Cosmology with a stiff matter era

We investigate models of interacting dark matter and dark energy for the\nuniverse in a spatially flat Friedmann-Robertson-Walker (FRW) space-time. We\nfind the "source equation" for the total energy density and determine the\nenergy density of each dark component. We introduce an effective one-fluid\ndescription to evidence that interacting and unified models are related with\neach other, analyze the effective model and obtain the attractor solutions. We\nstudy linear and nonlinear interactions, the former comprises a linear\ncombination of the dark matter and dark energy densities, their first\nderivatives, the total energy density, its first and second derivatives and a\nfunction of the scale factor. The latter is a possible generalization of the\nlinear interaction consisting of an aggregate of the above linear combination\nand a significant nonlinear term built with a rational function of the dark\nmatter and dark energy densities homogeneous of degree one. We solve the\nevolution equations of the dark components for both interactions and examine\nexhaustively several examples. There exist cases where the effective one-fluid\ndescription produces different alternatives to the $\\La$CDM model and cases\nwhere the problem of coincidence is alleviated. In addition, we find that some\nnonlinear interactions yield an effective one-fluid model with a Chaplygin gas\nequation of state, whereas others generate cosmological models with de Sitter\nand power-law expansions. We show that a generic nonlinear interaction induces\nan effective equation of state which depends on the scale factor in the same\nway that the variable modified Chaplygin gas model, giving rise to the "relaxed\nChaplygin gas model".\n

A field theory is proposed where the regular fermionic matter and the dark fermionic matter can be different states of the same "primordial" fermion fields. In regime of the fermion densities typical for normal particle physics, the primordial fermions split into three families identified with regular fermions. When fermion energy density becomes comparable with dark energy density, the theory allows transition to new type of states. The possibility of such Cosmo-Low Energy Physics (CLEP) states is demonstrated by means of solutions of the field theory equations describing FRW universe filled with homogeneous scalar field and uniformly distributed nonrelativistic neutrinos. Neutrinos in CLEP state are drawn into cosmological expansion by means of dynamically changing their own parameters. One of the features of the fermions in CLEP state is that in the late time universe their masses increase as a3/2 (a=a(t) is the scale factor). The energy density of the cold dark matter consisting of neutrinos in CLEP state scales as a sort of dark energy; this cold dark matter possesses negative pressure and for the late time universe its equation of state approaches that of the cosmological constant. The total energy density of such universe is less than it would be in the universe free of fermionic matter at all.

During the cosmic evolution process, as the temperature of a cosmological boson gas falls below a certain threshold, a Bose–Einstein condensation process can occur at various points throughout the cosmic history of the Universe. In this model, dark matter, conceptualized as a non-relativistic, Newtonian gravitational condensate is governed by the Gross–Pitaevskii–Poisson system. In our present study, we investigate the Bose–Einstein condensation process of bosonic DM by treating it as an approximate first-order phase transition within a modified cosmological framework, known as Tsallis cosmology. We examine the evolution of relevant physical quantities characterizing the evolution dynamics of the Universe, including energy density, temperature, redshift, scale factor, Hubble parameter, and dimensionless deceleration parameter before, during, and following the Bose–Einstein condensation phase transition takes place. Additionally, we especially investigate the specific era of the evolution of the Universe characterized by a mixture of normal and condensate phases of dark matter. We analyze the behavior of temporal evolution of an important time-dependent parameter, called the condensate dark matter fraction throughout the condensation process and find the time duration of condensation of dark matter in the Tsallis cosmological model. We see that the presence of Bose–Einstein condensate dark matter in the framework of Tsallis-modified cosmology significantly alters the cosmological evolution of the Universe as compared to the standard model of cosmology. We also find for a typical value of Tsallis non-extensive parameter β=0.35, the model could explain an accelerated Universe without invoking any additional energy component and solve the age problem of our Universe.

