Physics of Cosmic Dark Ages

Najmuj Sahadat Sarkar^*
*Correspondence: Najmuj Sahadat Sarkar, Department of Physics, Mahishadal Raj College, West Bengal, India, Tel: 6295454694, Email:

Keywords

Dark age • Dark matter • Universe • Hubble constant • WMAP • Lensing • FRW metric • Cosmology • Observation • Hydrogen • Extension of its universality for non-circular orbits

Introduction

When we look into a mirror 1 meter away, we see ourselves 6.7 milliseconds ahead. As the light rays emitted from us are hit by the mirror and come back to our eyes. If the mirror had been placed 10^19 cm ≈3 pc away we would have seen ourselves 21 years earlier. Looking into space means looking into the past in time. Light always travels at a finite speed. So looking at a distant region is like looking back in time in the universe. This applies to all types of telescopes in the universe. The statistical homogeneity of the universe on a large scale has helped to realize that the terms and conditions of the space in which we live were once different. This fortunate situation has made cosmology an empirical science. We don't need to guess how the universe evolved. By using a telescope we can easily see what the universe looked like in the early cosmic time. According to the theory, astronomers have traced the entire 13.7-billion-year-old cosmic history of the universe to specific galaxies and specific light sources [1]. If the distance is greater, the fainter flux of a fixed luminosity light source can be observed. The observation of the light sources of the early universe depends on the light gathering power of sensitive instruments and ground based telescopes. They are formed first in galaxies that reside within the dark matter concentration, whose typical mass increases with time. The first host stars have a mass of approximately 10^5 solar masses. Then the mass for the source of deionization is about, 10^7 solar masses to 10^9 solar masses. And now let's take our Milky Way galaxy at present, its mass is about 10^12 solar masses to 10^15 solar masses. That is, it appears that the star formation rate in the galaxies increased with the increase of time.

Description

Astronomer attempts are being made to resolve the evolution of cosmic gas by the absorption of background light by atomic hydrogen. The method they are using is the Lyman α line absorption method of the hydrogen resonance of light. This light is emitted from massive galaxies or quasars where another observation method has been applied, through the use of 21 cm hydrogen lines. This is for the Cosmic Microwave Background or CMB source [2]. As the universe expands, the photon's wavelength becomes more stretched. The factor by which the observed photon light wave is broadened (shifted toward the red part of the spectrum), relative to the emitted photon light wave, is expressed as (1+z). Here z is called the cosmological red shift. Astronomers have deduced, from the pattern of light spectra emitted by hydrogen and other chemical substances, that we will get the z redshift for each galaxy. From light emitted by galaxies, to observed light, scientists know that the universe is expanding by a factor of (1+z). And it is dimensionally linear. In this way, astronomers can calculate how far away a particular light source is and how old it is. With the help of large ground-based telescopes, scientists have been able to detect even faint light at great distances [3].

For that we may have to travel 12 billion years back in time. From this we understand that the first galaxies in the Universe formed about 850 million years after the big bang, when the redshift was z≈6.5 or greater. We can film the universe only when it is transparent. 400,000 years or so before the big bang, cosmic hydrogen disintegrated into electrons and protons (abbreviated ionization), and the universe was then opaque, with free electrons unable to escape from the dense plasma. Therefore, it is not possible for the telescope to create any kind of map or image. At that time the red shift was much higher than 10^3. However, the WMAP and COBE satellites have been able to provide the earliest possible images of the universe which shows the temperature distribution of the CMB across the sky. The CMB, which indicates the hotter, denser beginning of the Universe, has become an important tool in observational cosmology today. As the universe expands, it begins to cool. Moreover, its previous density was much higher than the current density. For a hundred thousand years that opaque plasma was bound by the thermal motion of free electrons, protons, and some cosmic gas plus some light nuclei. Much like the plasma trapped in our Sun. The ancient plasma then emitted some visible and some UV photons [4]. And spread across the universe. As stated earlier, after 380,000 years the temperature of the universe is about 3000k. Now the proton and neutron start moving so slowly that they are able to recombine to form neutral hydrogen atoms. Most photons scatter in a straight line in every possible direction. Photons separated from matter for the first time. This phenomenon is called photon decoupling. Today, the wavelength of photons has been red shifted due to the expansion of the universe. And it reaches the microwave range of the spectrum.

