Matter-dominated Era Research Articles

Cosmological dynamics of brane gravity: A global dynamical system perspective

The braneworld model of gravity is well-known for several notable cosmological features such as self-acceleration originating from a geometric and not matter source, effective dark energy behavior with phantom characteristics but not leading to a Big-Rip singularity, rough resemblance to the $\Lambda$CDM evolution, etc. The dynamical system tools usually allow us to obtain generic conclusions on the global dynamics of a system over a wide range of initial conditions. With this motivation, in order to recover the important features of the braneworld model from a more global perspective, here, we investigate the global cosmological dynamics of the braneworld model using dynamical system techniques. We first analyze the case where there is just a normal matter on the brane and then extend the analysis to the case with an extra scalar field also trapped on the brane. In the presence of a scalar field, potentials belonging to different classes are considered. The stability behavior of critical points is examined using linear stability analysis and when necessary center manifold theory as well as numerical perturbation techniques are also used. To understand the global dynamics of a dynamical system, we utilized the Poincar\'e compactification method to capture the properties of all possible critical points. Applying dynamical system analysis, we found that brane gravity is consistent with observed actions of the Universe. In particular, our analysis shows that important cosmological behaviors like the long-lasting matter-dominated era, late time acceleration as well as the avoidance of Big-Rip singularity can be realized in brane gravity for a wide range of initial conditions.

Constraining non-thermal dark matter by CMB

A period of early matter domination can give rise to the correct dark matter abundance for a broad range of dark matter annihilation rate ⟨ σann v ⟩f. Here, we examine this scenario for situations where ⟨ σann v ⟩f is below the nominal value for thermal dark matter 3 × 10−26 cm3 s−1 as possibly indicated by some recent experiments. We show that obtaining the correct relic abundance sets a lower bound on the duration of early matter domination era in this case. On the other hand, provided that the post-inflationary universe has an equation of state characterized by w ⩽ 1/3, the requirement that the scalar spectral index ns be within the observationally allowed range limits the duration of this epoch from above. By combining these considerations, we show that the current and future cosmic microwave background experiments can tightly constrain the parameter space for this scenario. In particular, models of inflation with a scalar-to-tensor ratio below \U0001d4aa(0.01) may disfavor non-thermal supersymmetric dark matter from a modulus-driven early matter domination epoch.

A study of perturbations in scalar–tensor theory using 1 + 3 covariant approach

This work discusses scalar–tensor theories of gravity, with a focus on the Brans–Dicke sub-class, and one that also takes note of the latter’s equivalence with [Formula: see text] gravitation theories. A [Formula: see text] covariant formalism is used in this case to discuss covariant perturbations on a background Friedmann–Laimaître–Robertson–Walker (FLRW) spacetime. Linear perturbation equations are developed based on gauge-invariant gradient variables. Both scalar and harmonic decompositions are applied to obtain second-order equations. These equations can then be used for further analysis of the behavior of the perturbation quantities in such a scalar–tensor theory of gravitation. Energy density perturbations are studied for two systems, namely for a scalar fluid-radiation system and for a scalar fluid-dust system, for [Formula: see text] models. For the matter-dominated era, it is shown that the dust energy density perturbations grow exponentially, a result which agrees with those already existing in the literatures. In the radiation-dominated era, it is found that the behavior of the radiation energy–density perturbations is oscillatory, with growing amplitudes for [Formula: see text], and with decaying amplitudes for [Formula: see text]. This is a new result.

Primordial black holes from inflaton and spectator field perturbations in a matter-dominated era

We study production of primordial black holes (PBHs) during an early matter-dominated phase. As a source of perturbations, we consider either the inflaton field with a running spectral index or a spectator field that has a blue spectrum and thus provides a significant contribution to the PBH production at small scales. First, we identify the region of the parameter space where a significant fraction of the observed dark matter can be produced, taking into account all current PBH constraints. Then, we present constraints on the amplitude and spectral index of the spectator field as a function of the reheating temperature. We also derive constraints on the running of the inflaton spectral index, ${\rm d}n/{\rm d}{\rm ln}k \lesssim -0.002$, which are comparable to those from the Planck satellite for a scenario where the spectator field is absent.

Interaction of viscous modified Chaplygin gas with f(R, T) gravity

We study the evolution of viscous modified Chaplygin gas (MCG) interacting with f(R, T) gravity in flat FRW universe, where T is the trace of energy–momentum tensor. The field equations are formulated for a particular model f(R, T) = R + 2[Formula: see text]T and constraints for the conservation of energy–momentum tensor are obtained. We investigate the behavior of total energy density, pressure and equation of state (EoS) parameter for emergent, intermediate as well as logamediate scenarios of the universe with two interacting models. It is found that the EoS parameter lies in the matter-dominated or quintessence era for all the three scenarios while the bulk viscosity enhances the expansion for the intermediate and logamediate scenarios.