Gravitational wave (GW) standard siren observations provide a rather useful tool to explore the evolution of the Universe. In this work, we wish to investigate whether dark sirens with neutron star (NS) deformation from third-generation GW detectors could help probe the interaction between dark energy and dark matter. We simulate the GW dark sirens of four detection strategies based on 3 yr observation and consider four phenomenological interacting dark energy (IDE) models to perform cosmological analysis. We find that GW dark sirens could provide tight constraints on Ωm and H 0 in the four IDE models but do not perform well in constraining the dimensionless coupling parameter β in models of the interaction proportional to the energy density of cold dark matter. Nevertheless, the parameter degeneracy orientations of cosmic microwave background (CMB) and GW are almost orthogonal, and thus, the combination of them could effectively break cosmological parameter degeneracies, with the constraint errors of β being 0.00068–0.018. In addition, we choose three typical equations of state (EoSs) of an NS, i.e., SLy, MPA1, and MS1, to investigate the effect of an NS’s EoS on cosmological analysis. The stiffer EoS could give tighter constraints than the softer EoS. Nonetheless, the combination of CMB and GW dark sirens (using different EoSs of an NS) shows basically the same constraint results of cosmological parameters. We conclude that the dark sirens from 3G GW detectors would play a crucial role in helping probe the interaction between dark energy and dark matter, and the CMB+GW results are basically not affected by the EoS of an NS.

We explore a cosmological model composed by a dark matter fluid interacting with a dark energy fluid. The interaction term has the non-linear λρmαρeβ form, where ρm and ρe are the energy densities of the dark matter and dark energy, respectively. The parameters α and β are in principle not constrained to take any particular values, and were estimated from observations. We perform an analytical study of the evolution equations, finding the fixed points and their stability properties in order to characterize suitable physical regions in the phase space of the dark matter and dark energy densities. The constants (λ,α,β) as well as wm and we of the EoS of dark matter and dark energy respectively, were estimated using the cosmological observations of the type Ia supernovae and the Hubble expansion rate H(z) data sets. We find that the best estimated values for the free parameters of the model correspond to a warm dark matter interacting with a phantom dark energy component, with a well goodness-of-fit to data. However, using the Bayesian Information Criterion (BIC) we find that this model is overcame by a warm dark matter – phantom dark energy model without interaction, as well as by the ΛCDM model. We find also a large dispersion on the best estimated values of the (λ,α,β) parameters, so even if we are not able to set strong constraints on their values, given the goodness-of-fit to data of the model, we find that a large variety of theirs values are well compatible with the observational data used.

In this article we describe a model of the universe consisting of a mixture of the ordinary matter and a so-called cosmic quaternionic field. The basic idea here consists in an attempt to interpret Λ as the energy density of the quaternionic field whose source is any form of energy including the proper energy density of this field. We set the energy density of this field to Λ and show that the ratio of ordinary dark matter energy density assigned to Λ is constant during the cosmic evolution. We investigate the interaction of the quaternionic field with the ordinary dark matter and show that this field exerts a force on the moving dark matter which might possible create the dark matter in the early universe. Such determined Λ fulfils the requirements asked from the dark energy. In this model of the universe, the cosmological constant, the fine-tuning and the age problems might be solved. Finally, we sketch the evolution of the universe with the cosmic quaternionic field and show that the energy density of the cosmic quaternionic field might be a possible candidate for the dark energy.

A formula for calculating dark energy is established through derivation. The result is tested on the basis of the available data from the MAX PLANCK Institute for Radio Astronomy. The universe's dark matter has been computed. There is a balance sheet created and the most important formulas compiled. Summary: The rudiments of a theory of dark energy. The theoretical result is confronted with the numerical value calculated from the available data. Excellent matching of numerical values resulting in three independent paths makes the approach plausible. The approach is credible because of the excellent matching of numerical values that produces three separate routes. The task at hand is comparable to Kepler's planetary orbital rules. Only Isaac Newton gave Kepler's laws a theoretical foundation, which Thomass Gornitz provides here. Niels Bohr, who computed the energy levels of the hydrogen atom and the frequencies of spectral lines, theoretically supported the empirical Balmer formula for the spectral line frequencies in the arc spectrum of the hydrogen atom. A mysterious element known as dark energy is theorized to accelerate the universe's expansion by repelling matter. Theorists have proposed a variety of methods to calculate dark energy over the years. Numerous theories, however, fail to apply a metric structure to gravity or energy momentum conservation even when they satisfy strict local tests. The most popular option for dark energy is the cosmological constant, often known as vacuum energy density. By its very nature, dark energy is a low-energy phenomenon that is dispersed. It is not present in galaxies or galaxies in clusters and it is probably unlikely to be found in laboratory research. The repellent dark energy that hastens the universe's expansion could be explained if the cosmological constant is the vacuum energy of space. Nobody, however, is aware of the cosmological constant's existence or the amount that might be assigned to it in order to calculate the universe's acceleration. Any two matter fields can interact with each other in particle physics or on a more theoretical level, according to a possible process called the interaction of dark matter and dark energy. The phenomenological theory in question has aroused the interest of the cosmology community for a number of reasons. As in the interaction model, where dark energy decays into dark matter, interacting models of DM and DE are an equivalent description of the dark sector of the universe that have undergone extensive research and are motivated by a viable explanation to the so called coincidence and cosmological constant concerns. Keywords Dark energy; Dark matter; Calculation; PLANCK time; Age of the universe; Cosmic information

