Imaging the Universe during the first hundreds of millions of years remains one of the exciting challenges facing modern cosmology. Observations of the redshifted 21 cm line of atomic hydrogen offer the potential of opening a new window into this epoch. The epoch between the formation of the cosmic microwave background radiation (CMB) and reionization is commonly referred to as the cosmic dark ages. In this epoch, matter is largely uniform and transparent to radiation. An exception to its transparency is the hyperfine transition of the hydrogen atom, between its electron ground state triplet and singlet states. The transition energy corresponds to a photon wavelength of 21 cm, the 21 cm line of hydrogen, which arises from the hyperfine splitting of the 1S ground state due to the interaction of the magnetic moments of the proton and the electron. This splitting leads to two distinct energy levels separated by ∆E = 5.9 × 10−6 eV, corresponding to a wavelength of 21.1 cm and a frequency of 1420 MHz. This frequency is one of the most precisely known quantities in astrophysics having been measured to great accuracy from studies of hydrogen masers. The thermal evolution of the intergalactic medium (IGM) can influence the global 21cm signal. On the other hand, Primordial black holes (PBHs) as part of the Dark Matter (DM) would modify the evolution of large-scale structures and the thermal history of the universe in different ways. We investigate the effect of accreting primordial black holes (PBHs) on the thermal history of the intergalactic medium (IGM), including the accretion of baryonic matter and dark matter particles. The variations of the thermal history of the IGM caused by accreting PBHs will result in the changes of the global 21-cm signal in the cosmic dawn. Matter infalling onto a PBH would accelerate, and by bremsstrahlung and other processes, would emit energetic radiation, escaping the local vicinity of the PBH and being deposited in the IGM. Hawking radiation from primordial black holes (PBH) can ionize and heat up neutral gas during the cosmic dark ages, leaving imprints on the global 21cm signal of neutral hydrogen Since PBHs can be regarded as discrete objects, if they are initially Poisson distributed, they should present a shot noise power spectrum, the shot noise isocurvature mode on small scales induced by the presence of PBHs can enhance the amount of low mass halos, or minihalos, and thus, the number of 21 cm absorption lines. We show that the number of light haloes can significantly increase in the presence of such isocurvature mode sourced by PBHs. and that thus PBHs can be more strongly constrained by 21cm observations. The concurrence of both effects imprints distinctive signatures in the number of absorbers, allowing to bound the abundance of PBHs with the help of 21 cm signal.

In the last decades, astrophysical and cosmological observations has reported the existence of dark matter (DM). There are several candidates for the cold dark matter component, including weakly interacting massive particles (WIMP’s), axions, or ultra-light axions which can be described by a coherent scalar field. Nevertheless, there are no direct astrophysical observations or accelerator detections of these particles and the nature of dark matter is still unknown.
An alternative hypothesis is to consider that primordial black holes (PBHs) are an important fraction (or all) of DM. In pioneer works, Zel’dovich & Novikov (1966) and Hawking (1971) discussed in the radiation era, before the formation of the first stars and galaxies, small perturbations of the energy-density of the universe on scales comparable to the particle horizon may become gravitationally unstable. The outcome of the collapse can be the direct formation of primordial black holes (PBHs). After the first detection of a gravitational wave event by the Laser Interferometer Gravitational-Wave Observatory (LIGO), included black holes with masses that could not be comfortably produced from the death of massive stars in standard stellar evolution scenarios, the interest in PBHs rekindled rapidly.
As PBHs do not form from dying stars, they can have any range of masses. However, there are some constrains on PBHs. The main constraints derive from PBH evaporations, various gravitational-lensing experiments, numerous dynamical effects, and PBH accretion. Finally, after imposing constraints, three possible mass windows for further investigation are as follows: the asteroid mass range (1016–1017 g), the sublunar mass range (1020– 1026 g) and the intermediate mass range (10–103M).
PBH mergers, accretion and evaporation can have an impact on the PBH bounds. While only a tiny fraction of PBHs detectable through their coalescence have experienced a previous merger event, PBHs may efficiently accrete during the cosmic history. In particular, if they do not represent the only DM component, PBHs may accrete a DM halo, thus increasing their gravitational potential and the ordinary gas accretion.
In this research we study the evolution of PBHs through accretion and evaporation across the radiation dominated and matter dominated era. Special attention is paid to the changes in the mass. We used spherical Bondi model to calculate the final mass of PBH. Our calculations show that during the radiation dominated era, the evaporation process is stopped by accretion, in other words, accretion is dominant process. We also demonstrate radiant accretion had a more significant role in increasing PBH mass than material accretion.
In the matter dominated era the process is a bit more complicated. As we expected, the accretion of matter is more effective than the accretion of radiation, but in general, the rate of mass increase in this era was lower than the radiation dominated era. In the matter dominated era, the mass growth rate is influenced by factors such as Compton drag, Compton cooling, Hubble expansion and decoupling. Our research on effects of PBHs on the thermal and ionization history of the universe and their signatures on the CMB anisotropies and spectrum will continue.

