Accelerated Expansion Research Articles

On the Interpretation of Cosmic Acceleration

In relativity, the Newtonian concepts of velocity and acceleration are observer-dependent quantities that vary with the chosen frame of reference. It is well established that in the comoving frame, cosmic expansion is currently accelerating; however, in the rest frame, this expansion is actually decelerating. In this paper, we explore the implications of this distinction. The traditional measure of cosmic acceleration, denoted by q, is derived from the comoving frame and describes the acceleration of the scale factor a for a 3D space-like homogeneous sphere. We introduce a new parameter qE representing the acceleration experienced between observers within the light cone. By comparing qE to the traditional q using observational data from Type Ia supernovae (SN) and the radial clustering of galaxies and quasars (BAO)—including the latest results from DESI2024—our analysis demonstrates that qE aligns more closely with these data. The core argument of the paper is that Λ—regardless of its origin—creates an event horizon that divides the manifold into two causally disconnected regions analogous to conditions inside a black hole’s interior, thereby allowing for a rest-frame perspective qE in which cosmic expansion appears to be decelerating and the horizon acts like a friction term. Such a horizon suggests that the universe cannot maintain homogeneity outside. The observed cosmological constant Λ can then be interpreted not as a driver of new dark energy or a modification of gravity but as a boundary term exerting an attractive force, akin to a rubber band, resisting further expansion and preventing event horizon crossings. This interpretation calls for a reconsideration of current cosmological models and the assumptions underlying them.

Impossibility of rips and cosmological singularities in a universe merging with baby universes

Understanding the late-time acceleration of the universe and its subtleties is one of the biggest mysteries in cosmology. A lot of different approaches have been put forward to deal with this, ranging from the conventional cosmological constant to various models of dark energy and beyond. Recently one very interesting approach to explaining the late time acceleration has been put forward, where the expansion of the universe is driven by mergers with other “baby” universes and has been shown to be quite viable as well from the point of view of recent observational data. So in this work we examine the possibility of various rip scenarios and other future cosmological singularities in such “multiversal” scenario, probing such singularities for the first time in a multi universe scenario. We examine two models of such a baby universe merging cosmology, and show that remarkably no rip scenario or future cosmological singularity is possible in such models.

Will future copper resources and supply be adequate to meet the net zero emission goal?

The fact that in recent times mineral exploration has been disappointing and that transition to clean energy to achieve net zero emission by 2050 will place extraordinary pressure on copper demand, are beyond dispute. The critical question is to what extent will copper supply be capable of satisfying growing demand in a net zero future. Reality is that global copper resources have been growing significantly and steadily for decades despite increasing mine production. Besides, with dwindling exploration discoveries, this increase is primarily attributable to expansion of the resources of existing deposits through a combination of better progressive delineation and re-assessment of classification of resources in response to economic and technological changes, the so-called Australasian Joint Ore Reserves Committee (JORC) ‘modifying factors’. Analysis of MinEx Consulting's global mineral deposit database indicates that just the resources of deposits discovered since 2010 have been growing at estimated Compound Annual Growth Rates (CAGRs) in the range 7.5% to 15.5%, but greater additional tonnage is associated with deposits discovered before 2010. The result is that tens of millions of tonnes of copper are added to the inventory each year, notwithstanding increasing production and mounting Environmental, Social and Governance (ESG) pressure sterilising some deposits. In essence, copper supply shortages are unlikely to result from depletion of copper resources but rather from possible inadequacy of mining and processing capacity. Geopolitical supply risk is also low compared to some other critical metals (e.g., Co and Ni) on account of the large number and geographical dispersion of copper deposits. Increases in price due to a perception of impending scarcity will ensure that future capacity will, at a minimum, continue to grow along its historical 3% CAGR. In addition, it will create strong incentives for above-trend capacity utilisation and improvement in recycling collection and recovery. This will be followed by acceleration of expansion of capacity at many existing mines, and development of deposits at the advanced feasibility stage, releasing copper to market at lower capital cost and on shorter timeframes than exploring for and developing new mines. Estimates of possible levels of above-trend increments in capacity for the various components of the current copper endowment show that, while shortages may occur, they will not be as serious as currently generally expected. This does not mean that net zero emission may not be delayed beyond 2050, but it is more likely that it may be delayed by a range of other constrains and impediments unrelated to availability of copper, and that such delays may give copper supply breathing time.

