Matter-dominated Phase Research Articles

Constraints on primordial black holes for nonstandard cosmologies

We study how the bounds on the abundance of Primordial Black Holes (PBHs) and the constraints on power spectrum are modified if a non-standard evolution phase takes place between the end of inflation and the Standard radiation-dominated (RD) universe after inflation. The constraints on PBH abundance and power spectrum are computed using the new, freely available, https://github.com/TadeoDGAguilar/PBHBeta PBHBeta library, which accounts for the effects of non-standard expansion and specific criteria for PBH formation in such non-standard scenarios. As working examples, we consider three different cases: a pure matter-dominated (MD) phase, a scalar field-dominated (φD) universe, and a stiff fluid-dominated (SD) scenario.While the background expansion is the same for the MD and φD scenarios, the PBH formation criteria lead to different constraints to power spectrum. On the other hand, the duration of the non-standard expansion phase alters the bounds, with longer MD periods resulting in weaker constraints on power spectrum, and longer SD scenarios leading to an enhanced abundance due to the dust-like redshifting of PBHs. The modifications to the constraints are reported in all cases and we highlight those where the power spectrum may be significantly constrained.

Distinguishing bounce and inflation via quantum signatures from cosmic microwave background

Cosmological inflation is a popular paradigm for understanding Cosmic Microwave Background Radiation (CMBR); however, it faces many conceptual challenges. An alternative mechanism to inflation for generating an almost scale-invariant spectrum of perturbations is a bouncing cosmology with an initial matter-dominated contraction phase, during which the modes corresponding to currently observed scales exited the Hubble radius. Bouncing cosmology avoids the initial singularity but has fine-tuning problems. Taking an agnostic view of the two early-universe paradigms, we propose a quantum measure — Dynamical Fidelity Susceptibility (DFS) of CMBR — that distinguishes the two scenarios. Taking two simple models with the same power-spectrum, we explicitly show that DFS behaves differently for the two scenarios. We discuss the possibility of using DFS as a distinguisher in the upcoming space missions.

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.

Cosmological solutions of chameleon scalar field model

We investigate cosmological solutions of the chameleon model with a non-minimal coupling between the matter and the scalar field through a conformal factor with gravitational strength. By considering the spatially flat FLRW metric and the matter density as a non-relativistic perfect fluid, we focus on the matter-dominated phase and the late-time accelerated-phase of the universe. In this regard, we manipulate and scrutinize the related field equations for the density parameters of the matter and the scalar fields with respect to the e-folding. Since the scalar field fluctuations depend on the background and the field equations become highly non-linear, we probe and derive the governing equations in the context of various cases of the relation between the kinetic and potential energies of the chameleon scalar field, or indeed, for some specific cases of the scalar field equation of state parameter. Thereupon, we schematically plot those density parameters for two different values of the chameleon non-minimal coupling parameter, and discuss the results. In the both considered phases, we specify that, when the kinetic energy of the chameleon scalar field is much less than its potential energy (i.e., when the scalar field equation of state parameter is ≃-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\simeq - 1 $$\\end{document}), the behavior of the chameleon model is similar to the ΛCDM\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda CDM$$\\end{document} model. Such compatibility suggests that the chameleon model is phenomenologically viable and can be tested with the observational data.

Dynamical systems analysis of an interacting scalar field model in an anisotropic universe

In this paper, we investigate a non-canonical scalar field model in the background dynamics of anisotropic Locally Rotationally Symmetric (LRS) Bianchi type I universe where gravity is coupled minimally to scalar field which is taken as dark energy and pressureless dust as dark matter are the main matter content of the universe. We perform dynamical system analysis to characterize the cosmological evolution of the model with and without interaction in the dark sector separately. First, we convert the evolution equation into an autonomous system of ordinary differential equations by using a suitable choice of dimensionless variables, which are normalized over the Hubble scale. We choose scalar field coupling and potential in such a way that the autonomous system converted to a 2D system. Linear stability theory is employed to the extracted critical points to find the nature. From the analysis, we find some interesting cosmological scenarios, such as late-time scalar-field dominated solutions, which evolve in the quintessence era, cannot solve the coincidence problem. Accelerated scaling attractors are also obtained that correspond to the late phase evolution in agreement with present observational data, and these solutions also provide possible mechanisms to alleviate the coincidence problem. A complete cosmic evolution is obtained from early inflation to a late-time dark energy-dominated phase, connecting through a matter-dominated transient phase of the universe. Furthermore, we find that for different values of the interaction parameter α, the evolutionary trajectories of the Hubble parameter, and the distance modulus forecasted by the model are in quite well agreement with observational datasets.

