Radiation-dominated Phase Research Articles

Primordial Black Holes: Formation, Spin and Type II

Primordial black holes (PBHs) may have formed through the gravitational collapse of cosmological perturbations that were generated and stretched during the inflationary era, later entering the cosmological horizon during the decelerating phase, if their amplitudes were sufficiently large. In this review paper, we will briefly introduce the basic concept of PBHs and review the formation dynamics through this mechanism, the estimation of the initial spins of PBHs and the time evolution of type II fluctuations, with a focus on the radiation-dominated and (early) matter-dominated phases.

Dark matter from mediator decay in early matter domination

We study dark matter production from mediator decays in scenarios with an epoch of early matter domination. Particles that mediate interactions between dark matter and the standard model particles are kinematically accessible to the thermal bath as long as their mass is below the reheating temperature of the Universe after inflation. Decay of on-shell mediators can then lead to copious production of dark matter during early matter domination or a preceding radiation-dominated phase. In particular, for mediators that are charged under the standard model, it can exceed the standard freeze-in channel due to inverse annihilations at much lower temperatures (often by many orders of magnitude). The requirement to obtain the correct relic abundance severely constrains the parameter space for dark matter masses above a few TeV. Published by the American Physical Society 2024

Dynamical system analysis of LRS-BI Universe with [formula omitted] gravity theory

Considering the Universe as a dynamic system, the understanding of its evolution is an interesting aspect of study in cosmology. Here, we investigate the anisotropic locally rotationally symmetric (LRS) Bianchi type-I (LRS-BI) spacetime under the f(Q) gravity of symmetric teleparallel theory equivalent to the GR (STEGR) as a dynamical system and try to understand the role of anisotropy in the evolution of its various phases. For this work, we consider two models, viz., f(Q)=−(Q+2Λ) and f(Q)=−βQn to study the critical points and stability of the LRS-BI Universe. In both the models, it is found that the various phases like radiation-dominated, matter-dominated, and dark energy-dominated phases are heteroclinically connected, and there is some role of anisotropy in the evolution of these phases of the Universe. However, for both the models, there are some unphysical solutions too depending upon the values of model parameters β and n along with the anisotropic parameter α.

Accelerating cosmological models in [formula omitted] gravity and the phase space analysis

The dynamical aspect of accelerating cosmological model has been studied in this paper in the context of modified symmetric teleparallel gravity, the f(Q) gravity. Initially, we have derived the dynamical parameters for two well known forms of f(Q) such as: (i) log-square-root form and (ii) exponential form. The equation of state (EoS) parameter for the dark energy in the f(Q) gravity in both the models emerges into a dynamical quantity. At present model-I shows the quintessence behaviour and behave like the ΛCDM at the late time whereas model-II shows phantom behaviour. Further, the dynamical system analysis has been performed to determine the cosmological behaviour of the models along with its stability behaviour. For both the models the critical points are obtained and analysed the stability at each critical points with phase portraits. The evolutionary behaviour of density parameters for the matter-dominated, radiation-dominated, and dark energy phases are also shown for both the models.

Dark matter and baryogenesis from visible-sector long-lived particles

We present a minimal extension of the standard model that includes a long-lived fermion with weak-scale mass and an ${\cal O}({\rm GeV})$ fermionic dark matter candidate both of which are coupled to quarks. Decays of a TeV-scale colored scalar in a radiation-dominated phase bring the former to a thermal abundance while also producing dark matter. The long-lived fermion then dominates the energy density of the Universe and drives a period of early matter domination. It decays to reheat the Universe, mainly through baryon-number-violating interactions that also generate a baryon asymmetry, with a small branching fraction to dark matter. We find the allowed parameter space of the model and show that it can be probed by proposed long-lived particle searches as well as next-generation neutron-antineutron oscillation experiments. This model provides a robust explanation of dark matter and baryogenesis as long as the Universe is in a radiation-dominated phase at $T \gtrsim {\cal O}({\rm TeV})$.