Teleparallel gravity and quintessence: The role of nonminimal boundary couplings

In this paper, we have outlined the development of an autonomous dynamical system within a general scalar-tensor gravity framework. This framework encompasses the overall structure of the non-minimally coupled scalar field functions for both the torsion scalar (T) and the boundary term (B). We have examined three well-motivated forms of potential functions and constrained the model parameters through dynamical system analysis. This analysis has played a crucial role in identifying cosmologically viable models. We have analysed the behaviour of dynamical parameters such as equation-of-state parameters, as well all the standard density parameters for radiation, matter, and dark energy to assess their compatibility with current observational data. The phase space diagrams are presented to support the stability conditions of the corresponding critical points. The Universe is apparent in its late-time cosmic acceleration phase via the dark energy-dominated critical points. Additionally, we compare our findings with the most prevailing ΛCDM model. The outcomes are further inspected using the cosmological data sets of Supernovae Ia and the Hubble rate H(z).

Polytropic gas cosmology and late-time acceleration

The accelerated expansion of the Universe has sparked significant interest in the mysterious concept of dark energy within cosmology. Various theories have been proposed to explain dark energy, and many models have been developed to understand its origins and properties. This research explores cosmic expansion using the Polytropic Gas (PG) approach, which combines Dark Matter (DM) and Dark Energy (DE) into a single mysterious fluid. We used the principles of general relativity and built our model within the homogeneous and isotropic framework of Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. We revised the Original Polytropic Gas (OPG) model to expand its applicability beyond the OPG, to the ΛCDM model. Our model's parameters were carefully adjusted to reflect key cosmological features of the variable PG approach. To validate our model, we performed a Markov chain Monte Carlo analysis using recent Supernova data from the Pantheon+ survey, 36 observational data points, 162 Gamma-Ray Bursts, and 24 binned Quasars distance modulus data. The AIC and BIC criteria indicate that our model is slightly preferred over the ΛCDM model based on observational data. We also tested our model with data, Supernova, Gamma-Ray Bursts, and Quasars and found that it exhibits a transition from a quintessential to phantom regime. The Polytropic dark fluid model (PDFM) is a promising candidate that effectively addresses the interplay between cosmic acceleration and dark energy.

Noether symmetries and conservation laws in some analytic spherically symmetric spacetimes of f(R, L m ) gravity

In general relativity, dark energy is usually illustrated by a cosmological constant(Λ), but f(R, L m ) gravity provides a different approach to cosmic acceleration by modifying the gravitational theory. In the present paper, the non-static spherically symmetric spacetimes have been derived by taking into account f(R, L m ) = f 1(R) + H(L m )f 2(R). Lie symmetry approach is operated to reduce the order of the partial differential equations corresponding to the field equations, which are further solved. Killing and Noether symmetries provides insights into the conservation laws. So, the obtained spacetimes have been investigated to obtain the Killing and Noether symmetries. The Lagrangian approach have been used to obtain the Noether symmetries. This study is well-structured, as it provides a justification for the well-established result that Noether symmetries encompass Killing symmetries [1]. Also the conserved quantities and commutators of Noether symmetries have been calculated.

Reconstruction of the Dark Energy Scalar Field Potential by Gaussian Process

Dark energy is believed to be responsible for the acceleration of the Universe. In this paper, we reconstruct the dark energy scalar field potential V(ϕ) using the Hubble parameter H(z) through Gaussian process analysis. Our goal is to investigate dark energy using various H(z) data sets and priors. We find that the selection of the prior and the H(z) data set significantly affects the reconstructed V(ϕ). We compare two models, Power Law and Free Field, to the reconstructed V(ϕ) by computing the reduced chi-square. The results suggest that the models are generally in agreement with the reconstructed potential within a 3σ confidence interval, except in the case of Observational H(z) data with the Planck 18 prior. Additionally, we simulate H(z) data to measure the effect of increasing the number of data points on the accuracy of reconstructed V(ϕ). We find that doubling the number of H(z) data points can improve the accuracy rate of reconstructed V(ϕ) by 5%–30%.

