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Let universe be completely made from hydrogen. And also we have redshift $z= 6$. with Hubble constant $H_{0} = 2.1941747572815535 imes 10^{-18}:mathrm{s}^{-1}$. We also know that density of the universe $ho =frac{3H^2}{8pi G}$ ($G= 6.67 imes 10^{-11}:mathrm{m^3 kg^{-1} s^{-2}}$).

Is the following approach right to find the number density of hydrogen in universe?

First we calculate density $ho =frac{3H^2}{8pi G}$, then we have $1+z = sqrt{frac{1+v/c}{1-v/c}}$. From that we get $v = H imes R$ and from this we calculate $R$, the radius of observable universe. With that, we calculate volume of universe $V = (4pi/3)R^3$ and we get Mass $M= ho V$. Then we calculate number of Hydrogen atoms with $N = M/m_{mathrm{hydrogen}}$. Now we have number density of hydrogen $ho = N/V$.

Is this solution right? Or we must solve it another way?

The source of question is National Olympiad of Iran which is not available in English so the above is my translation for the question.

So to estimate the answer, you need to convert the mass density to number density by $n_H = ho_H / m_H$. After getting the current number density you need to redshift it to finite $z$, here $z=6$. Keep in mind the density of hydrogen evolves $sim (1+z)^3$ due to the expansion of the universe.

That said, the assumption 'let universe be completely made from hydrogen' renders this question highly unrealistic, hence I agree with @James K that this is not real world astronomy. In the real world, only about 5% of the total energy is made of baryons, among which Hydrogen abundance is $sim 75\%$. Also, at redshift $zsim 6$, star formation etc. lowers the neutral hydrogen gas density, c.f. recent observations here and here.

## The Weight of the Universe – Physicists Challenge the Standard Model of Cosmology Bochum cosmologists headed by Professor Hendrik Hildebrandt have gained new insights into the density and structure of matter in the Universe. Several years ago, Hildebrandt had already been involved in a research consortium that had pointed out discrepancies in the data between different groups. The values determined for matter density and structure differed depending on the measurement method. A new analysis, which included additional infrared data, made the differences stand out even more. They could indicate that this is the flaw in the Standard Model of Cosmology.

Rubin, the science magazine of Ruhr-Universität Bochum, has published a report on Hendrik Hildebrandt’s research. The latest analysis of the research consortium, called Kilo-Degree Survey, was published in the journal Astronomy and Astrophysics in January 2020. Cosmologist Hendrik Hildebrandt is looking for answers to fundamental questions about the Universe, for example how great the density of matter is in space. Credit: © Roberto Schirdewahn

#### Two methods for determining the structure of matter

Research teams can calculate the density and structure of matter based on the cosmic microwave background, a radiation that was emitted shortly after the Big Bang and can still be measured today. This is the method used by the Planck Research Consortium.

The Kilo-Degree Survey team, as well as several other groups, determined the density and structure of matter using the gravitational lensing effect: as high-mass objects deflect light from galaxies, these galaxies appear in a distorted form in a different location than they actually are when viewed from Earth. Based on these distortions, cosmologists can deduce the mass of the deflecting objects and thus the total mass of the Universe. In order to do so, however, they need to know the distances between the light source, the deflecting object and the observer, among other things. The researchers determine these distances with the help of redshift, which means that the light of distant galaxies arrives on Earth shifted into the red range. In order to determine the density of matter in the universe using the gravitational lensing effect, cosmologists look at distant galaxies, which usually appear in the shape of an ellipse. These ellipses are randomly oriented in the sky.
On its way to Earth, the light from the galaxies passes high-mass objects, such as clusters of galaxies that contain large quantities of invisible dark matter. As a result light is deflected, and the galaxies appear distorted when viewed from Earth.
Since the light travels a long way, it is repeatedly deflected by high-mass objects. Light from galaxies that are close to each other mostly passes the same objects and is thus deflected in a similar way.
Neighboring galaxies therefore tend to be distorted in a similar way and point in the same direction, although the effect is exaggerated here. Researchers explore this tendency in order to deduce the mass of the deflecting objects.

#### New calibration using infrared data

To determine distances, cosmologists therefore take images of galaxies at different wavelengths, for example one in the blue, one in the green and one in the red range they then determine the brightness of the galaxies in the individual images. Hendrik Hildebrandt and his team also include several images from the infrared range in order to determine the distance more precisely.

