Energy Density Materials Research Articles

Charged analog of anisotropic dark energy star in Rastall gravity

Dark energy is one of the potential strategies for preventing compact objects from gravitationally collapsing into singularities. Because it is the cause of the accelerated expansion of our universe, it has the greatest impact on the cosmos. Thus, it is plausible that dark energy will interact with any stellar object that is compact in the universe [Phys. Rev. D 103 (2021) 084042]. Our main goal in this work is to create a simplified model, in the Rastall gravitational framework, of a charged strange star coupled to anisotropic dark energy in Krori–Barua spacetime [J. Phys. A, Math. Gen. 8 (1975) 508]. Here, we consider a specific strange star object, Her [Formula: see text], with observed values of mass [Formula: see text] and radius [Formula: see text] km, so that we can develop our model. In this context, we began by modeling dark energy using the equation of state (EoS), in which the dark energy density is proportional to the isotropic perfect fluid matter-energy density. The Darmois–Israel condition has been used to calculate the unknown constants that are present in the metric. We perform a detailed analysis of the model’s physical properties, including the mass–radius relation, pressure, density, metric function, and dark energy parameters for different Rastall coupling parameter values. We also examine the stability and force equilibrium of our proposed stellar configuration. Following a comprehensive theoretical analysis, we discovered that our suggested model is both singularity-free and meets all stability requirements needed to be a stable, physically reasonable stellar model.

A phenomenological approach to the dark energy models in the Finsler–Randers framework

This study extends two phenomenological models of dark energy within the framework of Finsler–Randers space–time, accommodating anisotropies. The models consider the cosmological constant Λ in two scenarios: one where Λ is proportional to the second time derivative of the scale factor ä, and another where it varies with the matter-energy density ρ. Earlier, such Λ-decaying cosmologies were proposed to address long-standing cosmological constant problems. However, following the discovery of late-time cosmic acceleration, the focus shifted to modeling dark energy. Since Λ is widely viewed as the most significant and suitable candidate for driving cosmic acceleration, it is worthwhile to revisit the phenomenological approach in this context. This work uses this approach to find solutions for the scale factor a(t) and other geometrical and physical parameters. Additionally, we analyze the evolution of density parameters Ωm, ΩΛ, and Ωκ, representing matter, dark energy, and curvature, from early to late times. The phenomenological approach is employed to solve the field equations, with model parameters constrained using recent observational data, yielding ranges consistent with observations. The solutions converge to the ΛCDM cosmology at early and late times. The added complexity introduced by Finsler–Randers geometry enhances accuracy compared to analogous solutions in Riemannian space–time.

Selecting energy–momentum trace dependent gravity theories with LSS

We study scalar cosmological perturbations in f(R,T) modified gravity theories, where T represents the trace of the energy–momentum tensor. We provide detailed equations for the matter energy density contrast. We solve them numerically to facilitate a comparison with available large-scale structure (LSS) formation observational data on fσ8, while also addressing the S8 tension. We identify f(R,T) models that either lead to growth enhancement or suppression. Since recent results in the literature indicate a preference for the latter feature, this type of analysis is quite useful for selecting viable modifications of gravity. The studied class of such f(R,T) models are either ruled out or severely restricted. After selecting the surviving f(R,T) models we show how they deal with the S8 tension.

Sodium chloride induced nitrogen salt with cyclo- N5 anions at high pressure

The energy landscape of sodium chloride-nitrogen mixtures has been comprehensively explored to examine the ability of the formation of unknown compounds under pressures of up to 100 GPa, using swarm-intelligence structure prediction methodology and first-principles calculations. We identified a thermodynamically stable NaN5ClN5 compound containing two cyclo-N5 species under pressures exceeding 53 GPa, representing milder conditions in comparison to those requisite for pure solid nitrogen. In NaN5ClN5, the high electron affinity of the cyclo-N5 motif allows it to oxidize the chlorine atoms, resulting in the formation of two cyclo-N5 anions. Additionally, the weak covalent interactions between Cl and nearby N atoms plays a key role in stabilization of structure. It has been demonstrated that simple NaN5 salt was a suitable precursor for the synthesis of NaN5ClN5 at high pressure. molecular dynamics simulations demonstrated the recoverability of NaN5ClN5 as a metastable phase at ambient pressure-temperature conditions. Additionally, NaN5ClN5 exhibits a higher energy density of 3.86 kJ/g and a lower mass density of 1.67 g/cm3 in comparison to metal pentazolate salts, highlighting its potential as a high energy-density material. Published by the American Physical Society 2024

