Breaking baryon-cosmology degeneracy with the electron density power spectrum
Andrina Nicola, Francisco Villaescusa-Navarro, David N. Spergel, Jo Dunkley, Daniel Anglés-Alcázar, Romeel Davé, Shy Genel, Lars Hernquist, Daisuke Nagai, Rache… 展开作者
Andrina Nicola, Francisco Villaescusa-Navarro, David N. Spergel, Jo Dunkley, Daniel Anglés-Alcázar, Romeel Davé, Shy Genel, Lars Hernquist, Daisuke Nagai, Rachel S. Somerville, Benjamin D. Wandelt
Uncertain feedback processes in galaxies affect the distribution of matter, currently limiting the power of weak lensing surveys. If we can identify cosmological statistics that are robust against these uncertainties, or constrain these effects by other means, then we can enhance the power of current and upcoming observations from weak lensing surveys such as DES, Euclid, the Rubin Observatory, and the Roman Space Telescope. In this work, we investigate the potential of the electron density auto-power spectrum as a robust probe of cosmology and baryonic feedback. We use a suite of (magneto-)hydrodynamic simulations from the CAMELS project and perform an idealized analysis to forecast statistical uncertainties on a limited set of cosmological and physically-motivated astrophysical parameters. We find that the electron number density auto-correlation, measurable through either kinematic Sunyaev-Zel'dovich observations or through Fast Radio Burst dispersion measures, provides tight constraints on $Ω_{m}$ and the mean baryon fraction in intermediate-mass halos, $\bar{f}_{\mathrm{bar}}$. By obtaining an empirical measure for the associated systematic uncertainties, we find these constraints to be largely robust to differences in baryonic feedback models implemented in hydrodynamic simulations. We further discuss the main caveats associated with our analysis, and point out possible directions for future work.
The small-scale cosmic microwave background (CMB) is dominated by anisotropies from the kinematic Sunyaev-Zeldovich (kSZ) effect, and upcoming experiments will measure it very precisely, but the optical depth degeneracy limits the cosmological information that can be extracted. At the same time, fast radio bursts (FRBs) are an exciting new frontier for astrophysics, but their usefulness as cosmological probes is currently unclear. We show that FRBs are uniquely suited for breaking the kSZ optical depth degeneracy. This opens up new possibilities for constraining cosmology with the kSZ effect, …
Massive neutrinos, due to their free streaming, produce a suppression in the matter power spectrum at intermediate and small scales which could be probed by galaxy clustering and/or weak lensing observables. This effect happens at scales that are also influenced by baryon feedback, i.e. galactic winds or Active Galactic Nuclei (AGN) feedback, which in realistic hydrodynamic simulations has also been shown to produce a suppression of power. Leaving aside, for the moment, the complex issue of galaxy bias, we focus here on matter clustering and tomographic weak lensing, we investigate the possibl…
Breaking the Mass-sheet Degeneracy in Time-delay Cosmology with Lensed and Unlensed Type Ia Supernovae
College of Physics, Hebei Normal University（河北师范大学物理学院）；Shijiazhuang Key Laboratory of Astronomy and Space Science, Hebei Normal University（河北师范大学石家庄天文与空间科学重点实验室）；School of Physics and Technology, Wuhan University（武汉大学物理科学与技术学院）
We present cosmological parameter measurements from the Deep Lens Survey (DLS) using galaxy-mass and galaxy-galaxy power spectra in the multipole range $\ell=250\sim2000$. We measure galaxy-galaxy power spectra from two lens bins centered at $z\sim0.27$ and $0.54$ and galaxy-mass power spectra by cross-correlating the positions of galaxies in these two lens bins with galaxy shapes in two source bins centered at $z\sim0.64$ and $1.1$. We marginalize over a baryonic feedback process using a single-parameter representation and a sum of neutrino masses, as well as photometric redshift and shear ca…
Modern weak-lensing observations are becoming increasingly sensitive to baryonic feedback processes which are still poorly understood. So far, this challenge has been faced either by imposing scale-cuts in the data or by modelling baryonic effects with simple, one-parameter models. In this paper, we rely on a more general, seven-parameter prescription of baryonic feedback effects, which is primarily motivated by observations and has been shown to agree with a plethora of hydrodynamical simulations. By combining weak-lensing data from the Kilo-Degree Survey (KiDS-1000) with observations of gas …