Previous analyses had already shown that the microwave background data from the Planck Consortium systematically deviate from the gravitational lensing effect data. Depending on the data set, the deviation was more or less pronounced it was most pronounced in the Kilo-Degree Survey. “Our data set is the only one based on the gravitational lensing effect and calibrated with additional infrared data,” says Hendrik Hildebrandt, Heisenberg professor and head of the RUB research group Observational Cosmology in Bochum. “This could be the reason for the greater deviation from the Planck data.”

To verify this discrepancy, the group evaluated the data set of another research consortium, the Dark Energy Survey, using a similar calibration. As a result, these values also deviated even more strongly from the Planck values. High-mass objects in the Universe are not perfect lenses. As they deflect light, they create distortions. The resulting images appear like looking through the foot of a wine glass. Credit: © Roberto Schirdewahn

#### Debate in expert circles

Scientists are currently debating whether the discrepancy between the data sets is actually an indication that the Standard Model of Cosmology is wrong or not. The Kilo-Degree Survey team is already working on a new analysis of a more comprehensive data set that could provide further insights. It is expected to provide even more precise data on matter density and structure in spring 2020.

Reference: “KiDS+VIKING-450: Cosmic shear tomography with optical and infrared data” by H. Hildebrandt, F. Köhlinger, J. L. van den Busch, B. Joachimi, C. Heymans, A. Kannawadi, A. H. Wright, M. Asgari, C. Blake, H. Hoekstra, S. Joudaki, K. Kuijken, L. Miller, C. B. Morrison, T. Tröster, A. Amon, M. Archidiacono, S. Brieden, A. Choi, J. T. A. de Jong, T. Erben, B. Giblin, A. Mead, J. A. Peacock, M. Radovich, P. Schneider, C. Sifón and M. Tewes, 13 January 2020, Astronomy & Astrophysics.
DOI: 10.1051/0004-6361/201834878

## Charge balance in observable universe

I've been wondering about the charge balance in the known universe, factors that might alter it, and the consequences of any small imbalance that might exist. This is a sort of layman's theory. I don't expect it to be right but I'd love to understand how it can be refuted. I am surely confused on any number of points, and ask only for help in putting my picture of how things work together a little bit more. These are just questions that come up as I am learning.

This is the line of reasoning that's been bothering me:

1) I've heard that when a particle crosses the event horizon of a black hole that its electromagnetic forces are transformed in such a way that they no longer have an effect outside the black hole. Is this true?

2) Since electrons have higher charge/mass than protons, protons should be gobbled up by black holes a little bit more easily than electrons. And once a proton goes in the electron will have an improved chance to escape due to the absence of the electric field attraction of the proton. Even if the electric field of the proton as seen by the electron does not go away entirely but is reduced along the gravitational gradient, that would still be enough to give the electron an improved chance to escape.

3) As a consequence there would be extra electrons in space. Because the electric field force is so much stronger than gravity, these free electrons would become almost uniformly distributed throughout the universe. Unlike escaped orbital electrons which have a very high energy due to the local charge imbalance these free electrons would have low energy. Would they have a correspondingly lower quantum energy level and wavelength?

4) In my simple understanding, interactions between free, low-energy electrons and electromagnetic waves would result in low-frequency electromagnetic noise that would be observable. If the free carrier density of space was low there would not necessarily be a detectable attenuation or band absorption or emission. Also because the electrons are very low energy the quantum interaction with electromagnetic radiation would have a different character than with orbitally bound or dislocated electrons we're familiar with. The same interactions would occur but at different frequencies. The band structure would be different because of starting at a much lower level, so absorption and emission of photon energy would have different spectra.

5) Electron mass would be a kind of "dark matter" that would alter large-scale gravitational calculations.

6) Because over time black holes would eat more protons, the number of low-energy free electrons would always increase. This would cause the universe to expand a little bit more rapidly over time.

7) Over time the free electrons would spread out faster than the momentum-driven expansion of the universe.

8) Because electrons would be almost uniformly distributed over a huge range of local space they would affect the speed of light by giving free space a tiny increase in refractive index. Our measured speed of light would already account for the current large-scale distribution. It's possible that this distribution could look uniform well past the point where charge-balanced matter exists in the universe.