Homogeneous and anisotropic cosmologies with affine EoS: a dynamical system perspective

We study a class of homogeneous and anisotropic geometries with affine equation of state (EoS) for different physically plausible scenarios of the universe evolution using dynamical system technique. We analyze the locally rotationally symmetric Bianchi I (LRS BI), Bianchi III (LRS BIII) and Bianchi V (LRS BV) geometry for the exhibition of the effects of affine EoS in the model. The model exhibits stable attractor which is also isotropic and thus, it may explain the late-time accelerated expansion of the universe. The model also possess stiff matter-, radiation- and matter-dominated phases prior to the dark energy assisted accelerating phase which are confirmed by the behaviours of effective equation of state and deceleration parameters. We use the statefinder diagnostic which is a geometrical diagnostic to explore model independent features of the cosmological dynamical system. The LRS BI, BIII and BV geometry based dynamical systems exhibit r=1,s=0(Lambda cold dark matter model) at late-times, which is compatible with the observations. The dynamical system for the Kantowski–Sachs model yields synchronous bounce on the basis of the model parameters. It also yields a late-time attractor which may explain the accelerated expansion of the universe in the model. The qualitative differences between LRS BIII and BV cosmological dynamical systems have also been discussed.

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.

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.

Late time acceleration in Palatini gravity

We investigate the effect of the quadratic correction αR2 and non-minimal coupling ξϕ2R on a quintessence model with an exponential potential V(ϕ) = M4exp(−λϕ) in the Palatini formulation of gravity. We use dynamical system techniques to analyze the attractor structure of the model and uncover the possible trajectories of the system. We find that the quadratic correction cannot play a role in the late time dynamics, except for unacceptably large values of the parameter α; although it can play a role at early times. We find viable evolutions, from a matter-dominated phase to an accelerated expansion phase, with the dynamics driven by the non-minimal coupling. These evolutions correspond to trajectories where the field ends up frozen, thus acting as a cosmological constant.

Axions in string theory — slaying the Hydra of dark radiation

It is widely believed that string theory easily allows for a QCD axion in the cosmologically favored mass range. The required small decay constant, fa ≪ MP, can be implemented by using a large compactification volume. This points to the Large Volume Scenario which in turn makes certain cosmological predictions: first, the closed string axion behaves similarly to a field-theoretic axion in the pre-inflationary scenario, i.e. the initial value can be tuned but one is constrained by isocurvature fluctuations. In addition, the volume represents a long-lived modulus that may lead to an early matter-dominated phase. Finally, the decay of the volume modulus to its own axion tends to overproduce dark radiation. In this paper we aim to carefully analyze the cosmology by studying models that not only allow for a QCD axion but also include inflation. Quite generally, limits on isocurvature fluctuations restrict us to relatively low-scale inflation, which in the present stringy context points to Kähler moduli inflation. As a novel feature we find that the lightest (volume) modulus couples strongly to the Higgs. It hence quickly decays to the SM, thus resolving the original dark radiation problem. This decay is much faster than that of the inflaton, implying that reheating is determined by the inflaton decay. The inflaton could potentially reintroduce a dark radiation problem since it decays to lighter moduli and their axions with equal rates. However, due its mixing with the QCD-saxion, the inflaton has also a direct decay rate to the SM, enhanced by the number of SM gauge bosons. This results in an amount of dark radiation that is consistent with present limits but potentially detectable in future measurements.