The matter creation cosmology is revisited, including the evolution of baryons and dark matter particles. The creation process affects only dark matter and not baryons. The dynamics of the $Λ$CDM model can be reproduced only if two conditions are satisfied: 1) the entropy density production rate and the particle density variation rate are equal and 2) the (negative) pressure associated to the creation process is constant. However, the matter creation model predicts a present dark matter-to-baryon ratio much larger than that observed in massive X-ray clusters of galaxies, representing a potenti…
Ongoing and planned weak lensing (WL) surveys are becoming deep enough to contain information on angular scales down to a few arcmin. To fully extract information from these small scales, we must capture non-Gaussian features in the cosmological WL signal while accurately accounting for baryonic effects. In this work, we account for baryonic physics via a baryonic correction model that modifies the matter distribution in dark matter-only $N$-body simulations, mimicking the effects of galaxy formation and feedback. We implement this model in a large suite of ray-tracing simulations, spanning a …
Diverse astrophysical observations suggest the existence of cold dark matter that interacts only gravitationally with radiation and ordinary baryonic matter. Any nonzero coupling between dark matter and baryons would provide a significant step towards understanding the particle nature of dark matter. Measurements of the cosmic microwave background (CMB) provide constraints on such a coupling that complement laboratory searches. In this work we place upper limits on a variety of models for dark matter elastic scattering with protons and electrons by combining large-scale CMB data from the Planc…
We conduct a pseudo-$C_\ell$ analysis of the tomographic cross-correlation between 1000 deg$^2$ of weak lensing data from the Kilo-Degree Survey (KiDS-1000) and the thermal Sunyaev-Zeldovich (tSZ) effect measured by Planck and the Atacama Cosmology Telescope (ACT). Using HMx, a halo-model-based approach that consistently models the gas, star, and dark matter components, we are able to derive constraints on both cosmology and baryon feedback for the first time from these data, marginalising over redshift uncertainties, intrinsic alignment of galaxies, and contamination by the cosmic infrared ba…
We quantify two main pathways through which baryonic physics biases cluster count cosmology. We create mock cluster samples that reproduce the baryon content inferred from X-ray observations. We link clusters to their counterparts in a dark matter-only universe, whose abundances can be predicted robustly, by assuming the dark matter density profile is not significantly affected by baryons. We derive weak lensing halo masses and infer the best-fitting cosmological parameters $Ω_\mathrm{m}$, $S_8=σ_8(Ω_\mathrm{m}/0.3)^{0.2}$, and $w_0$ from the mock cluster sample. We find that because of the ne…
The abundance of galaxy clusters as a function of mass and redshift is a well known powerful cosmological probe, which relies on underlying modelling assumptions on the mass-observable relations (MOR). Some of the MOR parameters can be constrained directly from multi-wavelength observations, as the normalization at some reference cosmology, the mass-slope, the redshift evolution and the intrinsic scatter. However, the cosmology dependence of MORs cannot be tested with multi-wavelength observations alone. We use {\tt Magneticum} simulations to explore the cosmology dependence of galaxy cluster …
Degeneracy is a method to accommodate exact, low energy vacuum states in scalar-tensor gravitational models despite the presence of an arbitrarily large vacuum energy. However, this approach requires very particular combinations of scalar field and metric couplings in the Lagrangian. In this work we study departures from the restrictive degeneracy condition -- starting from a fiducial model containing an exact Minkowski space solution, we break the degeneracy condition in numerous simple ways to test if the resulting models maintain certain key features -- specifically the dynamical cancellati…
Baryonic feedback effects lead to a suppression of the weak lensing angular power spectrum on small scales. The poorly constrained shape and amplitude of this suppression is an important source of uncertainties for upcoming cosmological weak lensing surveys such as Euclid or LSST. In this first paper in a series of two, we use simulations to build a Euclid-like tomographic mock data-set for the cosmic shear power spectrum and the corresponding covariance matrix, which are both corrected for baryonic effects following the baryonification method of Schneider et al. (2019). In addition, we develo…