Probing particle acceleration in Abell 2256: From 16 MHz to gamma rays

Merging galaxy clusters often host spectacular diffuse radio synchrotron sources. These sources can be explained by a non-thermal pool of relativistic electrons that are accelerated by shocks and turbulence in the intracluster medium. The origin of the pool and details of the cosmic ray transport and acceleration mechanisms in clusters are still open questions. Due to the often extremely steep spectral indices of diffuse radio emission, it is best studied at low frequencies. However, the lowest frequency window available to ground-based telescopes (10−30 MHz) has remained largely unexplored as radio frequency interference and calibration problems related to the ionosphere become severe. Here, we present LOFAR observations from 16 to 168 MHz targeting the famous cluster Abell 2256. In the deepest-ever images at decametre wavelengths, we detected and resolved the radio halo, radio shock, and various steep spectrum sources. We measured standard single power-law behaviour for the radio halo and radio shock spectra, with spectral indices of α = −1.56 ± 0.02 from 24 to 1500 MHz and α = −1.00 ± 0.02 from 24 to 3000 MHz, respectively. Additionally, we found significant spectral index and curvature fluctuations across the radio halo, indicating an inhomogeneous emitting volume. In contrast to the straight power-law spectra of the large-scale diffuse sources, the various AGN-related sources showed extreme steepening towards higher frequencies and flattening towards low frequencies. We also discovered a new fossil plasma source with a steep spectrum between 23 and 144 MHz, with α = −1.9 ± 0.1. Finally, by comparing radio and gamma-ray observations, we ruled out purely hadronic models for the radio halo origin in Abell 2256, unless the magnetic field strength in the cluster is exceptionally high, which is unsupportable by energetic arguments and inconsistent with the knowledge of other cluster magnetic fields.

Wormhole geometries supported by strange quark matter and phantom-like generalized Chaplygin gas within [formula omitted] gravity

A crucial aspect of wormhole (WH) physics is the inclusion of exotic matter, which requires violating the null energy condition. Here, we explore the potential for WHs to be sustained by quark matter under conditions of extreme density along with the phantom-like generalized cosmic Chaplygin gas (GCCG) in symmetric teleparallel gravity. Theoretical and experimental studies on baryon structures indicate that strange quark matter, composed of u (up), d (down), and s (strange) quarks, represents the most energy-efficient form of baryonic matter. Drawing from these theoretical insights, we use the Massachusetts Institute of Technology (MIT) bag model equation of state to characterize ordinary quark matter. By formulating specific configurations for the bag parameter, we develop several WH models corresponding to different shape functions for the isotropic and anisotropic cases. Our analysis strongly suggests that an isotropic WH is not theoretically possible. Furthermore, we investigate traversable WH solutions utilizing a phantom-like GCCG, examining their feasibility. This equation of state, capable of violating the null energy condition, can elucidate late-time cosmic acceleration through various beneficial parameters. In this framework, we derive WH solutions for both constant and variable redshift functions. We have employed the volume integral quantifier (VIQ) method for both studies to assess the quantity of exotic matter. Furthermore, we have done the equilibrium analysis through the Tolman–Oppenheimer–Volkoff (TOV) equation, which supports the viability of our constructed WH model.

The expansion behavior of the hyperbolic solution in f(R,G) gravity

In this study, our primary focus lies in meticulously exploring the intricacies of the universe by employing a flat Friedmann–Lemaître–Robertson–Walker (FLRW) model within the framework of [Formula: see text] gravity. In our analysis, the [Formula: see text] function is delineated as the sum of two distinct components, commencing with a quadratic correction of the geometric term denoted by [Formula: see text], structured as [Formula: see text], alongside a matter term denoted by [Formula: see text], where [Formula: see text] and [Formula: see text] symbolize the Ricci scalar and Gauss–Bonnet invariant, respectively. In the pursuit of solutions to the gravitational field equations within the [Formula: see text] formalism, we embrace a specific expression for the scale factor, represented as [Formula: see text] [D. Rabha and R. R. Baruah, The dynamics of a hyperbolic solution in [Formula: see text] gravity, Astron. Comput. 45 (2023) 100761]. In this context, the parameters [Formula: see text] and [Formula: see text] intricately shape the scale factor’s behavior. The model posits the intriguing prospect of perpetual cosmic acceleration when [Formula: see text], signifying a continuous expansion of the universe. Conversely, for [Formula: see text], the model proposes a pivotal transition from an early deceleration phase to the present accelerated epoch, a transformative shift in line with our understanding of cosmic evolution. Furthermore, the model demonstrates its credibility by satisfying Jean’s instability condition during the shift from a radiation-dominated era to a matter-dominated era, substantiating the formation of cosmic structures. In our analysis, a central focus is directed toward scrutinizing the equation of state parameter [Formula: see text] within our model. We delve into a comprehensive examination of the scalar field and meticulously assess the energy conditions surrounding the derived solution. To establish the robustness of our model, we deploy an array of diagnostic tools, including the Jerk, Snap, and Lerk parameters, along with the Om diagnostic, Classical stability of the model, and statefinder diagnostic tools, Observational Constraints on the Model Parameters. The outcomes, intertwined with a detailed analysis of both the results and the inherent intricacies of the model, are diligently clarified and presented.