New bound on low reheating temperature for dark matter in models with early matter domination

We investigate a new bound on the low reheating temperature in a scenario where the Universe experiences early matter-domination before reheating after which the standard big bang cosmology begins. In many models of dark matter (DM), the small scale fluctuations of DM grow during the early matter-domination era and seed the formation of the ultracompact minihalos (UCMHs). Using the constraints on the number of UCMHs from gamma-ray observations, we find a lower bound on the reheating temperature between ${\cal O}(10)~{\rm MeV} - {\cal O}(100)~{\rm MeV}$ for WIMP dark matter depending on the nature of DM. A similar bound could be obtained for non-WIMP dark matter by observing UCMHs gravitationally such as pulsar timing, microlensing and so on in some future observations.

Damping of gravitational waves in matter and [formula omitted]dominated era

The goal of this paper is studying the integro-differential equation of gravitational waves (GWs) in matter-dominated era while the presence of free streaming neutrinos is taken into account via stress tensor with high accuracy. Our focus is on GWs that enter the horizon in the matter dominated era and transmitted to the Λ− dominated era. The results show that the squared amplitude is reduced by ∼ 3% (61%) in the matter dominated era and this reduction is less after transition for the flat (closed) background. Finally, we compared with the radiation-dominated era for both flat and closed background as well. A stable global topological effect has been inferred from comparison of results for two cases.

Solar system tests for realistic f(T) models with non-minimal torsion\u2013matter coupling

In the previous paper, we have constructed two f(T) models with non-minimal torsion–matter coupling extension, which are successful in describing the evolution history of the Universe including the radiation-dominated era, the matter-dominated era, and the present accelerating expansion. Meantime, the significant advantage of these models is that they could avoid the cosmological constant problem of Lambda CDM. However, the non-minimal coupling between matter and torsion will affect the tests of the Solar system. In this paper, we study the effects of the Solar system in these models, including the gravitation redshift, geodetic effect and perihelion precession. We find that Model I can pass all three of the Solar system tests. For Model II, the parameter is constrained by the uncertainties of the planets’ estimated perihelion precessions.

Quasidecoupled state for dark matter in nonstandard thermal histories

Dark matter drops out of kinetic equilibrium with standard model particles when the momentum-transfer rate equals the expansion rate. In a radiation-dominated universe, this occurs at essentially the same time as dark matter kinetically decouples from the plasma. Dark matter may also fall out of kinetic equilibrium with standard model particles during an early matter-dominated era (EMDE), which occurs when the energy content of the Universe is dominated by either a decaying oscillating scalar field or a semistable massive particle before big bang nucleosynthesis. Until now, it has been assumed that kinetic decoupling during an EMDE happens similarly to the way it does in a radiation-dominated era. We show that this is not the case. By studying the evolution of the dark matter temperature, we establish a quasidecoupled state for dark matter in an EMDE, during which the dark matter temperature cools faster than the plasma temperature but slower than it would cool if the dark matter were fully decoupled. The dark matter does not fully decouple until the EMDE ends and the Universe becomes radiation dominated. We also extend the criteria for quasidecoupling to other nonstandard thermal histories and consider how quasidecoupling affects the free-streaming length of dark matter.

Gauge Dependence of Gravitational Waves Generated from Scalar Perturbations

Abstract A tensor-type cosmological perturbation, defined as a transverse and traceless spatial fluctuation, is often interpreted as gravitational waves. While decoupled from the scalar-type perturbations in linear order, the tensor perturbations can be sourced from the scalar-type in nonlinear order. The tensor perturbations generated by the quadratic combination of a linear scalar-type cosmological perturbation are widely studied in the literature, but all previous studies are based on a zero-shear gauge without proper justification. Here, we show that, being second order in perturbation, such an induced tensor perturbation is generically gauge dependent. In particular, the gravitational wave power spectrum depends on the hypersurface (temporal gauge) condition taken for the linear scalar perturbation. We further show that, during the matter-dominated era, the induced tensor modes dominate over the linearly evolved primordial gravitational wave amplitude for even for the gauge that gives the lowest induced tensor modes with the optimistic choice of primordial gravitational waves (r = 0.1). The induced tensor modes, therefore, must be modeled correctly specific to the observational strategy for the measurement of primordial gravitational waves from large-scale structure via, for example, the parity-odd mode of weak gravitational lensing, or clustering fossils.