Cosmological parameter constraints from the CMB power spectra alone suffer several well-known degeneracies. These degeneracies can be broken by numerical artefacts and also a variety of physical effects that become quantitatively important with high-accuracy data e.g. from the Planck satellite. We study degeneracies in models with flat and non-flat spatial sections, non-trivial dark energy and massive neutrinos, and investigate the importance of various physical degeneracy-breaking effects. We test the CAMB power spectrum code for numerical accuracy, and demonstrate that the numerical calculat…
We use a set of hydrodynamical (Hydro) and dark matter only (DMonly) simulations to calibrate the halo mass function (HMF). We explore the impact of baryons, propose an improved parametrization for spherical overdensity masses and identify differences between our DMonly HMF and previously published HMFs. We use the \textit{Magneticum} simulations, which are well suited because of their accurate treatment of baryons, high resolution, and large cosmological volumes of up to $(3818~\textrm{Mpc})^3$. Baryonic effects globally decrease the masses of galaxy clusters, which, at a given mass, results …
We present and test a framework that models the three-dimensional distribution of mass in the Universe as a function of cosmological and astrophysical parameters. Our approach combines two different techniques: a rescaling algorithm that modifies the cosmology of gravity-only N-body simulations, and a baryonification algorithm which mimics the effects of astrophysical processes induced by baryons, such as star formation and AGN feedback. We show how this approach can accurately reproduce the effects of baryons on the matter power spectrum of various state-of-the-art hydro-dynamical simulations…
We study the impact of baryonic physics on cosmological parameter estimation with weak lensing surveys. We run a set of cosmological hydrodynamics simulations with different galaxy formation models. We then perform ray-tracing simulations through the total matter density field to generate 100 independent convergence maps of 25 ${\rm deg}^2$ field-of-view, and use them to examine the ability of the following three lensing statistics as cosmological probes; power spectrum, peak counts, and Minkowski functionals. For the upcoming wide-field observations such as Subaru Hyper Suprime-Cam (HSC) surv…
Loop Quantum Cosmology is an appealing quantum completion of classical cosmology, which brings along various theoretical features which in many cases offer remedy or modify various classical cosmology aspects. In this paper we address the gravitational baryogenesis mechanism in the context of Loop Quantum Cosmology. As we demonstrate, when Loop Quantum Cosmology effects are taken into account in the resulting Friedmann equations for a flat Friedmann-Robertson-Walker Universe, then even for a radiation dominated Universe, the predicted baryon-to-entropy ratio from the gravitational baryogenesis…
We derive constraints on elastic scattering between baryons and dark matter using the cosmic microwave background (CMB) data from the Planck satellite and the Lyman-alpha forest data from the Sloan Digital Sky Survey. Elastic scattering allows baryons and dark matter to exchange momentum, affecting the dynamics of linear density perturbations in the early Universe. We derive constraints to scattering cross sections of the form sigma \propto v^n, allowing for a wide range of velocity dependencies with n between -4 and 2. We improve and correct previous estimates where they exist, including velo…
The anomalous 21 cm absorption feature reported by EDGES has galvanized the study of scenarios in which dark matter (DM) siphons off thermal energy from the Standard Model (SM) gas. In a departure from the much-discussed models that achieve cooling by DM scattering directly with SM particles, we show that the same end can be achieved through neutral atomic hydrogen $H$ mixing with a degenerate dark sector state $H'$. An analysis of in-medium $H$-$H'$ oscillations reveals viable parameter space for generic types of $H'$-DM interactions to provide the requisite cooling. This strategy stands in s…