Rapid in-Situ Electrochemical Formation of Partially Disordered Spinel from Mn-Rich Disordered Rocksalt Cathodes

We present the development of an electrochemical formation method that enables rapid and in-situ formation of a partially disordered spinel phase from an initially disordered rocksalt (DRX) cathode. Recent studies on Mn-rich DRX materials have demonstrated the emergence of a spinel-like phase during cycling, resulting in improved capacity retention, energy density, and rate capability compared to materials which do not transform1,2,3. However, this transformation process typically requires weeks of cycling at relatively low rates, posing significant challenges for the commercialization of such materials.To gain a deeper understanding of this transformation process, we carry-out a systematic study to determine whether the formation process of these spinel-like materials can be accelerated through a precycling formation process. By employing a novel electrochemical approach to purposefully stimulate the transformation, we successfully reduce the time required from several weeks to as little as one day for Mn-rich DRX. Extended cycling and synchrotron X-ray diffraction confirm that these materials exhibit both equivalent performance and resulting structure to those obtained through conventional cycling over a much longer duration. Further characterization of this material using HAADF and 4-D STEM reveals the complex local structure of the spinel-like partial ordering. It is hoped that such a practical electrochemical formation method will allow for an acceleration of research on these earth-abundant and energy-dense materials. Li, L.; Lun, Z.; Chen, D.; Yue, Y.; Tong, W.; Chen, G.; Ceder, G.; Wang, C. Fluorination-Enhanced Surface Stability of Cation-Disordered Rocksalt Cathodes for Li-Ion Batteries. Adv Funct Mater 2021, 31 (25), 2101888. https://doi.org/10.1002/adfm.202101888.Ahn, J.; Giovine, R.; Wu, V. C.; Koirala, K. P.; Wang, C.; Clément, R. J.; Chen, G. Ultrahigh-Capacity Rocksalt Cathodes Enabled by Cycling-Activated Structural Changes. Adv. Energy Mater. 2023. https://doi.org/10.1002/aenm.202300221. Cai, Z.; Ouyang, B.; Hau, H.-M.; Chen, T.; Giovine, R.; Koirala, K. P.; Li, L.; Ji, H.; Ha, Y.; Sun, Y.; Huang, J.; Chen, Y.; Wu, V.; Yang, W.; Wang, C.; Clément, R. J.; Lun, Z.; Ceder, G. In Situ Formed Partially Disordered Phases as Earth-Abundant Mn-Rich Cathode Materials. Nat. Energy 2023, 1–10. https://doi.org/10.1038/s41560-023-01375-9.

Why the big bang never happened

<p>If general relativity is correct, then the origin of the universe is a simple mathematical problem. The Friedmann equation in cosmology is a well-structured ordinary differential equation, and the global properties of its solutions can be qualitatively analyzed by the phase-trajectory method. In this paper we show that the total energy density of matter in the universe is positive, and the total pressure near the Big Bang is negative. By analyzing the global properties of the solutions to the Friedmann equation according to these two conditions of state functions, we find that the Big Bang is impossible, and the space must be a closed 3-dimensional sphere, the cosmological constant is likely to be zero, and the evolution of the universe should be cyclic. The analysis and the proof are simple and straight forward, therefore these conclusions should be reliable.</p>

A comprehensive data-driven odyssey to explore the equation of state of dark energy

For the first time, we reconstruct the dark energy equation of the state parameter w from the combination of background and perturbation observations, specifically combining the Hubble parameter data from cosmic chronometer observations and the logarithmic growth rate data from the growth rate observations. We do this analysis using posterior Gaussian process regression without considering any specific cosmological model or parametrization. However there are three main assumptions: (I) a flat Friedmann–Lemaître–Robertson–Walker (FLRW) metric is considered for the cosmological background, (II) there is no interaction between dark energy and matter sectors, and (III) for the growth of inhomogeneity, sub-Hubble approximation and linear perturbations are considered. This study is unique in the sense that the reconstruction of w is independent of any derived parameters such as the present values of the matter-energy density parameter and Hubble parameter. From the reconstruction, we look at how the dark energy equation of state evolves between redshifts 0 and 1.5, finding a slight hint of dynamical behavior in dark energy. However, the evidence is not significant. We also find a leaning towards non-phantom behavior over phantom behavior. We observe that the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document}CDM model (w=-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(w=-1)$$\\end{document} nearly touches the lower boundary of the 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document} confidence region in the redshift range 0.6≲z≲0.85.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.6 \\lesssim z \\lesssim 0.85.$$\\end{document} However, it comfortably resides within the 2σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma $$\\end{document} confidence region in the whole redshift range under investigation, 0≤z≤1.5.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0\\le z \\le 1.5.$$\\end{document} Consequently, the non-parametric, model-independent reconstruction of dark energy provides no compelling evidence to deviate from the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varLambda $$\\end{document}CDM model when considering cosmic chronometer and growth rate observations.