Dynamical systems analysis in f(T,phi ) gravity

Teleparallel based cosmological models provide a description of gravity in which torsion is the mediator of gravitation. Several extensions have been made within the so-called teleparallel equivalent of general relativity which is equivalent to general relativity at the level of the equations of motion where attempts are made to study the extensions of this form of gravity and to describe more general functions of the torsion scalar T. One of these extensions is f(T,phi ) gravity; T and phi respectively denote the torsion scalar and scalar field. In this work, the dynamical system analysis has been performed for this class of theories to obtain the cosmological behaviour of a number of models. Two models are presented here with some functional form of the torsion scalar and the critical points are obtained. For each critical point, the stability behaviour and the corresponding cosmology are shown. Through the graphical representation, the equation of state parameter and the density parameters for matter-dominated, radiation-dominated and dark energy phase are also presented for both the models.

Cosmic acceleration and ekpyrotic bounce with Chameleon field

In this paper, we explore the homogeneous and isotropic flat Friedmann–Robertson–Walker (FRW) model in Chameleon cosmology. By considering a non-minimal coupling between the scalar field and matter, we present a non-singular bouncing cosmological scenario of the universe. The universe initially exhibits the ekpyrotic phase during the contracting era, undergoes a non-singular bounce, and then in expanding era, it smoothly transits to the decelerating era having matter and radiation-dominated phases. Further, this decelerating era is smoothly connected to the late-time dark energy-dominated era of the present epoch. We use numerical solution techniques to solve non-minimally coupled gravity equations for understanding the evolution of scalar field along with other quantities like effective potential in the model. The model thus unifies an ekpyrotic, non-singular, asymmetric bounce with the dark energy era of the present epoch. We study the evolution of bouncing model and confront the model with observational results on the equation of state parameter by constraining the model parameters.

Cosmic dynamics and qualitative study of Rastall model with spatial curvature

We investigate the cosmic dynamics of Rastall gravity in nonflat Friedmann–Robertson–Walker (FRW) space–time with barotropic fluid. In this context, we are concerned about the class of model satisfying the affine equation of state. We derive the autonomous system for the Rastall model with barotropic fluid. We apply the derived system to investigate the critical points for expanding and bouncing cosmologies and their stable nature and cosmological properties. The expanding cosmology yields de Sitter universe at late times with decelerating past having matter and radiation-dominated phases. Investigation of autonomous system for bouncing cosmology yields oscillating solutions in positive spatial curvature region. We also investigate the consequences of setting-up a model of nonsingular universe by using energy conditions. The distinct features of the Rastall model compared to the standard model have been discussed in detail.

Reconstruction in the Horndeski theory within the scope of the Bianchi I cosmology

In this paper, [R. K. Muharlyamov and T. N. Pankratyeva, Eur. Phys. J. Plus 136, 590 (2021)] we have proposed a reconstruction method for the kinetic gravity braiding theory in the framework of the flat Friedman–Robertson–Walker spacetime. Here, we develop this method in the Bianchi I spacetime model for a subclass of the Horndeski theory: [Formula: see text], [Formula: see text], [Formula: see text]. The Hubble parameter [Formula: see text] and the canonical kinetic term [Formula: see text] are set a priori. The choice of the function [Formula: see text] determines the anisotropic properties of the Universe. This makes it possible to provide believable anisotropy. The presented method allows for a realistic model of the Universe to simply reconstruct some scalar field theory. Reconstruction example is given for anisotropic model of a post-inflationary transition to the radiation-dominated phase. The model is investigated for the absence ghosts and Laplacian instabilities.

Lagrangian formulation and implications of barotropic fluid cosmologies

In this paper, we investigate the behavior of cosmologies in homogeneous and isotropic background with a barotropic fluid. We solve the continuity equation and study several aspects of model including behavior of cosmological quantities like Hubble parameter, deceleration parameter, equation of state parameter along with statefinder diagnostic and validity of energy conditions. The [Formula: see text] plane is checked for identification of thawing and freezing regions. We derive the Lagrangian formulation with standard and non-standard kinetic terms for barotropic fluid model. It is demonstrated that the model possesses periodic potential in its Lagrangian description with standard kinetic terms. Using dynamical system analysis, we find the stability of solutions, too. We further explore the thermodynamic aspects at apparent horizon by investigating the validity of generalized second law of thermodynamics with equilibrium description. The model exhibits complete cosmological scenario for different values of model parameters and the inflationary scenario decays smoothly into radiation-dominated phase during its evolution. The model approaches to [Formula: see text] cold dark matter model during late times of its evolution.