We present high signal-to-noise measurements (up to 12$σ$) of the average thermal Sunyaev Zel'dovich (tSZ) effect from optically selected galaxy groups and clusters and estimate their baryon content within a 2.1$^\prime$ radius aperture. Sources from the Sloan Digital Sky Survey (SDSS) Baryon Oscillation Spectroscopic Survey (BOSS) DR15 catalog overlap with 3,700 sq. deg. of sky observed by the Atacama Cosmology Telescope (ACT) from 2008 to 2018 at 150 and 98 GHz (ACT DR5), and 2,089 sq. deg. of internal linear combination component-separated maps combining ACT and $\it{Planck}$ data (ACT DR4)…
We consider the perturbation dynamics for the cosmic baryon fluid and determine the corresponding power spectrum for a $Λ(t)$CDM model in which a cosmological term decays into dark matter linearly with the Hubble rate. The model is tested by a joint analysis of data from supernovae of type Ia (SNIa) (Constitution and Union 2.1), baryonic acoustic oscillation (BAO), the position of the first peak of the anisotropy spectrum of the cosmic microwave background (CMB) and large-scale-structure (LSS) data (SDSS DR7). While the homogeneous and isotropic background dynamics is only marginally influence…
We present a numerical analysis supporting the evidence that the redshift evolution of the drifting coefficient of the field cluster mass function is capable of breaking several cosmic degeneracies. This evidence is based on the data from the CoDECS and DUSTGRAIN-pathfinder simulations performed separately for various non-standard cosmologies including coupled dark energy, $f(R)$ gravity and combinations of $f(R)$ gravity with massive neutrinos as well as for the standard $Λ$CDM cosmology. We first numerically determine the field cluster mass functions at various redshifts in the range of $0\l…
Observational cosmology in the next decade will rely on probes of the distribution of matter in the redshift range between $0<z<3$ to elucidate the nature of dark matter and dark energy. In this redshift range, galaxy formation is known to have a significant impact on observables such as two-point correlations of galaxy shapes and positions, altering their amplitude and scale dependence beyond the expected statistical uncertainty of upcoming experiments at separations under 10 Mpc. Successful extraction of information in such a regime thus requires, at the very least, unbiased models for the i…
The baryonic Tully-Fisher relation as an independent direct probe of cosmology and of the nature of dark matter
Institute for Fundamental Physics of the Universe (IFPU)（宇宙基础物理研究所）；SISSA - International School for Advanced Studies（SISSA - 国际高等研究院）；INAF - Osservatorio Astronomico di Trieste（意大利国家天体物理研究所 - 的里雅斯特天文台）；INFN – National Institute for Nuclear Physics（意大利国家核物理研究所）
We study the fit of cosmological models with two additional free parameters $N_\mathrm{eff}$ and $ξ_e$ in addition to the parameters of $Λ$CDM. We introduce extra radiation components such as hot axions or sterile neutrinos in addition to the energy density of neutrinos with large neutrino degeneracy. Then, a larger $N_\mathrm{eff}$ is allowed without spoiling Big Bang Nucleosynthesis (BBN), as positive neutrino degeneracy $ξ_e$ could improve BBN fit. By analysing the data from Planck, baryon acoustic oscillation (BAO), BBN and type-Ia supernovae (SNeIa), it can be seen that the Hubble tension…
A new accelerating cosmology driven only by baryons plus cold dark matter (CDM) is proposed in the framework of general relativity. In this model the present accelerating stage of the Universe is powered by the negative pressure describing the gravitationally-induced particle production of cold dark matter particles. This kind of scenario has only one free parameter and the differential equation governing the evolution of the scale factor is exactly the same of the $Λ$CDM model. For a spatially flat Universe, as predicted by inflation ($Ω_{dm}+Ω_{baryon}=1$), it is found that the effectively o…
On the impact of baryons on the halo mass function, bias, and cluster cosmology
Università di Trieste（的里雅斯特大学）；INAF – Osservatorio Astronomico di Trieste（意大利国家天体物理研究所的里雅斯特天文台）；IFPU – Institute for Fundamental Physics of the Universe（宇宙基础物理研究所）；INFN – Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；University Observatory Munich（慕尼黑大学天文台）；Max-Planck-Institut fur Astrophysik（马克斯·普朗克天体物理学研究所）；Núcleo de Astrofísica e Cosmologia & Departamento de Física, Universidade Federal do Espírito Santo（圣埃斯皮里图联邦大学天体物理学与宇宙学中心及物理系）；Instituto de Física, Universidade Federal do Rio de Janeiro（里约热内卢联邦大学物理研究所）
We revise observational constraints on the class of models of modified gravity which at low redshifts lead to a power-law cosmology. To this end we use available public data on Supernova Ia and on baryon acoustic oscillations. We show that the expansion regime $a(t) \sim t^β$ with $β$ close to 3/2 a spatially flat universe is a good fit to these data.