9) There would be a slight charge gradient from the parts of space containing excess electrons to parts of space with no free electrons. Eventually at the edge of the expanding universe there would be no more free electrons. This should create a very tiny refractive index gradient across the known universe.

10) If you somehow model the Big Bang as particles and/or energy escaping from a black hole, you might have a charge balance difference from the start.

11) I wonder if a small charge imbalance would have any effect at all on most measurements we make. Even though there are many instances where we think of a free electron as being incredibly significant, it really seems to be a free electron at a certain energy level or field imbalance that we are concerned with.

12) Where the free-carrier lifetime of an electron in matter imposes a kind of viscosity on the electron gas, completely free electrons would behave as a non-viscous fluid and have the velocity distribution of an ideal gas. The net velocity of the fluid would be related to the relative locations and density of the sources and be very little affected by gravitational forces or the velocities of the sources.

## Hydrogen cloud

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Hydrogen cloud, also called H I region or H i region, interstellar matter in which hydrogen is mostly neutral, rather than ionized or molecular. Most of the matter between the stars in the Milky Way Galaxy, as well as in other spiral galaxies, occurs in the form of relatively cold neutral hydrogen gas. Neutral hydrogen clouds are easily detectable at radio wavelengths because they emit a characteristic energy at a wavelength of 21 cm.

Neutral hydrogen is dominant in clouds that have enough starlight to dissociate molecular hydrogen into atoms but lack hydrogen-ionizing photons from hot stars. These clouds can be seen as separate structures within the lower-density interstellar medium or else on the outer edges of the molecular clouds. Because a neutral cloud moves through space as a single entity, it often can be distinguished by the absorption line that its atoms or ions produce at their common radial velocity in the spectrum of a background star.

If neutral clouds at a typical pressure were left alone until they could reach an equilibrium state, they could exist at either of two temperatures: “cold” (about 80 K) or “warm” (about 8,000 K), both determined by the balance of heating and cooling rates. There should be little material in between. Observations show that these cold and warm clouds do exist, but roughly half the material is in clouds at intermediate temperatures, which implies that turbulence and collisions between clouds can prevent the equilibrium states from being reached. Cold H I regions are heated by electrons ejected from the dust grains by interstellar ultraviolet radiation incident upon such a cloud from outside. Cooling is mainly by C + because passing electrons or hydrogen atoms can excite it from its normal energy state, the lowest, to one slightly higher, which is then followed by emission of radiation at 158 micrometres. This line is observed to be very strong in the spectrum of the Milky Way Galaxy as a whole, which indicates that a great deal of energy is removed from interstellar gas by this process. Cold H I regions have densities of 10 to 100 hydrogen atoms per cubic cm. Warm H I regions are cooled by excitation of the n = 2 level of hydrogen, which is at a much higher energy than the lowest level of C + and therefore requires a higher temperature for its excitation. The density of 0.5 atom per cubic cm is much lower than in the colder regions. At any particular density there is far more neutral hydrogen available for cooling than C + .

## Contents

The Friedmann equations start with the simplifying assumption that the universe is spatially homogeneous and isotropic, i.e. the cosmological principle empirically, this is justified on scales larger than

100 Mpc. The cosmological principle implies that the metric of the universe must be of the form

Einstein's equations now relate the evolution of this scale factor to the pressure and energy of the matter in the universe. From FLRW metric we compute Christoffel symbols, then the Ricci tensor. With the stress–energy tensor for a perfect fluid, we substitute them into Einstein's field equations and the resulting equations are described below.

There are two independent Friedmann equations for modelling a homogeneous, isotropic universe. The first is:

which is derived from the 00 component of Einstein's field equations. The second is:

which is derived from the first together with the trace of Einstein's field equations (the dimension of the two equations is time −2 ).

a is the scale factor, G, Λ, and c are universal constants (G is Newton's gravitational constant, Λ is the cosmological constant (its dimension is length −2 ) and c is the speed of light in vacuum). ρ and p are the volumetric mass density (and not the volumetric energy density) and the pressure, respectively. k is constant throughout a particular solution, but may vary from one solution to another.