Reconstruction of the singularity-free f(R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f({\\mathcal {R}})$$\\end{document} gravity via Raychaudhuri equations

We study the bounce cosmology to construct a singularity-free f(R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f({\\mathcal {R}})$$\\end{document} model using the reconstruction technique. The formulation of the f(R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f({\\mathcal {R}})$$\\end{document} model is based on the Raychaudhari equation, a key element employed in reconstructed models to eliminate singularities. We explore the feasibility of obtaining stable gravitational Lagrangians, adhering to the conditions fR>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{{\\mathcal {R}}}>0$$\\end{document} and fRR>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_{{\\mathcal {R}}{\\mathcal {R}}}>0$$\\end{document}. Consequently, both models demonstrate stability, effectively avoiding the Dolgov–Kawasaki instability. Our assessment extends to testing the reconstructed model using energy conditions and the effective equation-of-state (EoS). Our findings indicate that the reconstructed super-bounce model facilitates the examination of a singularity-free accelerating universe for both phantom and non-phantom phases. However, in the case of the reconstructed oscillatory bounce model, two scenarios are considered with ω=-1/3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega =-\\,1/3$$\\end{document} and ω=-2/3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega =-\\,2/3$$\\end{document}. While the model proves suitable for studying a singular-free accelerating universe in the ω=-1/3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega =-\\,1/3$$\\end{document} case, it fails to demonstrate such behavior under energy conditions for the ω=-2/3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega =-\\,2/3$$\\end{document} scenario. The reconstructed models accommodate early-time bouncing behavior and late-time cosmic acceleration within a unified framework.

Different spectra of cosmic ray H, He, and heavier nuclei escaping compact star clusters

ABSTRACT Cosmic ray acceleration at the termination shock of compact star clusters has recently received much attention, mainly because of the detection of gamma-ray emission from some of such astrophysical sources. Here we focus on the acceleration of nuclei at the termination shock and we investigate the role played by proton energy losses and spallation reactions of nuclei, especially downstream of the shock. We show that for a reasonable choice of the mean gas density in the cavity excavated by the cluster wind, dominated by the presence of dense clouds, the spectrum of He nuclei escaping the bubble is systematically harder than the spectrum of hydrogen, in a manner that appears to be qualitatively consistent with the observed and yet unexplained phenomenon of discrepant hardening. We also find that, in this scenario, the spallation reactions of heavier nuclei are likely to be so severe that their spectra becomes very hard and with a low normalization, meaning that it is unlikely that heavy nuclei escaping star clusters can provide a sizeable contribution to the spectrum of cosmic rays at the Earth. Limitations and implications of this scenario are discussed.

Observational Evidence for Magnetic Field Amplification in SN 1006

We report the first observational evidence for magnetic field amplification in the northeast/southwest (NE/SW) shells of supernova remnant SN 1006, one of the most promising sites of cosmic ray acceleration. In previous studies, the strength of magnetic fields in these shells was estimated to be B SED ≃ 25 μG from the spectral energy distribution, where the synchrotron emission from relativistic electrons accounted for radio to X-rays, along with the inverse Compton emission extending from the GeV to TeV energy bands. However, the analysis of broadband radio data, ranging from 1.37 to 100 GHz, indicated that the radio spectrum steepened from α 1 = 0.52 ± 0.02 to α 2 = 1.34 ± 0.21 by Δα = 0.85 ± 0.21. This is naturally interpreted as a cooling break under a strong magnetic field of B brk ≥ 2 mG. Moreover, the high-resolution MeerKAT image indicated that the width of the radio NE/SW shells was broader than that of the X-ray shell by a factor of only 3−20, as measured by Chandra. Such narrow radio shells can be naturally explained if the magnetic field responsible for the radio emissions is B R ≥ 2 mG. Assuming that the magnetic field is locally enhanced by a factor of approximately a = 100 along the NE/SW shells, we argue that the filling factor, which is the volume ratio of such a magnetically enhanced region to that of the entire shell, must be as low as approximately k = 2.5 × 10−5.