We investigate observational constraints on the normal branch of the warped DGP braneworld cosmology by using observational data from Type Ia Supernovae (SNIa), Baryon Acoustic Oscillations (BAO), Cosmic Microwave Background (CMB) and Baryon Gas Mass Fraction of cluster of galaxies. The best fit values of model free parameters are: $Ω_m=0.240^{+0.050}_{-0.130}$ and $Ω_{r_c}=0.000^{+0.014}$ at $1σ$ confidence interval by using Gold sample SNIa+CMB shift parameter+BAO+Gas mass fraction of baryons in cluster of galaxies. The results for essence sample SNIa combined with CMB shift parameter, BAO a…
Line intensity mapping is rapidly gaining prominence as a tool to understand galaxy evolution and cosmology at high redshift. However, the standard power spectrum analysis for these surveys suffers from a tight degeneracy between the overall mean line intensity and the bias of the emitting galaxies. We outline a new formalism for the Voxel Intensity Distribution (VID), a one-point statistic which is known to contain information beyond the power spectrum. We use this new calculation to show for the first time that the VID can be used to break this key degeneracy in intensity mapping data.
FLAMINGO: The thermal history of the Universe from tSZ effect cross-correlations and its dependencies on cosmology and baryon physics
Astrophysics Research Institute, Liverpool John Moores University（利物浦约翰摩尔斯大学天体物理研究所）；Institute for Computational Cosmology, Department of Physics, University of Durham（达勒姆大学物理学院计算宇宙学研究所）；Leiden Observatory, Leiden University（莱顿大学莱顿天文台）；Lorentz Institute for Theoretical Physics, Leiden University（莱顿大学洛伦兹理论物理研究所）；South-Western Institute for Astronomy Research（西南天体物理研究所）
We show the advantages of a wedding cake design for Sunyaev-Zel'dovich cluster surveys. We show that by dividing up a cluster survey into a wide and a deep survey, one can essentially recover the cosmological information that would be diluted in a single survey of the same duration due to the uncertainties in our understanding of cluster physics. The parameter degeneracy directions of the deep and wide surveys are slightly different, and combining them breaks these degeneracies effectively. A variable depth survey with a few thousand clusters is as effective at constraining cosmological parame…
We discuss the cosmological consequences of an interacting model in the dark sector in which the $Λ$ component evolves as a truncated power series of the Hubble parameter. In order to constrain the free parameters of the model we carry out a joint statistical analysis involving observational data from current type Ia supernovae, recent estimates of the cosmic microwave background shift parameter and baryon acoustic oscillations measurements. Finally, we adopt a theoretical method to derive the coupled scalar field version for this non-equilibrium decaying vacuum accelerating cosmology.
KiDS-1000: Improved constraints on cosmology, intrinsic alignments and baryonic feedback from clipped cosmic shear
Institute for Astronomy, University of Edinburgh（爱丁堡大学天体物理研究所）；School of Mathematics, Statistics and Physics, Newcastle University（纽卡斯尔大学数学、统计与物理学院）；Department of Physics and Astronomy, Astronomy and Plasma Physics (AoP) Division, Chalmers University of Technology（查尔姆斯理工大学天文与等离子体物理系天文学与等离子体物理部）；Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB)（鲁尔大学波鸿分校物理与天文学院天体物理研究所）
Context. Time delay lensing is a powerful tool to measure the Hubble constant $H_0$. In order to obtain an accurate estimate of $H_0$ from a sample of time delay strong lenses, however, it is necessary to have a very good knowledge of the mass structure of the lens galaxies. Strong lensing data on their own are not sufficient to break the degeneracy between $H_0$ and the lens model parameters, on a single object basis. Aims. The goal of this study is to determine whether it is possible to break the $H_0$-lens structure degeneracy with the statistical combination of a large sample of time-delay…
Small-scale inhomogeneities in the baryon density around recombination have been proposed as a solution to the tension between local and global determinations of the Hubble constant. These baryon clumping models make distinct predictions for the cosmic microwave background anisotropy power spectra on small angular scales. We use recent data from the Atacama Cosmology Telescope to test these predictions. No evidence for baryon clumping is found, assuming a range of parameterizations for time-independent baryon density probability distribution functions. The inferred Hubble constant remains in s…
We set constraints on moduli cosmology from the production of dark matter -- radiation and baryon -- radiation isocurvature fluctuations through modulus decay, assuming the modulus remains light during inflation. We find that the moduli problem becomes worse at the perturbative level as a significant part of the parameter space m_σ(modulus mass) -- σ_{inf} (modulus vev at the end of inflation) is constrained by the non-observation of significant isocurvature fluctuations. We discuss in detail the evolution of the modulus vev and perturbations, in particular the consequences of Hubble scale cor…
The creation of cold dark matter cosmology model is studied beyond the linear perturbation level. The skewness is explicitly computed and the results are compared to those from the $Λ$CDM model. It is explicitly shown that both models have the same signature for the skewness and cannot be distinguished by using this observable.