Curvature Profiles as Starting Conditions for the Creation of Primordial Black Holes

This research is part of a larger project to look at the development there were a number of primordial black holes during the radiation-dominated phase of the early universe (PBHs). We offer a beginning arrangement in dimensions of a curving profile, which encapsulates initial circumstances for higher intensity metric disruptions while staying away first from undifferentiated Newman framework, which again is essential for PBH formation, while operating within hexagonal symmetry. When the variance of both the structure is significantly bigger than the cosmic boundary, we employ an iterative bordering answer to connect the bends curve to the spectrometric work and motion fields, which may have been considered of as minor perturbations of the average results at an acceptable enough period. For volume and velocity profiles, we propose broad analytic solutions. These discoveries allow us to look into the personality creation of PBHs in a range of cosmological settings, where the cosmic fluid can be seen as an infinite mix of numerous components of complex equations of state. As a result of the start time, we give analytical answers for volume and mobility characteristics. After that, two different approaches are used to define the curved.

Reconstruction method in the kinetic gravity braiding theory with shift-symmetric

We present a reconstruction method for flat Friedman-Robertson-Walker (FRW) spacetime in a subclass of Horndeski theory -- specifically shiftsymmetric, the kinetic gravity braiding (KGB) theory with a non-vanishing conserved current. Choosing the form of the Hubble parameter and kinetic density $X$, we restore the functions $G_2$, $G_3$ of the KGB model. In order to determine whether the model is free of ghosts and Laplacian instabilities and thus cosmologically viable, two conditions related to scalar perturbations are checked. Initially, the Lagrangian does not include the term that describes, for example, the perfect fluid with the EoS parameter $w\neq -1$. This fluid can provide a dynamic solution $H(t)$, $X(t)$. In the presented method, dynamic solutions are provided by a nonzero scalar charge associated with the shift symmetry $\phi\rightarrow\phi+\phi_0$. Reconstruction examples are given for models: an perfect fluid, a unified description dark energy-dark matter, a post-inflationary transition to the radiation-dominated phase.

Spins of Primordial Black Holes Formed in the Radiation-dominated Phase of the Universe: First-order Effect

Abstract The standard deviation of the initial values of the nondimensional Kerr parameter a * of primordial black holes (PBHs) that formed in the radiation-dominated phase of the universe is estimated to the first order of perturbation for the narrow power spectrum. Evaluating the angular momentum at turnaround based on linearly extrapolated transfer functions and peak theory, we obtain the expression 〈 a * 2 〉 ≃ 4.0 × 10 − 3 M / M H − 1 / 3 1 − γ 2 1 − 0.072 log 10 ( β 0 ( M H ) / ( 1.3 × 10 − 15 ) ) − 1 , where M H , β 0(M H ), and γ are the mass within the Hubble horizon at the horizon entry of the overdense region, the fraction of the universe which collapsed to PBHs at the scale of M H , and a quantity that characterizes the width of the power spectrum, respectively. This implies that for M ≃ M H , the higher the probability of the PBH formation, the larger the standard deviation of the spins, while PBHs of M ≪ M H that formed through near-critical collapse may have larger spins than those of M ≃ M H . In comparison to the previous estimate, the new estimate has an explicit dependence on the ratio M/M H and no direct dependence on the current dark matter density. On the other hand, it suggests that the first-order effect can be numerically comparable to the second-order one.