Stability investigations of de Sitter inflationary solutions in power-law extensions of the Starobinsky model

In this paper, we would like to examine whether stable de Sitter inflationary solutions appear within power-law extensions of the Starobinsky model. In particular, we will address general constraints for the existence along with the stability of de Sitter inflationary solutions in a general case involving not only the Starobinsky R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R^2$$\\end{document} term but also an additional power-law Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R^n$$\\end{document} one. According to the obtained results, we will be able to identify which extension is more suitable for an early inflationary phase rather than a late-time cosmic acceleration phase. To be more specific, we will consider several values of n to see whether the corresponding de Sitter inflationary solutions are stable or not.

Cosmological test of dark energy parametrizations within the framework of Horava-Lifshitz gravity via baryon acoustic oscillation

We conduct an investigation to explore late-time cosmic acceleration through various dark energy parametrizations (Wettrich, Efstathiou, and Ma-Zhang) within the Horava-Lifshitz gravity framework. As an alternative to general relativity, this theory introduces anisotropic scaling at ultraviolet scales. Our primary objective is to constrain the key cosmic parameters and baryon acoustic oscillation (BAO) scale, specifically the sound horizon (rd ), by utilizing 24 uncorrelated measurements of BAOs derived from recent galaxy surveys spanning a redshift range from z = 0.106 to z = 2.33. Additionally, we integrate the most recent Hubble constant measurement by Riess in 2022 (denoted as R22) as an extra prior. For the parametrizations of Wettrich, Efstathiou, and Ma-Zhang, our analysis of BAO data yields sound horizon results of rd = 148.1560 ± 2.7688 Mpc, rd = 148.6168 ± 10.2469 Mpc, and rd = 147.9737 ± 10.6096 Mpc, respectively. Incorporating the R22 prior into the BAO dataset results in rd = 139.5806 ± 3.8522 Mpc, rd = 139.728025 ± 2.7858 Mpc, and rd = 139.6001 ± 2.7441 Mpc. These outcomes highlight a distinct inconsistency between early and late observational measurements, analogous to the H 0 tension. A notable observation is that, when we do not include the R22 prior, the outcomes for rd tend to be in agreement with Planck and SDSS results. Following this, we conducted a cosmography test and comparative study of each parametrization within the Lambda Cold Dark Matter paradigm. Our diagnostic analyses demonstrate that all models fit seamlessly within the phantom region. All dark energy parametrizations predict an equation of state parameter close to = –1, indicating a behavior similar to that of a cosmological constant. The statistical analysis indicates that neither of the two models can be ruled out based on the latest observational measurements.

Significance of a quadratically varying deceleration parameter in scalar field-dominated model and cosmic acceleration

In this study, we explore the enigma of late-time cosmic acceleration in the framework of a general scalar field playing the role of dark energy. Our investigation yields an exact solution to Einstein’s field equations, achieved through a parametrization of the deceleration parameter [Formula: see text] in quadratic form in the homogeneous and isotropic background geometry represented by Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. This parametrization unveils a seamless transition from a decelerated to an accelerated phase in the cosmic evolution. Furthermore, we leverage this parametrization to reconstruct cosmological parameters with respect to redshift z, elucidating their dependency on certain model parameters that govern the universe’s evolutionary trajectory. The model parameters are subsequently constrained using diverse observational datasets. We provide a comprehensive analysis of the evolution of geometrical and physical parameters, complete with the numerically constrained values. To gain deeper insights into the nature of dark energy, we employ Statefinder diagnostics, conducting a thorough examination. Our findings shed light on the intricate interplay between cosmic acceleration, quintessential dark energy and the parametrization of deceleration parameter, offering valuable insights into the fundamental dynamics of the universe.