General features of generation of the cosmological charge asymmetry in CPT non-invariant world are discussed. If the effects of CPT violation manifest themselves only in mass differences of particles and antiparticles, the baryon asymmetry of the universe hardly can be explained solely by breaking of CPT invariance. However, CPT non-invariant theories may lead to a new effect of distorting the usual equilibrium distributions. If this takes place, CPT violation may explain the baryon asymmetry of the universe.
In many strongly-interacting models of electroweak symmetry breaking the lowest-lying observable particle is a pseudo-Goldstone boson of approximate scale symmetry, the pseudo-dilaton. Its interactions with Standard Model particles can be described using a low-energy effective nonlinear chiral Lagrangian supplemented by terms that restore approximate scale symmetry, yielding couplings of the pseudo-dilaton that differ from those of a Standard Model Higgs boson by fixed factors. We review the experimental constraints on such a pseudo-dilaton in light of new data from the LHC and elsewhere. The …
We consider the possibility that dark energy and baryons might scatter off each other. The type of interaction we consider leads to a pure momentum exchange, and does not affect the background evolution of the expansion history. We parametrize this interaction in an effective way at the level of Boltzmann equations. We compute the effect of dark energy-baryon scattering on cosmological observables, focusing on the Cosmic Microwave Background (CMB) temperature anisotropy power spectrum and the matter power spectrum. Surprisingly, we find that even huge dark energy-baryon cross-sections $σ_{xb} …
In the early Universe, strongly interacting matter was a quark-gluon plasma. Both lattice computations and heavy ion collision experiments however tell us that, in the absence of chemical potentials, no plasma survives at $T <\sim 150$ MeV. The cosmological Quark-Hadron transition, however, seems to have been a crossover; cosmological consequences envisaged when it was believed to be a phase transition no longer hold. In this paper we discuss whether even a crossover transition can leave an imprint that cosmological observations can seek or, viceversa, there are questions cosmology should addr…
We study the effect of neutrino degeneracy on primordial nucleosynthesis in a universe in which the cosmological scale factor evolves linearly with time. The degeneracy parameter of electron type neutrinos ($ξ_e$) determines the $n/p$ (neutron to proton) ratio, which in turn determines the abundance of $^4$He in a manner quite distinct from the Standard Scenario. The observed abundances of $^4$He, $\mathrm{Y}_P$=0.254$\pm$0.003, and the minimum metallicity that is essential for fragmentation and cooling processes in star forming prestellar gas clouds (Z = Z$_{cr}$ = 10$^{-6}$Z$_\odot$), constr…
Interpreting the stacked kinetic SZ signal II: the degeneracy between satellite galaxies and baryonic feedback
Institute of Astronomy, University of Cambridge（剑桥大学天文学研究所）；Kavli Institute for Cosmology Cambridge（卡弗里宇宙学剑桥研究所）；Donostia International Physics Center（多诺斯蒂亚国际物理中心）；IKERBASQUE, Basque Foundation for Science（伊克巴萨奎，巴斯克科学基金会）
The effect of baryons on the matter power spectrum is likely to have an observable effect for future galaxy surveys, like Euclid or LSST. As a first step towards a fully predictive theory, we investigate the effect of non-radiative hydrodynamics on the structure of galaxy groups sized halos, which contribute the most to the weak lensing power spectrum. We perform high resolution (more than one million particles per halo and one kilo-parsec resolution) non-radiative hydrodynamical zoom-in simulations of a sample of 16 halos, comparing the profiles to popular analytical models. We find that the …
A cosmological model in an Einstein-Cartan framework endowed with torsion is studied. For a torsion function assumed to be proportional to Hubble expansion function, namely $ϕ=-αH$, the contribution of torsion function as a dark matter component is studied in two different approaches. In the first one, the total matter energy density is altered by torsion coupling $α$, giving rise to an effective dark matter and cosmological constant terms that reproduce quite well the flat cosmic concordance model. In the second approach, starting with just standard baryonic matter plus a cosmological constan…