The temperature of the observed spectrum of CMB photons shows a slight deviation of one part in 10, 0000 parts. This proves that conditions in the early universe were fairly uniform. This is the moment just before cosmic recombination (when matter tries to beat radiation). Gravity then amplifies the subtle fluctuations in density and temperature in the CMB started doing in regions where the density was slightly higher than the average density, the gravitational force showed a stronger effect. Finally after a hundred million years matter stopped contracting in all those dense regions. Even over dense regions stop expanding [5]. Due to its effect, large structures like galaxies are formed in those parts later. Moreover, the gas inside the collapsed objects cooled to form the first stars. These are population 3 stars who will explode later to create population 2 stars like the sun! Moreover, the deviation of this density can tell why there are more galaxies in the universe. If gravity had a strong effect in the presence of dark matter, an unknown substance would dominate the total matter density (83%) present in the universe. And that actually happened. Dark matter exerts a strange influence on the motion of stars and interstellar gases near the centers of galaxies. Therefore, dynamically-relaxed dark matter concentrations present in galaxies are known as "halos" for short. It has been observed that the radius of dark matter halos is 10 times larger than the radius of galaxies.

According to the Standard Cosmological Model, dark matter is essentially cold in nature (according to the CDM model). It behaves like a few collisions fewer particles, which were formed in the matter-dominated stage of the universe and whose thermal velocity is very negligible. But I guess they can form strong gravitational field. This model is able to analyze how both large galaxies and large scale structure patterns evolved from very tiny fluctuations. In all the observations we have made or carried out on a large scale, the distribution pattern of galaxies exactly matches the statistical pattern of the CMB. And it supports billions of billions of years of cosmic evolution. On a smaller scale, this model analyses how those regions whose density was higher than the average density of the rest formed 'halos' in the present universe through gravitational contraction. But the beginning was from small scale to large scale. According to this hierarchical model of galaxy formation, small proto-galaxies were first formed in the universe [6]. Then they increase both their size and mass by collapsing gas and dust over many years. At each snapshot of cosmic evolution, the additional presence of contracting halos is computed through numerical simulations of the initial conditions (halos mass dominated by dark matter). According to the general theory of galaxy formation, stars formed from gas that somehow entered these halos and the cooler-dense regions slowly collapsed into star clusters. Gravity can explain how gas and matter entered deep potential wells within dark matter halos and then formed large galaxies and cosmic structures. This happened when our universe was only 200 million years old.

One might think, or hope, that the gases outside the halos would remain undisturbed, that is, their nature would not change. But observation has shown that gases cannot exist in a neutral state (neutral state is the normal atomic state). They will mostly be converted into ionized state by UV radiation emitted from the galaxy. All these diffuse gases will spread across the intergalactic space i.e. IGM or Inter Galactic Medium. The universe was shrouded in darkness for some 100 to 200 million years after recombination. This is called the Cosmic Dark Ages. At that time the Universe was filled with Diffuse Atomic Hydrogen. As galaxies slowly began to form, ionized diffuse hydrogen began to move closer to those structures. The IGM re-ionized them less than a billion years after the Big Bang. Now we are able to uncover new images of cosmic dark ages. Currently, the biggest obstacle in the study or observation of cosmological models is the deionization state and how the first class galaxies were formed in the universe? Science writers have named it "Cosmic Dawn". Their stories begin almost identically with "Many years ago when the universe was shrouded in a blanket of darkness". During the Dark Age the universe was as dark as it was for the last time. At that time there was no planet, no sun, no galaxy or any life form in space. There was only a mist of hydrogen gas, encased in darkness [7]. Today, telescopes around the world are trying to understand the reason for the appearance of that primordial hydrogen gas coil. When the Dark Age ended, new galaxies were first formed. Although those ancient atoms are very exclusive, various researchers are trying to figure it out. New studies and other astrophysical journals have revealed that the MWA (Murchison Widefield Array) radio telescope has gone deep into the cosmic past and attempted to resolve the origin of hydrogen. They found nothing. Tried to change the setting of the telescope, but nothing caught their eye. We can confidently say that if the signal of neutral hydrogen atoms is higher than any theorized limit then cosmologists think we can detect them. This means that efforts are still underway to find that molecule (Figure 1).