We see that in the Friedmann equations, a(t) does not depend on which coordinate system we chose for spatial slices. There are two commonly used choices for a and k which describe the same physics:

• k = +1, 0 or −1 depending on whether the shape of the universe is a closed 3-sphere, flat (i.e. Euclidean space) or an open 3-hyperboloid, respectively.  If k = +1, then a is the radius of curvature of the universe. If k = 0, then a may be fixed to any arbitrary positive number at one particular time. If k = −1, then (loosely speaking) one can say that i ⋅ a is the radius of curvature of the universe.
• a is the scale factor which is taken to be 1 at the present time. k is the spatial curvature when a = 1 (i.e. today). If the shape of the universe is hyperspherical and R t > is the radius of curvature ( R 0 > in the present-day), then a = R t / R 0 /R_<0>> . If k is positive, then the universe is hyperspherical. If k is zero, then the universe is flat. If k is negative, then the universe is hyperbolic.

Using the first equation, the second equation can be re-expressed as

These equations are sometimes simplified by replacing

The simplified form of the second equation is invariant under this transformation.

The Hubble parameter can change over time if other parts of the equation are time dependent (in particular the mass density, the vacuum energy, or the spatial curvature). Evaluating the Hubble parameter at the present time yields Hubble's constant which is the proportionality constant of Hubble's law. Applied to a fluid with a given equation of state, the Friedmann equations yield the time evolution and geometry of the universe as a function of the fluid density.

Some cosmologists call the second of these two equations the Friedmann acceleration equation and reserve the term Friedmann equation for only the first equation.

To date, the critical density is estimated to be approximately five atoms (of monatomic hydrogen) per cubic metre, whereas the average density of ordinary matter in the Universe is believed to be 0.2–0.25 atoms per cubic metre.  

A much greater density comes from the unidentified dark matter both ordinary and dark matter contribute in favour of contraction of the universe. However, the largest part comes from so-called dark energy, which accounts for the cosmological constant term. Although the total density is equal to the critical density (exactly, up to measurement error), the dark energy does not lead to contraction of the universe but rather may accelerate its expansion. Therefore, the universe will likely expand forever. 

An expression for the critical density is found by assuming Λ to be zero (as it is for all basic Friedmann universes) and setting the normalised spatial curvature, k, equal to zero. When the substitutions are applied to the first of the Friedmann equations we find:

The density parameter (useful for comparing different cosmological models) is then defined as:

The first Friedmann equation is often seen in terms of the present values of the density parameters, that is 

The Friedmann equations can be solved exactly in presence of a perfect fluid with equation of state

In spatially flat case (k = 0), the solution for the scale factor is

Another important example is the case of a radiation-dominated universe, i.e., when w = 1 / 3 . This leads to

Note that this solution is not valid for domination of the cosmological constant, which corresponds to an w = − 1 . In this case the energy density is constant and the scale factor grows exponentially.

Solutions for other values of k can be found at Tersic, Balsa. "Lecture Notes on Astrophysics" (PDF) . Retrieved 20 July 2011 . .

### Mixtures Edit

If the matter is a mixture of two or more non-interacting fluids each with such an equation of state, then

holds separately for each such fluid f. In each case,

For example, one can form a linear combination of such terms

### Detailed derivation Edit

To make the solutions more explicit, we can derive the full relationships from the first Friedman equation:

Solutions for the dependence of the scale factor with respect to time for universes dominated by each component can be found. In each we also have assumed that Ω 0 , k ≈ 0 approx 0> , which is the same as assuming that the dominating source of energy density is ≈ 1 .

which recovers the aforementioned a ∝ t 2 3 <3>>>

## Approximating density of hydrogen in [observable] universe - Astronomy

The dominant Big Bang model of contemporary cosmology is based partly on Einstein&rsquos general theory of relativity and partly on the Standard Model of particle physics, which in turn is based on quantum mechanics and quantum field theories. By applying the mathematical equations of these theories to observations and measurements of the universe today, cosmologists can predict&mdashor rather, retrodict&mdashwhat the universe was like at times further and further into the past.

The basic strategy is this. First, estimate the average density of matter and energy in the observable universe as it is today. Then use general relativity, together with the Hubble constant, to retrodict how the size and density of the observable universe has changed over time. By calculating the average density at any given time in the past, we can also estimate the average temperature at that time, since the compression of matter and energy results in higher temperatures and conversely, allowing a system to expand results in lower temperatures. Finally, when the average temperature and density at any given time has been determined, the Standard Model of particle physics can be used to predict what sorts of particles existed at that time.