Constraints on dark energy models from the Horndeski theory

In light of the cosmological observations, we investigate dark energy models from the Horndeski theory of gravity. In particular, we consider cosmological models with the derivative self-interaction of the scalar field and the derivative coupling between the scalar field and gravity. We choose the self-interaction term to have an exponential function of the scalar field with both positive and negative exponents. For the function that has a positive exponent, our result shows that the derivative self-interaction term plays an important role in the late-time universe. On the other hand, to reproduce the right cosmic history, the derivative coupling between the scalar field and gravity must dominate during the radiation-dominated phase. However, the importance of such a coupling in the present universe found to be negligible due to its drastic decrease over time. Moreover, the propagation speed of gravitational waves estimated for our model is within the observational bounds, and our model satisfies the observational constraints on the dark energy equation of state.

F(R) gravity phase space in the presence of thermal effects

Abstract In this paper, we shall consider f ( R ) gravity and its cosmological implications, when an extra matter term generated by thermal effects is added by hand in the Lagrangian. We formulate the equations of motion of the theory as a dynamical system, that can be treated as an autonomous one only for specific solutions for the Hubble rate, which are of cosmological interest. Particularly, we focus our analysis on subspaces of the total phase space, corresponding to (quasi-)de Sitter accelerating expansion, matter-dominated and radiation-dominated solutions. In all the aforementioned cases, the dynamical system is an autonomous dynamical system. With regard to the thermal term effects, these are expected to significantly affect the evolution near a Big Rip singularity, and we also consider this case in terms of the corresponding dynamical system, in which case the system is non-autonomous, and we attempt to extract analytical and numerical solutions that can assess the specific cases. This course is taken twice: the first for the vacuum theory and the second when two perfect fluids (dust and radiation) are included as matter sources in the field equations. In both cases, we reach similar conclusions. The results of this theory do not differ significantly from the results of the pure f ( R ) in the de Sitter and quasi-de Sitter phases, as the same fixed points are attained, so for sure the late-time era de Sitter is not affected. However, in the matter-dominated and radiation-dominated phases, the fixed points attained are affected by the presence of the thermal term, so surely the thermal effects would destroy the matter and radiation domination eras. However, with regard to the Big Rip case, several instabilities are found in the dynamical system, since the initial conditions dramatically affect the behavior of the dynamical system near the starting point of the e -foldings number evolution. Finally, we consider the effects of the thermal term on the late-time evolution of the Universe, by examining several statefinder quantities. Our findings indicate that these are reportable only under extreme fine tuning of the multiplicative coefficient of the thermal term.

Viability of slow-roll inflation in light of the non-zero k min measured in the cosmic microwave background power spectrum

Slow-roll inflation may simultaneously solve the horizon problem and generate a near scale-free fluctuation spectrum P ( k ). These two processes are intimately connected via the initiation and duration of the inflationary phase. But a recent study based on the latest Planck release suggests that P ( k ) has a hard cut-off, k min ≠ 0 , inconsistent with this conventional picture. Here, we demonstrate quantitatively that most—perhaps all—slow-roll inflationary models fail to accommodate this minimum cut-off. We show that the small parameter ϵ must be ≳ 0.9 throughout the inflationary period to comply with the data, seriously violating the slow-roll approximation. Models with such an ϵ predict extremely red spectral indices, at odds with the measured value. We also consider extensions to the basic picture (suggested by several earlier workers) by adding a kinetic-dominated or radiation-dominated phase preceding the slow-roll expansion. Our approach differs from previously published treatments principally because we require these modifications not only to fit the measured fluctuation spectrum but also simultaneously to fix the horizon problem. We show, however, that even such measures preclude a joint resolution of the horizon problem and the missing correlations at large angles.

ΛCDM periodic cosmology

ABSTRACT We examine the possibility that Universe expansion be made of some Λ-cold dark matter (ΛCDM) expansions repeating periodically, separated by some inflation- and radiation-dominated phases. This so-called ΛCDM periodic cosmology is motivated by the possibility that inflation and the present phase of accelerated expansion be due to the same dark energy. Then, in a phase space showing the variation of matter density parameter Ωm with respect to this of the radiation Ωr, the curve Ωm(Ωr) looks like a closed trajectory that Universe could run through forever. In this case, the end of the expansion acceleration of the ΛCDM phase is the beginning of a new inflation phase. We show that such a scenario implies the coupling of matter and/or radiation to dark energy. We consider the simplest of these ΛCDM periodic models i.e. a vacuum energy coupled to radiation. From matter domination phase to today, it behaves like a ΛCDM model, then followed by an inflation phase. But a sudden and fast decay of the dark energy into radiation periodically ends the expansion acceleration. This leads to a radiation-dominated Universe preceding a new ΛCDM type expansion. The model is constrained with Markov Chain Monte Carlo simulations using supernovae, Hubble expansion, Baryon Acoustic Oscillations (BAO), and cosmic microwave background data and fits the data as well as the ΛCDM one.