Bulk viscosity, interaction and the viability of phantom solutions

We study the dynamics of a bulk viscosity model in the Eckart approach for a spatially flat Friedmann–Robertson–Walker (FRW) Universe. We have included radiation and dark energy, assumed as perfect fluids, and dark matter treated as an imperfect fluid having bulk viscosity. We also introduce an interaction term between the dark matter and dark energy components. Considering that the bulk viscosity is proportional to the dark matter energy density and imposing a complete cosmological dynamics, we find bounds on the bulk viscosity in order to reproduce a matter-dominated era (MDE). This constraint is independent of the interaction term. Some late time phantom solutions are mathematically possible. However, the constraint imposed by a MDE restricts the interaction parameter, in the phantom solutions, to a region consistent with a null value, eliminating the possibility of late time stable solutions with w<-1. From the different cases that we study, the only possible scenario, with bulk viscosity and interaction term, belongs to the quintessence region. In the latter case, we find bounds on the interaction parameter compatible with latest observational data.

Perturbative instability of inflationary cosmology from quantum potentials

It was argued that the Raychaudhuri equation with a quantum correction term seems to avoid the Big Bang singularity and to characterize an everlasting Universe [PLB741,276(2015)]. Critical comments on both conclusions and on the correctness of the key expressions of this work were discussed in literature [MPLA31(2016)1650044]. In the present work, we have analyzed the perturbative (in)stability conditions in the inflationary era of the early Universe. We conclude that both unstable and stable modes are incompatible with the corresponding ones obtained in the standard FLRW Universe. We have shown that unstable modes do exist at small (an)isotropic perturbation and for different equations of state. Inequalities for both unstable and stable solutions with the standard FLRW space were derived. They reveal that in the FLRW flat Universe both perturbative instability and stability are likely. While negative stability modes have been obtained for radiation- and matter-dominated eras, merely, instability modes exist in case of a finite cosmological constant and also if the vacuum energy dominates the cosmic background geometry.

Comment on “Kinetic decoupling of WIMPs: Analytic expressions”

Visinelli and Gondolo (2015, hereafter VG15) derived analytic expressions for the evolution of the dark matter temperature in a generic cosmological model. They then calculated the dark matter kinetic decoupling temperature $T_{\mathrm{kd}}$ and compared their results to the Gelmini and Gondolo (2008, hereafter GG08) calculation of $T_{\mathrm{kd}}$ in an early matter-dominated era (EMDE), which occurs when the Universe is dominated by either a decaying oscillating scalar field or a semistable massive particle before Big Bang nucleosynthesis. VG15 found that dark matter decouples at a lower temperature in an EMDE than it would in a radiation-dominated era, while GG08 found that dark matter decouples at a higher temperature in an EMDE than it would in a radiation-dominated era. VG15 attributed this discrepancy to the presence of a matching constant that ensures that the dark matter temperature is continuous during the transition from the EMDE to the subsequent radiation-dominated era and concluded that the GG08 result is incorrect. We show that the disparity is due to the fact that VG15 compared $T_\mathrm{kd}$ in an EMDE to the decoupling temperature in a radiation-dominated universe that would result in the same dark matter temperature at late times. Since decoupling during an EMDE leaves the dark matter colder than it would be if it decoupled during radiation domination, this temperature is much higher than $T_\mathrm{kd}$ in a standard thermal history, which is indeed lower than $T_{\mathrm{kd}}$ in an EMDE, as stated by GG08.

Structure formation in the Deser-Woodard nonlocal gravity model: a reappraisal

In this work, we extend previous analyses of the structure formation in the f(□−1R) model of nonlocal gravity proposed by Deser and Woodard (DW), which reproduces the background expansion of ΛCDM with no need of a cosmological constant nor of any dimensional constant beside Newton's one. A previous analysis based on redshift-space distortions (RSD) data concluded that the model was ruled out. In this work we revisit the issue and find that, when recast in a localized model, the DW model is not ruled out and actually gives a better fit to RSD data than ΛCDM. In fact, the DW model presents a suppressed growth of matter perturbations with respect to ΛCDM and a slightly lower value of σ8, as favored by observations. We also produce analytical approximations of the two modified gravity functions, i.e. the anisotropic stress η and the relative change of Newton's constant Y, and of fσ8(z) as a function of redshift. Finally, we also show how much the fit depends on initial conditions when these are generalized with respect to a standard matter-dominated era.

Unification of late- and early-time acceleration, with that of the intermediate eras, by scalar fields

In this work we shall investigate how to realize a cosmological evolution which describes all the evolution eras of our Universe, by using scalar-tensor theories. Particularly, we shall use single scalar and two-scalar theories, and by employing several well known reconstruction schemes, we shall investigate which scalar-tensor theories can realize the unification cosmology. For both the single and two-scalar theories, we find the kinetic terms and the potential of the theory and we also address the issue of the stability of the solutions towards linear perturbations. As we show, in the two-scalar description no instabilities occur, but in the single scalar description, certain solutions are unstable. Also we demonstrate that in the single scalar case, the power spectrum corresponding to early times is nearly scale invariant and compatible with the latest observational data. Finally, we perform an analysis of the effective equation of state, and we show that the EoS describes in a unified way early and late-time acceleration, and in addition it also describes the radiation and matter domination era between the acceleration eras.