Background gravitational waves as signature of the accelerated cosmic expansion

We propose a toy model of a spherical universe made up of an exotic dark gas with temperature T in thermal equilibrium with a black-body in adiabatic expansion. Each particle of this exotic gas mimics a kind of particle of dark energy. So, each dark particle occupies a very small area of space so-called Planck area [Formula: see text], which represents the minimum area of the whole space-time given by the spherical surface with area [Formula: see text], where [Formula: see text] is the Hubble radius. We realize that such spherical surface is the surface of the black-body for representing the dark universe as if it were the surface of an expanding balloon. Thus, we are able to derive the law of universal gravitation, thus leading us to understand the cosmological anti-gravity. We estimate the tiny order of magnitude of the cosmological constant and the acceleration of expansion of the dark sphere. In this toy model, as the dark universe can be thought of as a large black body, when we obtain its power and frequency of emission of radiation, we find very low values. We conclude that such radiation and frequency of the black body made up of dark energy is a background gravitational wave with very low frequency in the order of [Formula: see text] due to the slight stretching of the fabric of space-time.

An Analytical Model for Cosmology with a Single Input, the Redshift

We propose an analytical model for cosmology which requires only one parameter as an input. This parameter is the redshift. The model is based on conservation of energy, Planck’s Radiation Law, and the relation between energy and frequency of waves. The model yields the current age of the universe, the age of the universe at the CMB emission, as well as the time histories of its expansion velocity and acceleration. The model also is used to show the existence of a constant energy per unit area, associated with the momentum energy of photons, which generates the pressure that perpetuates the expansion of the universe. The model is completely independent of the ɅCDM model but implicitly includes the effects of gravity. Using the model we show the existence of a constant in nature that under certain assumptions can represent the Hubble constant. We have used the model to derive the Hubble constants measured by Reiss et al. and by the Planck Collaboration. Using the model we show that the path of light in the Planck collaboration measurement is along a circular arc, while the Reiss et al. measurement path is exactly along the chord of the same circular arc. The difference in the light travel times along these two paths matches exactly the difference between the two measured values for the Hubble constant, as measured by Reiss et al. and as measured by the Planck Collaboration. This result explains the cause of tension between the two methods of measurement.

Background gravitational waves as signature of the adiabatic expansion of a black body that represents the dark universe

We propose a toy model of a spherical universe made up of an exotic dark gas with temperature T in thermal equilibrium with a black body in adiabatic expansion. Each particle of this exotic gas mimics a kind of particle of dark energy represented by the vacuum energy, being quantized into virtual particles with extremely small masses that form such gas representing the own tissue of the expanding space–time governed by a negative pressure whose origin is the equation of state of vacuum, i.e., p = −ρ, where ρ is the vacuum energy density. So, each vacuum particle occupies a tiny area of space so-called Planck area [Formula: see text], which represents the minimum area of the whole space–time given by the spherical surface with area [Formula: see text], where RH is the Hubble radius. We realize that such spherical surface is the surface of the black body for representing the dark universe as if it were the surface of an expanding balloon. Thus, we are able to derive the law of universal gravitation, thus leading us to understand the cosmological anti-gravity. We estimate the very small order of magnitude of the cosmological constant and the acceleration of expansion of the dark sphere. In this toy model, as the dark universe can be thought of as a large black body, when we obtain its power and frequency of emission of radiation, we find very low values. We conclude that such radiation and frequency of the black body made up of dark energy is a background gravitational wave with very low frequency in the order of 10−17Hz due to the slight stretching of the fabric of space–time.

Quintessence and the Higgs portal in the Carroll limit

A cosmological model based on two scalar fields is proposed. The first of these, φ, has mass μ, while the second, χ, is massless. The pair are coupled through a “Higgs portal”. First, we show how the model reproduces the Friedmann equations if the square of the mass of the φ field is proportional to the cosmological constant and χ represents the quintessence field. Quantum corrections break the conformal symmetry, and the χ field acquires a mass equal to 3gΛ. The perturbative approach with g≪1 is consistent with the bounds for mχ; moreover, by using dimensional analysis, we estimate mχ≪H0≈10−33 eV, which is in accordance with what is expected in the quintessence scenario. The acceleration of the universe is proportional to χ2, we conclude that for very long times, the solution of the equation of motion approaches 〈χ〉∼mχ/λ and the universe continues to accelerate, with a constant acceleration.