Primordial black holes from spectator field bubbles

We study the evolution of light spectator fields in an asymmetric polynomial potential. During inflation, stochastic fluctuations displace the spectator field from the global minimum of its potential, populating the false vacuum state and thereby allowing for the formation of false vacuum bubbles. By using a lattice simulation, we show that these bubbles begin to contract once they re-enter the horizon and, if sufficiently large, collapse into black holes. This process generally results in the formation of primordial black holes, which, due to the specific shape of their mass function, are constrained to yield at most 1% of the total dark matter abundance. However, the resulting population can source gravitational wave signals observable at the LIGO-Virgo experiments, provide seeds for supermassive black holes or cause a transient matter-dominated phase in the early Universe.

Continuous cosmic evolution with diffusive barotropic fluid: First-order thermodynamic phase transition

In the background of homogeneous and isotropic flat FLRW model, a complete cosmic scenario from nonsingular emergent scenario to the present late time acceleration through inflationary era and matter-dominated epoch has been presented in this work with cosmic matter in the form of diffusive barotropic fluid. By proper choices of the diffusion parameter and using Friedmann equations, it is possible to show the transitions: Emergent scenario[Formula: see text]Inflationary era[Formula: see text]matter-dominated phase[Formula: see text]Late time acceleration epoch. In analogy with analytic continuation, it is found that the above evolution will be continuous for suitable values of the parameters involved. Finally, possible first-order thermodynamic phase transition has been analyzed for such cosmic evolution.

Neutrinos as a probe of curvature

Neutrinos, as the anisotropic stress tensor, have a damping effect on the tensor mode perturbation from inflation to the Λ dominated era. First, we study the squared amplitude reduction for the wavelength entering the horizon during radiation and matter-dominated phases in the negatively curved de Sitter spacetime. Then, by comparing with other spatial spacetimes, K=0 and K=1, the highest difference between closed and open cases is seen in the matter-dominated era. Thus, neutrinos can be added as another candidate for determining the nature of space-time.

Is asymptotically Weyl-invariant gravity viable?

We explore the cosmological viability of a theory of gravity defined by the Lagrangian $f(\mathcal{R})=\mathcal{R}^{n\left(\mathcal{R}\right)}$ in the Palatini formalism, where $n\left(\mathcal{R}\right)$ is a dimensionless function of the Palatini scalar curvature $\mathcal{R}$ that interpolates between general relativity when $n\left(\mathcal{R}\right)=1$ and a locally scale-invariant and superficially renormalizable theory when $n\left(\mathcal{R}\right)=2$. We refer to this model as asymptotically Weyl-invariant gravity (AWIG). We analyse perhaps the simplest possible implementation of AWIG. A phase space analysis yields three fixed points with effective equation of states corresponding to de Sitter, radiation and matter-dominated phases. An analysis of the deceleration parameter suggests our model is consistent with an early and late period of accelerated cosmic expansion, with an intermediate period of decelerated expansion. We show that the model contains no obvious curvature singularities. Therefore, AWIG appears to be cosmologically viable, at least for the simple implementation explored.

Baryogenesis through asymmetric Hawking radiation from primordial black holes as dark matter

We examine the extent to which primordial black holes (PBHs) can constitute the observed dark matter while also giving rise to the measured matter-antimatter asymmetry and account for the observed baryon abundance through asymmetric Hawking radiation generated by a derivative coupling of curvature to the baryon-lepton current. We consider both broad and monochromatic mass spectra for this purpose. For the monochromatic spectrum we find that the correct dark matter and baryon energy densities are recovered for peak masses of the spectrum of $M_{\rm pk} \geq 10^{12}$ kg whereas for the broad case the observed energy densities can be reproduced regardless of peak mass. Adopting some simplifications for the early-time expansion history as a first approximation, we also find that the measured baryon asymmetry can be recovered within an order of magnitude. We argue furthermore that the correct value of the baryon-lepton yield can in principle be retrieved for scenarios where a significant amount of the radiation is produced by PBH decay during or after reheating, as is expected when the decaying PBHs also cause reheating, or when an early matter-dominated phase is considered. We conclude from this first analysis that the model merits further investigation.