Freeze-in production of dark matter prior to early matter domination

Freeze-out or freeze-in during a period of early matter domination can yield the correct dark matter abundance for small values of the velocity-averaged annihilation cross section, $\langle \sigma_{\rm ann} v \rangle_{\rm f} < 3 \times 10^{-26}$ cm$^3$ s$^{-1}$. However, in a generic non-standard thermal history, such a period is typically preceded by other phases. Here, we study production of dark matter in a simple post-inflationary history where a radiation-dominated phase after reheating is followed by an epoch of early matter domination. Focusing on the freeze-in regime, we show that dark matter production prior to early matter domination can dominate the relic abundance in large parts of the parameter space, including weak scale dark matter masses, and the allowed regions are highly dependent on the entire post-inflationary history. Moreover, for a very broad range of $\langle \sigma_{\rm ann} v \rangle_{\rm f}$ spanning over several decades, dark matter particles can start in chemical equilibrium early on and decouple during early matter domination, thereby rendering the relic abundance essentially independent of $\langle \sigma_{\rm ann} v \rangle_{\rm f}$. We briefly discuss connections to different observables as a possible means to test the elusive freeze-in scenario in this case.

Viability of Slow-Roll Inflation in Light of the Non-Zero K_min Measured in the Cmb Power Spectrum

Slow-roll inflation may simultaneously solve the horizon problem and generate a near scale-free fluctuation spectrum $P(k)$. These two processes are intimately connected via the initiation and duration of the inflationary phase. But a recent study based on the latest {\it Planck} release suggests that $P(k)$ has a hard cutoff, $k_{\rm min}\not=0$, inconsistent with this conventional picture. Here we demonstrate quantitatively that most — perhaps all — slow-roll inflationary models fail to accommodate this minimum cutoff. We show that the small parameter $\epsilon$ must be $\gtrsim 0.9$ throughout the inflationary period to comply with the data, seriously violating the slow-roll approximation. Models with such an $\epsilon$ predict extremely red spectral indices, at odds with the measured value. We also consider extensions to the basic picture (suggested by several earlier workers) by adding a kinetic-dominated or radiation-dominated phase preceding the slow-roll expansion. Our approach differs from previously published treatments principally because we require these modifications to — not only fit the measured fluctuation spectrum, but to simultaneously also — fix the horizon problem. We show, however, that even such measures preclude a joint resolution of the horizon problem and the missing correlations at large angles.

The quasi-steady-state cosmology in a radiation-dominated phase

Analytical solutions for radiation-dominated phase of Quasi-Steady-State Cosmology (QSSC) in Friedmann–Robertson–Walker models are obtained. We find that matter density is positive in all the cases [Formula: see text]. The nature of Hubble parameter (H) in [Formula: see text] is discussed. The deceleration parameter [Formula: see text] is marginally less than zero indicating accelerating universe. The scale factor [Formula: see text] is graphically shown with time. The model represents oscillating universe between the above-mentioned limits. Because of the bounce in QSSC, the maximum density phase is still matter-dominated. The models represent singularity-free model. We also find that the models have event horizon i.e. no observer beyond the proper distance [Formula: see text] can communicate each other in FRW models for radiation-dominated phase in the frame work of QSSC. The FRW models are special classes of Bianchi type I, V, IX spacetimes with zero, negative and positive curvatures, respectively. Initially i.e. at [Formula: see text], the models represent steady model. We have tried to show how a good fit can be obtained to the observations in the framework of QSSC during radiation-dominated phase. The present model is free from singularity, particle horizon and provides a natural explanation for the flatness problem. Therefore, our model is superior to other models.