Effective field theories for dark matter pairs in the early universe: center-of-mass recoil effects

For non-relativistic thermal dark matter, close-to-threshold effects largely dominate the evolution of the number density for most of the times after thermal freeze-out, and hence affect the cosmological relic density. A precise evaluation of the relevant interaction rates in a thermal medium representing the early universe includes accounting for the relative motion of the dark matter particles and the thermal medium. We consider a model of dark fermions interacting with a plasma of dark gauge bosons, which is equivalent to thermal QED. The temperature is taken to be smaller than the dark fermion mass and the inverse of the typical size of the dark fermion-antifermion bound states, which allows for the use of non-relativistic effective field theories. For the annihilation cross section, bound-state formation cross section, bound-state dissociation width and bound-state transition width of dark matter fermion-antifermion pairs, we compute the leading recoil effects in the reference frame of both the plasma and the center-of-mass of the fermion-antifermion pair. We explicitly verify the Lorentz transformations among these quantities. We evaluate the impact of the recoil corrections on the dark matter energy density. Our results can be directly applied to account for the relative motion of quarkonia in the quark-gluon plasma formed in heavy-ion collisions. They may be also used to precisely assess thermal effects in atomic clocks based on atomic transitions; the present work provides a first field theory derivation of time dilation for these processes in vacuum and in a medium.

Constraints on the Minimally Extended Varying Speed of Light Model Using Pantheon Dataset+

In the context of the minimally extended varying speed of light (meVSL) model, both the absolute magnitude and the luminosity distance of type Ia supernovae (SNe Ia) deviate from those predicted by general relativity (GR). Using data from the Pantheon+ survey, we assess the plausibility of various dark energy models within the framework of meVSL. Both the constant equation of state (EoS) of the dark energy model (ωCDM) and the Chevallier–Polarski–Linder (CPL) parameterization model (ω=ω0+ωa(1−a)) indicate potential variations in the cosmic speed of light at the 1−σ confidence level. For Ωm0=0.30,0.31, and 0.32 with (ω0,ωa)=(−1,0), the 1−σ range of c˙0/c0(10−13yr−1) is (−8.76, −0.89), (−11.8, 3.93), and (−14.8, −6.98), respectively. Meanwhile, the 1−σ range of c˙0/c0(10−12yr−1) for CPL dark energy models with −1.05≤ω0≤−0.95 and 0.28≤Ωm0≤0.32 is (−6.31, −2.98). The value of c at z=3 can exceed that of the present by 0.2∼3% for ωCDM models and 5∼13% for CPL models. Additionally, for viable models except for the CPL model with Ωm0=0.28, we find −25.6≤G˙0/G0(10−12yr−1)≤−0.36. For this particular model, we obtain an increasing rate of the gravitational constant within the range 1.65≤G˙0/G0(10−12yr−1)≤3.79. We obtain some models that do not require dark matter energy density through statistical interpretation. However, this is merely an effect of the degeneracy between model parameters and energy density and does not imply that dark matter is unnecessary.

