It is not clear in the end which is philosophically preferable: a singularity or eternal existence.  That decision will depend on what criteria of desirability one uses.

While infinity is a highly useful mathematical device, one can make a strong argument that infinities do not exist in the physical universe (or even multiverse).  Quantum physics already gives us a possible clue about the infinitely small: we appear not to be able to subdivide space or time any further than the Planck length (1.616 x 10-35 meter) or the Planck time (5.39 x 10-44 second).  We would not be able to distinguish between two points less than a Planck length apart, nor two moments in time less than a Planck time apart.  While harder to envision, might not there also be an upper limit to size?  And time?

Thesis D2: Testable physics cannot explain the initial state and hence specific nature of the universe.
A choice between different contingent possibilities has somehow occurred; the fundamental issue is what underlies this choice.  Why does the universe have one specific form rather than another, when other forms consistent with physical laws seem perfectly possible?  The reasons underlying the choice between different contingent possibilities for the universe (why one occurred rather than another) cannot be explored scientifically.  It is an issue to be examined through philosophy or metaphysics.

Metaphysics is the part of philosophy that deals with existence, space, time, cause and effect, and the like.  Metaphysics begins where physics necessarily ends due to observational limitations.

Did anything exist before the Big Bang?

Was there a Big Bang?

What are the physical properties of the very early universe, when energy densities existed that are far beyond our ability to recreate in the laboratory?

What lies beyond our particle horizon?

Are there other universes?

Why does anything exist at all?

References
Ellis, G. F. R. 2006, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

Liddle, A.R. 2015, An Introduction to Modern Cosmology, 3rd ed., Wiley, ISBN: 978-1-118-50214-3.

## Windows to the Earliest: Neutrinos and Gravitational Waves

We continue our series of excerpts (and discussion) from the outstanding survey paper by George F. R. Ellis, Issues in the Philosophy of Cosmology.

Thesis B7…
Neutrinos and gravitational waves will in principle allow us to peer back to much earlier times (the time of neutrino decoupling and the quantum gravity era respectively), but are much harder to observe at all, let alone in useful directional detail.  Nevertheless the latter has the potential to open up to us access to eras quite unobservable in any other way.  Maybe they will give us unexpected information on processes in the very early universe which would count as new features of physical cosmology.

The cosmic microwave background (CMB, T = 2.73 K) points us to a time 380,000 years after the Big Bang when the average temperature of the universe was around 3000 K.  But there must also exist abundant low-energy neutrinos (cosmic neutrino background, CNB, CνB, relic neutrinos) that provide a window to our universe just one second after the Big Bang during the radiation dominated era.  That’s when neutrinos decoupled from normal baryonic matter.

As the universe expanded, these relic neutrinos cooled from a temperature of 1010 K down to about 1.95 K in our present era, but such low-energy neutrinos almost never interact with normal matter.  Even though the density of these relic neutrinos should be at least 340 neutrinos per cm3 (including 56 electron neutrinos per cm3 which will presumably be easier to detect), detecting them at all will be exceedingly difficult.

Neutrinos interact with matter only through the weak nuclear force (which has a very short range), and low-energy neutrinos are much more difficult to detect than higher-energy neutrinos—if they can be detected at all.  If neutrinos have mass, then they will also interact gravitationally with other particles having mass, but this interaction is no doubt unmeasurable due to the neutrino’s tiny mass and the weakness of the gravitational force between subatomic particles.

The cosmic gravitational background (CGB) points us to the time of the Big Bang itself.  Faessler, et al. (2016) state

The inflationary expansion of the Universe by about a factor 1026 between roughly 10-35 to 10-33 seconds after the BB couples according to General Relativity to gravitational waves, which decouple after this time and their fluctuations are the seed for Galaxy Clusters and even Galaxies. These decoupled gravitational waves run since then with only very minor distortions through the Universe and contain a memory to the BB.

References
Ellis, G. F. R. 2006, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

Faessler, A., Hodák, R., Kovalenko, S., and Šimkovic, F. 2016
[https://arxiv.org/abs/1602.03347]

## Beginnings, Quantum Gravity, and Inflation

We continue our series on the outstanding survey paper by George F. R. Ellis, Issues in the Philosophy of Cosmology.