In this way, we can rewind history (so to speak) all the way back to a fraction of a second after the Big Bang. Below is a brief summary of important phases in the history of the universe, according to these calculations:

The Planck epoch (0 - 10 -43 seconds)

Retrodictions based on general relativity imply that the universe (or at least the presently observable part of it As mentioned in a &ldquofine print&rdquo section on the previous page, the universe might be infinite in size, in which case it would have been infinitely large even at the time of the Big Bang. Nevertheless, general relativity implies that the presently observable part of the universe was infinitesimally small at the beginning of time. ) was initially smaller than one Planck length&mdasha unit of length approximately equal to 1.6 × 10 -35 meters, which is more than a billion, billion times smaller than the diameter of a proton. The density and temperature of the universe at that time would have been incomprehensibly high, and the Standard Model of particle physics almost certainly does not apply to such extreme conditions. For this reason, it is impossible to determine what the universe was like during this brief initial phase, but theorists speculate that even elementary particles could not have existed near the beginning of the Big Bang.

No one knows whether the universe was ever really that small, of course. General relativity is probably invalid at the microphysical level where quantum effects are significant so it may yield incorrect predictions about the earliest moments after the Big Bang. If the universe actually did begin in the way general relativity suggests, though, it would have been far too hot to be described adequately by the Standard Model of particle physics.

During this phase, the universe rapidly expanded and cooled to 10 15 K or so. (That&rsquos a quadrillion degrees Celsius.) According to the Standard Model, this absurdly high temperature is nonetheless cool enough for elementary particles&mdashquarks and leptons&mdashto form.

Some theorists speculate that the universe underwent a brief period of extremely rapid expansion, called or the , sometime during this period. This inflation hypothesis is one possible explanation for the low-entropy condition of the early universe, as mentioned in chapter 3.

During this phase, which ended about 1 second after the universe came into existence, the universe had cooled to less than a trillion kelvins. That&rsquos still ridiculously hot, but it&rsquos cool enough for the strong force to bind quarks together, forming protons and neutrons.

This is the earliest phase for which the predictions of the Standard Model can be experimentally tested. Temperatures up to several trillion kelvins have been produced by accelerating atomic nuclei to nearly the speed of light, then slamming them together head-on inside the Large Hadron Collider. The CERN facility set a record in August 2012, achieving temperatures around 5.5 trillion kelvins by colliding lead ions in the LHC. See this press release for more information. In these experiments, physicists found evidence that the colliding protons and neutrons had briefly &ldquomelted&rdquo into a soup of quarks and gluons. Quarks and gluons cannot be directly observed, because they quickly recombine to form new composite particles. But some exotic particles detected in the LHC were of types predicted to form out of quark-gluon plasma, providing evidence that the protons had indeed &ldquomelted.&rdquo Although this doesn&rsquot prove that the theory provides an accurate description of the early universe, it does indicate that the Standard Model yields reliable predictions even for temperatures up to a few trillion kelvins.

Approximately three minutes after the Big Bang, the universe had expanded and cooled enough for the strong force to hold protons and neutrons together, forming larger atomic nuclei through nuclear fusion. The process of nuclear fusion (or , as it is called in this context) lasted until around 20 minutes after the Bang. By that time, the universe had expanded and cooled too much: its temperature and pressure were too low for nuclear fusion to continue.

Because the period of nucleosynthesis lasted only a few minutes, there wasn&rsquot enough time for large nuclei to form. The majority of atomic nuclei formed during this period would have been isotopes of hydrogen, followed by helium and perhaps small amounts of lithium. This is an especially significant claim of the Big Bang model, because it is one of very few retrodictions about the early universe that we can test by observing the universe today. Using spectroscopy to determine what types of atoms are most abundant in stars and galaxies throughout the universe now, astronomers have determined that hydrogen is by far the most common element, followed by helium, just as we would expect if the Big Bang model&rsquos account of nucleosynthesis is correct. Cosmologists consider this an important piece of evidence supporting the Big Bang model.