Right-handed neutrino as a common progenitor of baryon number asymmetry and dark matter

Cosmological and astrophysical observations suggest that both energy densities of baryon and dark matter take the same order values in the present Universe. We propose a scenario to give an answer for this problem in a scotogenic model and its extension. The model naturally provides dark matter candidates as its crucial ingredients to explain the small neutrino mass. If a neutral component of an inert doublet scalar plays a role of dark matter and leptogenesis occurs at TeV scales, both dark matter abundance and baryon number asymmetry could be explained with a same mother particle. Coincidence between the order of their energy densities might be understood through such a background. Published by the American Physical Society 2024

Forecasting the BAO measurements of the CSST galaxy and AGN spectroscopic surveys

ABSTRACT The spectroscopic survey of the China’s Space Survey Telescope (CSST) is expected to obtain a huge number of slitless spectra, including more than one hundred million galaxy spectra and millions of active galactic nuclei (AGNs) spectra. By making use of these spectra, we can measure the Baryon Acoustic Oscillation (BAO) signals over large redshift ranges with excellent precisions. In this work, we predict the CSST measurements of the post-reconstruction galaxy power spectra at $0\lt z\lt 1.2$ and pre-reconstruction AGN power spectra at $0\lt z\lt 4$, and derive the BAO signals at different redshift bins by constraining the BAO scaling parameters using the Markov Chain Monte Carlo method. Our result shows that the CSST spectroscopic survey can provide accurate BAO measurements with precisions higher than 1 and 3 per cent for the galaxy and AGN surveys, respectively. By comparing with current measurements in the same range at low redshifts, this can improve the precisions by a factor of $2\sim 3$, and similar precisions can be obtained in the pessimistic case. We also investigate the constraints on the cosmological parameters using the measured BAO data by the CSST, and obtain stringent constraint results for the energy density of dark matter, Hubble constant, and equation of state of dark energy.

Dynamical Explanation of the Dark Matter and Baryon Energy Density Coincidence.

The near equality of the dark matter and baryon energy densities is a remarkable coincidence, especially when one realizes that the baryon mass is exponentially sensitive to UV parameters in the form of dimensional transmutation. We explore a new dynamical mechanism, where in the presence of an arbitrary number density of baryons and dark matter, a scalar adjusts the masses of dark matter and baryons until the two energy densities are comparable. In this manner, the coincidence is explained regardless of the microscopic identity of dark matter and how it was produced. This new scalar causes a variety of experimental effects such as a new force and a (dark) matter density-dependent proton mass.

Reconstruction of symmetric teleparallel gravity with energy conditions

This research investigates the impact of modified gravity on cosmic scales, focusing on [Formula: see text] cosmology. By applying energy conditions, the study reconstructs various [Formula: see text] models, considering an accelerating Universe, quintessence, and a cosmological constant [Formula: see text]. Using up-to-date observational data, including the Supernova Pantheon sample and cosmic chronometer data, Hubble constants [Formula: see text] are estimated as [Formula: see text] km/s/Mpc (from [Formula: see text] data) and [Formula: see text] km/s/Mpc (from pantheon compilation of SN Ia data). The matter energy density parameter ([Formula: see text]) is calculated as [Formula: see text] (OHD) and [Formula: see text] (SN Ia). Furthermore, as a function of red-shift [Formula: see text], explicit expressions of [Formula: see text] and the EOS parameter [Formula: see text] are produced, and their graphical analysis describes the late time acceleration of the Universe without the usage of dark energy.

Evolving wormhole geometry from dark matter energy density

We analyse traversable wormholes defined by the dynamic line elements that asymptotically approach Friedmann–Robertson–Walker (FRW) universe. These dynamical wormholes is supported by the galactic dark matter as well as perfect isotropic fluid. We will discuss several evolving Lorentzian wormholes comprising with different perfect isotropic fluids in addition to various scale factors. We will speculate the various significance, features and throat energy conditions for these evolving traversable Lorentzian wormholes.

Holographic massive plasma state in Friedman universe: cosmological fine-tuning and coincidence problems

Massive particle and antiparticle pair production andoscillation on the horizon form a holographic and massive pair plasma state in the Friedman Universe. Via this state, the Einsteincosmology term (dark energy) interacts with matter and radiation and is time-varying Λ̃ in the Universe's evolution.It is determined by a close set of ordinary differential equations for dark energy, matter, and radiation energy densities. The solutions are unique, provided the initial conditions given by observations.In inflation and reheating, dark energy density decreases from the inflation scale, converting to matter and radiation energy densities.In standard cosmology, matter and radiation energy densities convert to dark energy density, reaching the present Universe. By comparing with ΛCDM, quintessence and dark energy interacting models, we show thatthese results can be the possible solutions for cosmological fine-tuning and coincidence problems.