Research into active galactic nuclei (AGNs)– the compact, luminous hearts of many galaxies– is at the forefront of modern astrophysics. Understanding these objects requires extensive knowledge in many different areas: accretion disks, the physics of dust and ionized gas, astronomical spectroscopy, star formation, and the cosmological evolution of galaxies and black holes. We are also witnessing the nearly explosion of the field of active galactic nuclei. From a narrow discipline dealing with massive active black holes (BHs) and their immediate surroundings, it now includes the host galaxies of such BHs, the correlated evolution of BHs and galaxies, and the physics of extremely energetic phenomena like γ-ray jets. More than 1000 articles are being published in refereed journals every year about this topic, and the numbers are still growing The names “active galaxies” and “active galactic nuclei” (AGNs) are related to the main feature that distinguishes these objects from inactive (normal or regular) galaxies: the presence of supermassive accreting black holes (BHs) in their centers. As of 2011, there were approximately a million known sources of this type selected by their color and several hundred thousand by basic spectroscopy and accurate redshifts. It is estimated that in the local universe, at z ≤ 0.1, about 1 out of 50 galaxies contains a fast-accreting supermassive BH, and about 1 in 3 contains a slowly accreting supermassive BH. In this research we model the main features of AGNs by focusing on the supermassive black holes at the center of these galaxies as well as using machine learning coding. We also study the black holes mass evaluation through cosmic time and all the relative phenomena which has effects on the black hole mass function- such as black hole accretion process and Hawking evaporation- to investigate weather these black holes in AGN are primordial in origin and generate the galaxies or not. further more we shall connect the discussion with one of the most important questions in cosmology. What is dark matter made of? We know that primordial black holes (PBHs) represent a natural candidate for one of the components of the dark matter (DM) in the Universe. PBH formation is already present in standard cosmologies, although extremely unlikely. However, their production usually requires some exotic inflationary scenarios or physics beyond the Standard Model (BSM) in order to obtain a large enough abundance.More importantly, the existence of PBHs would provide valuable hints about the still unknown physics of the very early Universe, and may allow to probe high-energy scales and super symmetric theories . In this Study as we are focusing on black holes which potentially could be primordial rather than stellar black holes,and we have already examined some of their characteristic signals, such as the emission of particles due to Hawking evaporation and the accretion of the surrounding matter, we shall briefly discuss the most relevant aspects of PBHs as DM, such as the mechanism of formation, the initial abundance, mass distribution and other PBH features, which could leave imprints on different observables, and finally current observational constraints on their population are summarized.

When we look out at the Universe, we can only see a fraction of the matter we know must be there. In fact, for every gram's worth of atoms in the Universe, there are at least five times more invisible material called dark matter. So far scientists have failed to detect it, despite spending decades searching. However, some theories are more likely to be successful than others, here are the five candidates for particles that have the best chance; the WIMP (Weakly Interacting Massive Particle), the axion, self-interacting dark matter, exotic stars, PBH (Primordial Black Holes). Primordial Black Holes are known as the best candidates for dark matter. These black holes were made in radiation-dominated era when no baryonic matter existed, so basically they were made of non-baryonic matter due to over-density. Over the first few months of coincident measurement, the LIGO interferometers have detected gravitational waves from several mergers of black hole binaries.
Two of these events involved the mergers of black holes with masses estimated to be near 30 M . While these may simply be the endpoints of massive stars, an alternative explanation that is tempting to consider is that these are primordial black holes (PBHs) , which are formed deep in the radiation-dominated era. This idea is especially intriguing as there remains the possibility that such PBHs could account for the dark matter (DM) in the Universe. But the question is how can we calculate these PBHs merger rate?!
For this, we will define a function called density contrast (δ), and according to spherical collapse model, regions with δ(x,t)>δ_(c )~1.686 will have collapsed to produce dark matter. Using top-hat filter as our window function we can simply calculate the variance of density field. Since we can equally label a filter by its size R or mass M, we can write σ^2 (R)=σ^2 (M), the latter is mass variance. We are also able to relate mass variance to Gaussian random field δ(x). according to spherical collapse model, regions in the linear density field with δ>δ_c have collapsed to produce virialized dark matter haloes. One of the formalisms that can be used to predict halo mass functions is Press-Schechter model, in 1974 Press & Schechter postulated that the probability that δ_M>δ_c (t) is the same as the mass fraction that at time t is contained in haloes with mass greater than M. In other words, We consider Press-Schechter (PS) formalism to derive an extended mass function for primordial black holes (PBHs), considering their formation by the collapse of energy density fluctuations. Said fluctuations are assumed to obey Gaussian statistics and they are obtained from a primordial power spectrum of broken power-law form with a blue spectral index for small scales which are difficult to explain by stellar collapse.
Then we define Press-Schechter mass function which is the number of haloes with mass in range [M, M+dM ] per volume. Merger rate is then proportional to the integral of mass function.