We establish the Hamiltonian analysis and the canonical path integral for a local formulation of vacuum energy sequestering. In particular, by considering the state of the universe as a superposition of vacuum states corresponding to different values of the cosmological and gravitational constants, the path integral is extended to include integrations over the cosmological and gravitational constants. The result is an extension of the Ng-van Dam form of the path integral of unimodular gravity. It is argued to imply a relation between the fraction of the most likely values of the gravitational and cosmological constants and the average values of the energy density and pressure of matter over spacetime. Finally, we construct and analyze a BRST-exact formulation of the theory, which can be considered as a topological field theory.

In this paper we place observational constraints on the interactionand spatial curvature in the holographic dark energy model. Weconsider three kinds of phenomenological interactions betweenholographic dark energy and matter, i.e., the interaction term Qis proportional to the energy densities of dark energy(ρΛ), matter (ρm), and matter plus dark energy(ρm+ρΛ). For probing the interaction and spatialcurvature in the holographic dark energy model, we use the latestobservational data including the type Ia supernovae (SNIa)Constitution data, the shift parameter of the cosmic microwavebackground (CMB) given by the five-year Wilkinson MicrowaveAnisotropy Probe (WMAP5) observations, and the baryon acousticoscillation (BAO) measurement from the Sloan Digital Sky Survey(SDSS). Our results show that the interaction and spatial curvaturein the holographic dark energy model are both rather small. Besides,it is interesting to find that there exists significant degeneracybetween the phenomenological interaction and the spatial curvaturein the holographic dark energy model.

The evolution of the wave function in quantum mechanics is deterministic like that of classical waves. Only when we bring in observers the fundamentally different quantum reality emerges. Similarly the introduction of observers changes the nature of spacetime by causing a split between past and future, concepts that are not well defined in the observer-free world. The induced temporal boundary leads to a resonance condition for the oscillatory vacuum solutions of the metric in Euclidean time. It corresponds to an exponential de Sitter evolution in real time, which can be represented by a cosmological constant , where r u is the radius of the particle horizon at the epoch when the observer exists. For the present epoch we get a value of Λ that agrees with the observed value within 2σ of the observational errors. This explanation resolves the cosmic coincidence problem. Our epoch in cosmic history does not herald the onset of an inflationary phase driven by some dark energy. We show that the observed accelerated expansion that is deduced from the redshifts is an ‘edge effect’ due to the observer-induced boundary and not representative of the intrinsic evolution. The new theory satisfies the BBN (Big Bang nucleosynthesis) and CMB (cosmic microwave background) observational constraints equally well as the concordance model of standard cosmology. There is no link between the dark energy and dark matter problems. Previous conclusions that dark matter is mainly non-baryonic are not affected.