A double take on early and interacting dark energy from JWST

The very first light captured by the James Webb Space Telescope (JWST) revealed a population of galaxies at very high redshifts more massive than expected in the canonical ΛCDM model of structure formation. Barring, among others, a systematic origin of the issue, in this paper, we test alternative cosmological perturbation histories. We argue that models with a larger matter component Ω m and/or a larger scalar spectral index ns can substantially improve the fit to JWST measurements. In this regard, phenomenological extensions related to the dark energy sector of the theory are appealing alternatives, with Early Dark Energy emerging as an excellent candidate to explain (at least in part) the unexpected JWST preference for larger stellar mass densities. Conversely, Interacting Dark Energy models, despite producing higher values of matter clustering parameters such as σ 8, are generally disfavored by JWST measurements. This is due to the energy-momentum flow from the dark matter to the dark energy sector, implying a smaller matter energy density. Upcoming observations may either strengthen the evidence or falsify some of these appealing phenomenological alternatives to the simplest ΛCDM picture.

Analytical Gaussian process cosmography: unveiling insights into matter-energy density parameter at present

In this study, we introduce a novel analytical Gaussian Process (GP) cosmography methodology, leveraging the differentiable properties of GPs to derive key cosmological quantities analytically. Our approach combines cosmic chronometer (CC) Hubble parameter data with growth rate (f) observations to constrain the Ωm0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _{\ extrm{m0}}$$\\end{document} parameter, offering insights into the underlying dynamics of the Universe. By formulating a consistency relation independent of specific cosmological models, we analyze under a flat FLRW metric and first-order Newtonian perturbation theory framework. Our analytical approach simplifies the process of Gaussian Process regression (GPR), providing a more efficient means of handling large datasets while offering deeper interpretability of results. We demonstrate the effectiveness of our methodology by deriving precise constraints on Ωm0h2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _{\ extrm{m0}}h^2$$\\end{document}, revealing Ωm0h2=0.139±0.017\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _\ extrm{m0}h^2=0.139\\pm 0.017$$\\end{document}. Moreover, leveraging H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} observations, we further constrain Ωm0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _{\ extrm{m0}}$$\\end{document}, uncovering an inverse correlation between mean H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} and Ωm0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _{\ extrm{m0}}$$\\end{document}. Our investigation offers a proof of concept for analytical GP cosmography, highlighting the advantages of analytical methods in cosmological parameter estimation.

Anisotropic f(Q) gravity model with bulk viscosity

This study investigates the dynamics of a spatially homogeneous and anisotropic LRS Bianchi type-I Universe with viscous fluid in the framework of [Formula: see text] symmetric teleparallel gravity. We assume a linear form for [Formula: see text] and introduce hypotheses regarding the relationship between the expansion and shear scalars, as well as the Hubble parameter and bulk viscous coefficient. The model is constrained using three observational datasets: the Hubble dataset (31 data points), the Pantheon SN dataset (1048 data points), and the BAO dataset (6 data points). The calculated cosmological parameters indicate expected behavior for matter-energy density and bulk viscous pressure, supporting the universe’s accelerating expansion. Diagnostic tests suggest that the model aligns with a [Formula: see text]CDM model in the far future and resides in the quintessence region. These findings are consistent with recent observational data and contribute to our understanding of cosmic evolution within the context of modified gravity and bulk viscosity.

Gravitational repulsion in an expanding ball of dust

In general relativity, there is a velocity dependent term in the gravitational acceleration of a test particle for an observer at infinity. Depending on the direction of motion and the speed, that term can be repulsive. We show that this is also the case in the Parametrized Post-Newtonian (PPN) formalism. We compute the magnitude of that repulsive term for an expanding sphere of dust observed at infinity, and find that it could mimic the effect of a cosmological constant. The time evolution of such an expanding ball of dust for an observer at infinity is calculated, and compared with the standard ΛCDM model. We find that the so-called coincidence problem does not exist for such a model as the energy density attributed to the expansion is always of the same order as the matter energy density.

Mass density vs. energy density at cosmological scales

In the presence of the gravitational field, the energy density of matter no longer coincides with its mass density. A discrepancy exists, of course, also between the associated power spectra. Within the Λ CDM model, we derive a formula that relates the power spectrum of the energy density to that of the mass density and test it with the help of N-body simulations run in comoving boxes of 2.816 Gpc/h. The results confirm the validity of the derived formula and simultaneously show that the power spectra diverge significantly from one another at large cosmological scales.