Although the first atomic nuclei formed a few minutes after the Big Bang, the universe would have to expand a lot in order to cool enough for electrons to stick to those nuclei and form whole atoms. According to the Big Bang model, the universe was filled with glowing-hot plasma for hundreds of thousands of years after the period of nucleosynthesis ended. ( is a state of matter that occurs at high temperatures. It&rsquos like a gas, except that the electrons are moving too fast to stick to the atomic nuclei.) It took nearly 380,000 years for the universe to cool down to only 4,000 kelvins&mdashstill more than twice as hot as the flame of a butane torch. At that temperature, electrons could finally attach to protons, forming neutral hydrogen atoms. The Cosmic Microwave Background

The CMB radiation comes from all directions. This map of the CMB, created by the Wilkinson Microwave Anisotropy Probe (WMAP), shows subtle variations in the radiation. These variations correspond to slight differences in the temperature and pressure at various places in the early universe.

This phase of the Big Bang model also yields a measurable prediction about the universe we observe today. Hydrogen gas is transparent to light, but hydrogen plasma is not: photons are scattered by the free electrons in plasma. When the universe finally cooled to the point where hydrogen plasma turned into hydrogen gas, light which had been trapped by the glowing plasma was suddenly released. In other words, photons that had been bouncing randomly inside the plasma were suddenly free to travel in a straight line (or geodesic) through spacetime. Although this happened billions of years ago, according to the Standard Model, some of the light released at that time is just reaching us now, coming from somewhere billions of light years away. It isn&rsquot visible light, though. It originated as infrared light from the hot plasma but as it traveled for billions of years through the ever-expanding universe, the stretching of spacetime also affected its wavelength, stretching infrared photons into microwave photons. This faint glow of microwave light from the most distant reaches of the observable universe is known as the .

After the glowing hydrogen plasma cooled into hydrogen gas, the universe remained dark for hundreds of millions of years&mdasha period affectionately termed the &ldquoCosmic Dark Ages.&rdquo Then, sometime around 300 million years after the Big Bang, new light began to shine. Stars and galaxies were forming. We&rsquoll examine that process on the next few pages.

## The avarage density of the universe If you took all the matter in the observable universe and spread it evenly throughout.

What would the avarage density be? also what would the avarage density be if you included dark matter and dark enery in this calculation?

Preferably in kg/m 3 and hydrogen atoms/m 3 To give you a number, the average energy density in the universe is about 10 -26 kg/m 3 , which corresponds to about six hydrogen atoms / m 3 . About 5% of this energy is found in ordinary matter, about 23% of it in dark matter, and about 70% of it in dark energy. So that's about 0.3 hydrogen atoms per cubic meter of ordinary matter, if that's what you wanted to know.

But there's something very special about the energy density of the universe that makes this very interesting. If you know how dense the universe is, you can predict its overall geometry and future—if it will one day collapse on itself, or expand forever, or what. It turns out that we are exactly on the threshold between the two, as far as we can measure.

## Universe in video

What would an imaginary journey throughout the known universe?
To help you visualize this cosmic journey round trip, the American Museum of Natural History has produced a film with virtual images of such a trip.
The video begins with an aerial view of the Himalayas. It zooms spectacular showing in succession, the orbits of artificial satellites of the Earth, Moon, the orbits of planets, constellations, the Sun, the solar system, the sphere occupied by the emission of the first radio signals from the humanity, the Milky Way, nearby galaxies, distant galaxies and quasars up to diffuse cosmic radiation reaching issued by the Big Bang, the glow of the first fossil of the universe transparent light that was emitted at birth of the Universe less than a million years after the Big Bang. We capture this day that light is the cosmic radiation or cosmic microwave background (CMB). The CMB is the "first light" of the universe, published shortly after the Big Bang, there are about 13.7 billion years, when the light began to travel freely for the first time. The huge fireball that followed the Big Bang has cooled slowly to become a background of microwaves. To make this film, the scientists used data from the Digital Universe Atlas. All celestial objects in this video are shown to scale given the data known in 2009 by science.

nota: the Big Bang model favors the existence of a phase of cosmic inflation very brief but during which the universe would have grown extremely rapidly. It is from here that most of the material particles of the universe were created at high temperature, triggering the emission of large amounts of light, called cosmic microwave background. This radiation is now observed with great accuracy by space probes.

### Video: Video on a space trip, round trip between Earth and the cosmic horizon of the known Universe. The Known Universe - Credit & Copyright: American Museum of Natural History

I think the question could be interpreted as follows: Is there any non-degenerate cone, with apex at a point on Earth, whose intersection with the sphere that is the observable universe, contains no radiating matter?