Primordial power spectrum from a matter-ekpyrotic bounce scenario in loop quantum cosmology

A union of matter bounce and Ekpyrotic scenarios is often studied in an attempt to combine the most promising features of these two models. Since non-perturbative quantum geometric effects in loop quantum cosmology (LQC) result in natural bouncing scenarios without any violation of energy conditions or fine tuning, an investigation of matter-Ekpyrotic bounce scenario is interesting to explore in this quantum gravitational setting. In this work, we explore this unified phenomenological model for a spatially flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe in LQC filled with dust and a scalar field in an Ekpyrotic scenario like negative potential. Background dynamics and the power spectrum of the comoving curvature perturbations are numerically analyzed with various initial conditions and a suitable choice of the initial states. By varying the initial conditions we consider different cases of dust and Ekpyrotic field domination in the contracting phase. We use the dressed metric approach to numerically compute the primordial power spectrum of the comoving curvature perturbations which turns out to be almost scale invariant for the modes which exit the horizon in the matter-dominated phase. But, in contrast with a constant magnitude power spectrum obtained under approximation of a constant Ekpyrotic equation of state using deformed algebra approach in an earlier work, we find that the magnitude of power spectrum changes during evolution. Our analysis shows that the bouncing regime only leaves imprints on the modes outside the scale-invariant regime. However, an analysis of the spectral index shows inconsistency with the observational data, thus making further improvements in such a model necessary.

Formation of inflaton halos after inflation

The early Universe may have passed through an extended period of matter-dominated expansion following inflation and prior to the onset of radiation domination. Subhorizon density perturbations grow gravitationally during such an epoch, collapsing into bound structures if it lasts long enough. The strong analogy between this phase and structure formation in the present-day Universe allows the use of $N$-body simulations and approximate methods for halo formation to model the fragmentation of the inflaton condensate into inflaton halos. For a simple model we find that these halos have masses of up to 20 kg and radii of the order of ${10}^{\ensuremath{-}20}\text{ }\text{ }\mathrm{m}$, roughly ${10}^{\ensuremath{-}24}$ seconds after the big bang. We find that the $N$-body halo mass function matches predictions of the mass-peak patch method and the Press-Schechter formalism within the expected range of scales. A long matter-dominated phase would imply that reheating and thermalization occurs in a universe with large variations in density, potentially modifying the dynamics of this process. In addition, large overdensities can source gravitational waves and may lead to the formation of primordial black holes.

LRS Bianchi type-I bouncing cosmological models in f(R,T) gravity

In this work, we have investigated the cosmological bouncing solution in LRS Bianchi-I space-time in framework of [Formula: see text] gravity. Our study in this paper is based on the modeling of matter bounce scenario in which the universe starts with a matter-dominated contraction phase and transitions into an ekpyrotic phase. Mathematical simulations have been done in the modified general theory of relativity in the form of [Formula: see text] theory proposed by Harko et al. [f(R, T) gravity, Phys. Rev. D 84 (2011) 024020], whose functional form is as [Formula: see text] where [Formula: see text] is Ricci scalar, [Formula: see text] is trace of energy–momentum tensor and [Formula: see text] is constant. Taking the non-vanishing scale factor in LRS Bianchi-I space-time, the geometrical parameters such as Hubble parameter and deceleration parameter have been derived and their subsequent use in the expression of pressure, density and EoS parameter [Formula: see text] confirms qualitatively the initial conditions of the universe at the bounce. With the non-vanishing nature of scale factor, initial universe in finite means ruled out the initial singularity problem. The analysis of violation of energy conditions near the bouncing region and stability of the model shows that the matter bounce approach is highly unstable at the bounce but the rapid decay of perturbations away from the bounce supports the stability of the model.

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.

Anisotropic dark energy cosmological model with cosmic strings

This study deals with a spatially homogeneous locally rotationally symmetric Bianchi type-I dark energy cosmological model containing a one-dimensional cosmic string fluid source. Einstein’s field equations are solved by using a relation between the metric potentials and hybrid expansion law of the average scale factor. We discuss the accelerated expansion of our model through the equation of state (EOS; ωde) and deceleration parameter (q). We observe that in the evolution of our model, the EOS parameter starts from matter-dominated phase ωde > −1/3 and ultimately attains a constant value in the quintessence region (−1 < ωde < −1/3). The EOS parameter of the model never crosses the phantom divide line (ωde = −1). These facts are consistent with recent observations. We also discuss some other physical parameters.