We study Friedmann-Robertson-Walker cosmological models with mattercontent composed of two perfect fluids ρ1 and ρ2, withbarotropic pressure densities p1/ρ1 = ω1 = const and p2/ρ2 = ω2 = const, where one of the energy densities is givenby ρ1 = C1aα+C2aβ, with C1, C2, αand β taking constant values. We solve the field equations byusing the conservation equation without breaking it into twointeracting parts with the help of a coupling interacting term Q.Nevertheless, with the found solution may be associated aninteracting term Q, and then a number of cosmological interactingmodels studied in the literature correspond to particular cases ofour cosmological model. Specifically those models having constantcoupling parameters α̃, β̃ andinteracting terms given by Q = α̃HρDM,Q = α̃HρDE, Q = α̃H(ρDM+ρDE) and Q = α̃HρDM+β̃HρDE, where ρDM andρDE are the energy densities of dark matter and darkenergy respectively. The studied set of solutions contains a classof cosmological models presenting a scaling behavior at early and atlate times. On the other hand the two-fluid cosmological modelsconsidered in this paper also permit a three fluid interpretationwhich is also discussed. In this reinterpretation, for flatFriedmann-Robertson-Walker cosmologies, the requirement ofpositivity of energy densities of the dark matter and dark energycomponents allows the state parameter of dark energy to be in therange −1.37≲ωDE < −1/3.

By introducing the Bose-Einstein condensation dynamics (BEC), we develop a unified model of dark energy and dark matter. The two phases of BEC (= dark energy) and normal gas (= dark matter) transform with each other through the phase transition. We study the present mild acceleration, the inflation in the early universe, and the reduction of the cosmological constant. We find the stagflation regime when the cosmic expansion stops and the uniform mode of BEC becomes unstable. We also comment on the possibility that BEC generation/decay series might have continued all the time in the cosmic history from the inflation to present.

In order to test if there is energy transfer between dark energy (DE) and dark matter (DM), we investigate cosmological constraints on two forms of nontrivial interaction between the DM sector and the sector responsible for the acceleration of the universe, in light of the newly revised observations including OHD, CMB, BAO and SNe Ia. More precisely, we find the same tendencies for both phenomenological forms of the interaction term Q = 3γHρ, i.e. the parameter γ to be a small number, |γ| ≈ 10-2. However, concerning the sign of the interaction parameter, we observe that γ &gt; 0 when the interaction between dark sectors is proportional to the energy density of dust matter, whereas the negative coupling (γ &lt; 0) is preferred by observations when the interaction term is proportional to DE density. We further discuss two possible explanations to this incompatibility and apply a quantitative criteria to judge the severity of the coincidence problem. Results suggest that the γm IDE model with a positive coupling may alleviate the coincidence problem, since its coincidence index C is smaller than that for the γd IDE model, the interacting quintessence and phantom models by four orders of magnitude.

We study quintessence cosmology with an effective Λ-term in Lyra manifold. We consider three different models by choosing variable Λ depending on time, the Hubble parameter and the energy density of dark matter and dark energy. Dark energy is assumed as quintessence which interacts with the dark matter. Using numerical analysis we investigate the behavior of cosmological parameters in three different models and compare our results with observational data. State-finder diagnostic is also performed for all models.

Observations have confirmed the accelerated expansion of the universe. The accelerated expansion can be modelled by invoking a cosmological constant or a dynamical model of dark energy. A key difference between these models is that the equation of state parameter w for dark energy differs from −1 in dynamical dark energy (DDE) models. Further, the equation of state parameter is not constant for a general DDE model. Such differences can be probed using the variation of scale factor with time by measuring distances. Another significant difference between the cosmological constant and DDE models is that the latter must cluster. Linear perturbation analysis indicates that perturbations in quintessence models of dark energy do not grow to have a significant amplitude at small length scales. In this paper we study the response of quintessence dark energy to non-linear perturbations in dark matter. We use a fully relativistic model for spherically symmetric perturbations. In this study we focus on thawing models. We find that in response to non-linear perturbations in dark matter, dark energy perturbations grow at a faster rate than expected in linear perturbation theory. We find that dark energy perturbation remains localised and does not diffuse out to larger scales. The dominant drivers of the evolution of dark energy perturbations are the local Hubble flow and a supression of gradients of the scalar field. We also find that the equation of state parameter w changes in response to perturbations in dark matter such that it also becomes a function of position. The variation of w in space is correlated with density contrast for matter. Variation of w and perturbations in dark energy are more pronounced in response to large scale perturbations in matter while the dependence on the amplitude of matter perturbations is much weaker.