I think some minimum threshold of radiation density to count as 'radiating matter' might need to be set because any particle can undergo nuclear decay and radiate, which would mean that one isolated particle of Hydrogen would be enough to render a cone 'occupied'.

Lets assume that all the stars, galaxies, clusters, are all magically equally bright in the night sky to our eyes.

What I'm really asking is if there would be any line of sight that wouldn't end up on the surface of a luminous object.

Let me know if I'm not making sense.

Aside from the CMB, which originated when the universe was opaque and therefore was itself a single luminous object, the answer to that is no. The best visual range idea of what the universe might look like with more powerful eyes is the Hubble [Ultra] Deep Field pictures: Note that this is also at a magnification/resolution beyond human sight, so at human resolution this would appear to be a near uniformly bright field, a la some regions of the Milky Way.

Aside from the CMB, which originated when the universe was opaque and therefore was itself a single luminous object, the answer to that is no. The best visual range idea of what the universe might look like with more powerful eyes is the Hubble [Ultra] Deep Field pictures:

Note that this is also at a magnification/resolution beyond human sight, so at human resolution this would appear to be a near uniformly bright field, a la some regions of the Milky Way.

Right, I was wondering about this image. I'm not sure about how deep into the past those galaxies are, though. Is this really the edge of our observable universe?

Yes, given the eye resolving capability it would probably look like a close to uniformly bright sky.

I see. I was kinda imagining this exercise including all those galaxies that can only be detected outside of the visible spectrum, but as if they magically became visible to us. Like literally make all luminous objects within the observable universe visible to the naked eye.

But I guess there would still be a lot of 'empty' space between baryonic matter for lines of sight to pass through.

I think the question could be interpreted as follows: Is there any non-degenerate cone, with apex at a point on Earth, whose intersection with the sphere that is the observable universe, contains no radiating matter?

I think some minimum threshold of radiation density to count as 'radiating matter' might need to be set because any particle can undergo nuclear decay and radiate, which would mean that one isolated particle of Hydrogen would be enough to render a cone 'occupied'.

Sorry, I see what you mean now. Imagine that we look through the cross section (arbitrarily small radius) of the intersection between the cone and the sphere to see if there's any 'radiating' matter inside the cone. This is exactly what I mean. (planets, comets, anything bigger than a dust particle also counts)

I should have said all with equal apparent magnitude. Sorry for the confusion. The question of visibility is one point that is likely cleared out. The other is the cone intersection (arbitrarily small cross section, so pretty much a 'line'), which andrewkirk understood right away.

My bad for not formulating this right.

@Vanadium 50 was more on point than you realized. The brightness of point sources of light falls with the square of distance, but galaxies are not point sources, they are extended objects. And their apparent size also gets smaller with the square of distance, making the intensity of the light from that smaller area roughly the same. That's the reason the HUDF can detect galaxies of vastly different distances in the same exposure their surface brightnesses are similar.

The caveat of redshift means that in particular with the HUDF pictures, some galaxies become redshifted out of the frequency range of the detector.

In any case, my understanding is that the HUDF does not miss a large fraction of the galaxies in our observable universe, but I don't have a ready link to a source for that. I'm going to take a somewhat of a guess and say it can see about half.

The point of @russ_watters and @Vanadium 50 about apparent brightness of galaxies per unit solid angle being broadly constant makes me feel that the answer to the question must be Yes - there would be dark spots (empty cones). Otherwise we would have a solid white night sky, like a scaled-down version of Olbers' paradox.

The only thing that might prevent that conclusion is the red shift issue. My guess is that, if we exclude the CMBR then, even if we count all sources within the observable universe, regardless of the frequency at which their light would arrive here, there would still be plenty of dark spots - ie cones from which the only incoming radiation is from the CMBR. But that is just a guess. Maybe the amount of incoming radiation at very low frequencies is so much more than that in the visible range that it fills in all the holes.

@Vanadium 50 was more on point than you realized. The brightness of point sources of light falls with the square of distance, but galaxies are not point sources, they are extended objects. And their apparent size also gets smaller with the square of distance, making the intensity of the light from that smaller area roughly the same. That's the reason the HUDF can detect galaxies of vastly different distances in the same exposure their surface brightnesses are similar.

The caveat of redshift means that in particular with the HUDF pictures, some galaxies become redshifted out of the frequency range of the detector.