Now researchers know that the footprint or existence of neutral hydrogen is fainter than expected. The force flowing through the early universe was so strong that the electrons in each atom were ejected from the atom and positively charged the nucleus. The first of these atoms was the positively charged hydrogen ion. Over thousands of years, the universe cooled and gave these hydrogen ions a chance to regain their electrons. Again the universe is filled with neutral atoms again. These neutral hydrogen atoms are thought to be the dominant feature of the cosmic dark ages. Finally, when enough of those neutral hydrogen atoms collapse under the influence of gravity to form a star, the atoms are, again, ionized by the energy scattered from the star. Scientists know that neutral hydrogen emits radiation at a wavelength of 21 cm. However, as the universe has expanded over the past 12 billion years, so have those wavelengths.

The new researchers estimated that the wavelength of neutral hydrogen was extended to about 2 meters. The research team used MWA to receive this signal from space. The problem is there are many sources in the universe that radiate at the same wavelength. The intensity values of all these sources were higher than the signals we wanted to detect. Even an FM radio signal reflected from an aircraft passing over the telescope can affect the observational data. For which there is a risk of error. Therefore, researchers have been able to identify certain systems to avoid errors in their observations. After taking a snapshot of 1,200 radio waves in the sky, the researchers determined that each 2-meter emission signal came from a neutral hydrogen atom signal. Although the valuable nuclear signal remains undiscovered, new research has succeeded in determining what future searches for neutral hydrogen should look like. According to the researchers, these findings make a strong case that MWA experiments are now on the right track. With further research, it may soon be possible to bring the last part of the cosmic dark ages to light. Below, for the sake of simplicity, the events are listed as follows:-

Dark ages (z>35)

Before the first stars formed, the hydrogen gas collided with CMB photons and absorbed them. As the universe expands, the gas cools rapidly. And 21 cm signal can be observed in absorption band. Any additional heating process may affect the characteristics of the 21 cm signal.

First light and first stars (35>z>20)

After the first star is formed, there is re-emission and absorption of UV photons through the WF mechanism, which helps to "turn on" the 21 cm signal. Despite the 21 cm absorption signal, the IGM gases are slightly cooled.

First accreting black holes (20>z>15)

Black holes form from the remnants of the first stars. Accreting gases are slowly shock heated, and emit X-ray wavelength radiation which helps warm the cooler gases (~ 10 K). This heating transformation helps to spin-flip the signal. Absorption changes to emission (since the gas is then, comparatively, warmer than the CMB).

Epoch of deionization (15>z>6)

As the gas warms, the emission process begins to saturate (until the stars and photons emitted from the black hole are ionizing the gas in the IGM). Rapid destruction in the deionization process slightly attenuates the 21 cm signal of neutral gases. Such observations are mainly space based, since the H = 21 cm line is red shifted at wavelengths where ionospheric opacity becomes very important [when z=20, the transition is red shifted to λ4m (67 MHz) and for z=70 the transition is red shifted up to λ15m (20 MHz). Incidentally these two measurements exist in nature. The average 21 cm spectrum of the sky is an elementary quantity. This is indeed a "turning point" in astronomy. The spectrum, and its nature, can be used to determine the timing of major events in the universe. This measurement can potentially be accomplished with a single small antenna.