Instabilities in tensorial nonlocal gravity

We discuss the cosmological implications of nonlocal modifications of general relativity containing tensorial structures. Assuming the presence of standard radiation- and matter-dominated eras, we show that, except in very particular cases, the nonlocal terms contribute a rapidly growing energy density. These models therefore generically do not have a stable cosmological evolution.

Holographic dark energy with the sign-changeable interaction term

We use three infrared (IR) cutoffs, including the future event horizon, the Hubble and Granda–Oliveros (GO) cutoffs, to construct three holographic models of dark energy (DE). Additionally, we consider a Friedmann–Robertson–Walker (FRW) universe filled by a dark matter (DM) and a DE that interact with each other through a mutual sign-changeable interaction with positive coupling constant. Thereinafter, we address the evolution of the some cosmological parameters, such as the equation of state (EoS) and dimensionless density parameters of DE as well as the deceleration parameter, during the cosmic evolution from the matter-dominated era until the late-time acceleration. We observe that a holographic dark energy (HDE) model with Hubble cutoff interacting with DM cannot be in line with the current universe. Our study shows that models with the future event horizon as the IR cutoff or the GO cutoff are in good agreement with the observational data. In fact, we find out that these two recent models can predict the universe transition from a deceleration phase to the acceleration one in a compatible way with observations. The three obtained models may also allow the EoS parameter to cross the phantom line, a result which depends on the values of the system’s constants such as the value of the interaction coupling constant.

PRIMORDIAL BLACK HOLE FORMATION IN THE MATTER-DOMINATED PHASE OF THE UNIVERSE

ABSTRACT We investigate primordial black hole formation in the matter-dominated phase of the universe, where nonspherical effects in gravitational collapse play a crucial role. This is in contrast to the black hole formation in a radiation-dominated era. We apply the Zel’dovich approximation, Thorne’s hoop conjecture, and Doroshkevich’s probability distribution and subsequently derive the production probability of primordial black holes. The numerical result obtained is applicable even if the density fluctuation σ at horizon entry is of the order of unity. For , we find a semi-analytic formula , which is comparable to the Khlopov–Polnarev formula. We find that the production probability in the matter-dominated era is much larger than that in the radiation-dominated era for , while they are comparable with each other for . We also discuss how σ can be written in terms of primordial curvature perturbations.

Determining cosmology for a nonlocal realization of MOND

We numerically determine the cosmological branch of the free function in a nonlocal metric-based modification of gravity which provides a relativistic generalization of Milgrom's Modified Newtonian Dynamics. We are able to reproduce the $\Lambda$CDM expansion history over virtually all of cosmic history, including the era of radiation domination during Big Bang Nucleosynthesis, the era of matter domination during Recombination, and most of the era of vacuum energy domination. The very late period of $0 \leq z < 0.0880$, during which the model deviates from the $\Lambda$CDM expansion history, is interesting because it causes the current value of the Hubble parameter to be about 4.5\% larger than it would be for the $\Lambda$CDM model. This may resolve the tension between inferences of $H_0$ which are based on data from large redshift and inferences based on Hubble plots.

Supersymmetric axion grand unified theories and their predictions

We introduce a class of unified supersymmetric axion theories with unified and PQ symmetries broken by the same set of fields at a scale $\sim 2\times 10^{16}$ GeV. A typical domain wall number of order 30 leads to an axion decay constant $f_a$ of order $10^{15}$ GeV. Inflation generates a large saxion condensate giving a reheat temperature $T_R$ below the QCD scale for supersymmetry breaking of order $1-10$ TeV. Axion field oscillations commence in the saxion matter-dominated era near the QCD scale, and recent lattice computations of the temperature dependence of the axion mass in this era allow a controlled calculation of the axion dark matter abundance. A successful prediction of this abundance results for an initial axion misalignment angle of order unity, $\theta_i \sim 1$. A highly correlated set of predictions is discussed for $f_a$, $T_R$, the supersymmetric Higgs mass parameter $\mu$, the amount of dark radiation $\Delta N_{eff}$, the proton decay rate $\Gamma(p \rightarrow e^+ \pi^0)$, isocurvature density perturbations and the $B$-mode of the cosmic microwave background. The last two are particularly interesting when the energy scale of inflation is also of order $10^{16}$ GeV.