In any case, my understanding is that the HUDF does not miss a large fraction of the galaxies in our observable universe, but I don't have a ready link to a source for that. I'm going to take a somewhat of a guess and say it can see about half.

The point of @russ_watters and @Vanadium 50 about apparent brightness of galaxies per unit solid angle being broadly constant makes me feel that the answer to the question must be Yes - there would be dark spots (empty cones). Otherwise we would have a solid white night sky, like a scaled-down version of Olbers' paradox.

The only thing that might prevent that conclusion is the red shift issue. My guess is that, if we exclude the CMBR then, even if we count all sources within the observable universe, regardless of the frequency at which their light would arrive here, there would still be plenty of dark spots - ie cones from which the only incoming radiation is from the CMBR. But that is just a guess. Maybe the amount of incoming radiation at very low frequencies is so much more than that in the visible range that it fills in all the holes.

## Approximating density of hydrogen in [observable] universe - Astronomy

After recombination, early in the history of the universe, baryonic matter was in the form of neutral hydrogen. Imprinted on the hydrogen distribution were the primordial density fluctuations that were detected and mapped by COBE and the subsequent cosmic microwave background (CMB) experiments. The surface of last scattering delineated by the CMB at a redshift of about 1000 is the most distant structure in the universe that we observe today. The next most distant structures we see are galaxies and quasars at redshifts of 5 to 6. Sometime between a redshift of 1000 and a redshift of 6, the neutral hydrogen collapsed to form structures, the first stars and/or quasars were formed, the galaxies assembled, and the intergalactic medium was reionized. This important time in the history of our universe is commonly referred to as the epoch of reionization.''

Optical spectra of the the most distant quasars show Lyman-alpha absorption troughs that suggest that universe was largely neutral above a redshift of 6. However, the recent polarization results from the WMAP mission suggest that reionization occurred at a much higher redshift (about 20). Reconciling these different measurements may involve a fairly complicated reionization history. It should be possible to observe some of the processes at work during the epoch of reionization. Several observable signatures are provided by the neutral hydrogen through observations of the 1.4 GHz line, redshifted to frequencies of tens to hundreds of MHz. The first of these is a possible "reionization step" in the spectrum corresponding to the fairly abrupt transition to full reionization that occured at the end of the epoch of reionization. After the formation of the first stars and/or quasars, the process of reionization probably proceeded relatively slowly as the Stromgren spheres began to grow. However, a sudden transition to complete reionization might occur when the Stromgren spheres overlap and the mean free path of photons increase by around two orders of magnitude. Numerical simulations provide a striking demonstration of this transition.

Another observable signature is the "reheating" of the neutral hydrogen that occurs when the primordial density enhancements collapse under the influence of gravity, the gas becomes hot, and it becomes visible by emitting in the redshifted neutral hydrogen line. The figure below on the left, taken from Tozzi et al. (2000, ApJ, 528, 597), shows a simulation of how these structures would appear to a radio telescope tuned to receive signals at a frequency of 150 MHz, corresponding to a redshift of 8.5. The figure below on the right shows the reheated structures at z=8 but now in the form of a power spectrum. The superimposed light grey area are the measurements errors we expect with the Mileura Widefield Array (see below) the dark grey area are those errors combined with the cosmic variance. Both these figures assume no reionization has taken place at z=8, which is probably unlikely. However, it is useful to consider the un-reionized case as a reference.  As the neutral hydrogen continues to collapse, yet another observable signature occurs when the first stars and/or quasars form. Radiation from these bright objects ionizes the nearby neutral hydrogen, causing regions of ionized gas that appear as dark patches where the 21cm line is no longer radiating. A simulation of this process is shown below (Furlanetto, Sokasian, and Hernquist, 2004, MNRAS, 347, 187) in the nine pictures that show the same slice of the universe at redshifts 12.1, 11.1, 10.4, 9.8, 9.2, 8.7, 8.3, 7.9, and 7.6. At early times (upper left corner), the hydrogen is still neutral, and glows at radio wavelengths. At later times (lower right corner) the hydrogen is almost completely ionized and appears dark. In between there are interesting structures as the ionization fronts propagate through the hydrogen. The neutral hydrogen features shown above should be detectable with a large radio telescope operating at low frequencies. The Kavli Institute's radio astronomy group is part of a collaboration that is building a low-frequency array at Mileura Station in Western Australia.