Einstein was the first to realize the modern explanation of the entire universe and its physical form known as the "Cosmological Principle". The distribution of matter and energy in the universe on a large scale is homogeneous and isotropic. Today we understand the universe-wide distribution of galaxies, the X-ray background, the distribution of some faint radio galaxies, importantly the CMB isotropy [8]. Although the constraint of homogeneity is not too strict. According to a cosmological model, where the universe is isotropic, the universe is slightly inhomogeneous in the tiny spherical shells surrounding our special location. And it's not something to ignore. In general relativity, a homogeneous and isotropic space is defined by the FRW metric which is written as follows:-

Here c is the speed of light, a(t) is the cosmic scale factor, which expands at time t, (R,θ,φ) is the spherical commoving coordinate. Here the k constant analyses the geometry of the metric. A value of k of zero indicates a flat universe. A positive value of k indicates a closed universe. Again, if the value of k is negative, it indicates an open universe. An observer who is stationary will always remain stationary. But in that case (R,θ,φ) will be fixed, and their physical separation will increase with time, which is proportional to a(t). A particular Observer can see the nearest Observer at physical distance "D" whose receding Hubble velocity will be H(t)D. And hubble constant, at time t will be H(t)=da(t)/(a)dt Suppose light is emitted from a source at time t and observed at time t=0. In this case redshift z=1/[a(t)–1]. Where we are considering a(t=0)=1. From Einstein's field equation of general relativity, the Friedmann equation can finally be found [9].

This equation relates the expansion of the universe and the energy content of matter present in it. The constant k determines the geometric structure of the universe. This is positive for a closed universe as mentioned earlier. For an open universe k is negative. Again for a flat universe it is zero. For each component of energy density ρ, there is an equation of state, namely: p=p(ρ) of density ρ, a(t) varies with (according to the thermodynamic relation).

And the formula for critical density will be:

Equation 2 becomes simpler if k=0. Ratio of the total density of the universe to the critical density gives us:

Ω=ρ/ρc (Equation 5)

The universe has been dominated by different parameters at different times. For example, Ω(m) refers to the sum of dark matter and ordinary matter. Ω(r) this parameter characterizes the radiation dominated universe. Again Ω(Λ) refers to dark energy or vacuum energy dominated universe. So:-

where H₀ and Ω₀=Ω(m)+Ω(Λ)+Ω(r) are determined by the current H and Ω. Theoretically we see that the mathematical relationship between Ω(k) and Ω(m) will be:

Ω(k)=–k/H₀²=1–Ω(m)... (Equation 7)

According to the simple Einstein D-Sitter model [Ω(m)=1, Ω(Λ)=Ω(r)=Ω(k)=0], the scale factor is proportional to the 2/3 power of the time, i.e. a(t)∝t ^2/3. Even in non-zero models of Ω(Λ) or Ω(k), [high redshift Einstein-de Sitter scaling rules] (1+z)>>|Ω(m)⁻¹–1| is Ω(r) is ignored in all those cases. The rule for determining the age of the universe according to this high redshift z model is:-

Some physical parameters have been revealed in the recent observations we have made. They are of very narrow range. Specifically we live in a universe where the cosmological constant (Λ) dominates and cold dark matter dominates, abbreviated Λ CDM cosmology [but Ω(k)≈0 can be assumed in the present universe]. It depicts the scale invariant primordial power spectrum of the density fluctuation, i.e. n≈1. But initial power spectrum will be P(k)=|δ(k)|²∝kⁿ, in this case δ(k) wave number of fourier mode will be k. Moreover currently the value of hubble constant is H₀=100h km s⁻¹ Mpc⁻¹, where h=0.71. Moreover, the total normalization of the power spectrum is expressed by σ₈. On the other hand, the 8h⁻¹Mpc radius is taken as the root-mean-square amplitude of the mass fluctuation within the sphere. For example, according to data determined by WMAP and gravitational lensing observations, σ₈=0.826, n=1, h=0.71, Ω(m)=0.299, Ω(Λ)=0.701 and Ω(b)=0.05 [10].

Conclusion

Basically Cosmic Dark Age is unknown to everyone because for some 100 million years our universe was shrouded in darkness. So no light was present at that time to study the Dark Age. But my study will basically help to understand this cosmic Dark Age briefly.

Acknowledgement

I like to thanks my parents who believed in me for this paper. Also, many thanks to professor and astronomer Sabyasachi Pal who constantly encouraged me to try new things. Moreover, many thanks to the members of this Journal.

Conflict of Interest

None.

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