2.6  Inflation
Particle horizons in inflationary FL models will be much larger than in the standard models with ordinary matter, allowing causal connection of matter on scales larger than the visual horizon, and inflation also will sweep topological defects outside the visible domain.

The particle horizon is the distance beyond which light would have not yet had time to reach us in all the time since the Big Bang.  The visual horizon is the distance beyond which the universe was still opaque to photons due to high temperature and density.  The visual horizon, therefore, is not as far away as the particle horizon.  FL stands for Friedmann-Lemaître, the standard models of a flat, open, or closed universe.

What is inflation?  At the moment of the Big Bang, the expansion of the universe accelerated exponentially for a very short period of time.  This caused portions of space that had been close enough together to be causally connected to become causally disconnected.  While inflation does a very good job of explaining many observed features of our universe, such as its uniformity in all directions, at this point it is an untestable hypothesis (unlike special and general relativity), and the underlying physical principles are completely unknown.

2.7  The very early universe
Quantum gravity processes are presumed to have dominated the very earliest times, preceding inflation.  There are many theories of the quantum origin of the universe, but none has attained dominance.  The problem is that we do not have a good theory of quantum gravity, so all these attempts are essentially different proposals for extrapolating known physics into the unknown.  A key issue is whether quantum effects can remove the initial singularity and make possible universes without a beginning.  Preliminary results suggest that this may be so.

We currently live in a universe where the density may be too low to observe how gravity behaves at the quantum level.  Though we may never be able to build a particle accelerator with energies high enough to explore quantum gravity, quantum gravity might possibly play a detectable role in high-density stars such as white dwarfs, neutron stars, or black holes.  At the time of the Big Bang, however, the density of the universe was so high that quantum gravity certainly must have played a role in the subsequent development of our universe.

Do we live in the universe that had no beginning and will have no end?  A universe that is supratemporal—existing outside of time—because it has always existed and always will exist?  Admittedly, this is an idea that appeals to me, but at present it is little more than conjecture, or, perhaps, even wishful thinking.

2.7.1  Is there a quantum gravity epoch?
A key issue is whether the start of the universe was very special or generic.

Will science ever be able to answer this question?  I sincerely hope so.

2.8.1  Some misunderstandings
Two distantly separated fundamental observers in a surface {t = const} can have a relative velocity greater than c if their spatial separation is large enough.  No violation of special relativity is implied, as this is not a local velocity difference, and no information is transferred between distant galaxies moving apart at these speeds.  For example, there is presently a sphere around us of matter receding from us at the speed of light; matter beyond this sphere is moving away from us at a speed greater than the speed of light.  The matter that emitted the CBR was moving away from us at a speed of about 61c when it did so.

Thus, there are (many) places in our universe that are receding from us so fast that light will never have a chance to reach us from there.  Indeed, the cosmic background radiation that pervades our universe today was emitted by matter that was receding from us at 61 times the speed of light at that time.  That matter never was nor ever will be visible to us, but the electromagnetic radiation it emitted then, at the time of decoupling, is everywhere around us.  Think of it as an afterglow.

References
Ellis, G. F. R. 2006, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

## The Language We Use

Much has been said about how television, movies, video games, and the internet contributes to the culture of violence in our uncivilization, and this extends to even the language we use to describe events, activities, and phenomena.  Even astronomy is not immune from pervasive, perverse imagery.  Little things add up.  For example, why do we call THE event 13.8 billion years ago the Big Bang instead of something like the Great Flaring Forth?  And, instead of telling a group of eager young stargazers, “Our next target will be M13” why not say something like “Our next destination will be M13”?  And why do we call a smaller galaxy merging with a larger one “galactic cannibalism”?  You get the idea.

Fred Rogers (1928-2003) had it right: “Of course, I get angry.  Of course, I get sad.  I have a full range of emotions.  I also have a whole smorgasbord of ways of dealing with my feelings.  That is what we should give children.  Give them ways to express their rage without hurting themselves or somebody else.  That’s what the world needs.”

Think about it.  Then do something about it.