Abstract: A constant early dark energy (EDE) component contributing a fraction ${f}_{\mathrm{EDE}}({z}_{c})\ensuremath{\sim}10%$ of the energy density of the universe around ${z}_{c}\ensuremath{\simeq}3500$ and diluting as or faster than radiation afterwards, can provide a simple resolution to the Hubble tension, the $\ensuremath{\sim}5\ensuremath{\sigma}$ discrepancy---in the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ context---between the ${H}_{0}$ value derived from early- and late-universe observations. However, it has been pointed out that including Large-Scale Structure (LSS) data, which are in $\ensuremath{\sim}3\ensuremath{\sigma}$ tension with $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ and EDE cosmologies, might break some parameter degeneracy and alter these conclusions. We reassess the viability of the EDE against a host of high- and low-redshift measurements, by combining LSS observations from recent weak lensing (WL) surveys with CMB, baryon acoustic oscillation (BAO), growth function (FS) and Supernova Ia (SNIa) data. Introducing a model whose only parameter is ${f}_{\mathrm{EDE}}({z}_{c})$, we report in agreement with past work a $\ensuremath{\sim}2\ensuremath{\sigma}$ preference for nonzero ${f}_{\mathrm{EDE}}({z}_{c})$ from Planck CMB data alone, while the tension with the local ${H}_{0}$ measurement from sh0es is reduced below $2\ensuremath{\sigma}$. Adding BAO, FS and SNIa does not affect this conclusion, while the inclusion of a prior on ${H}_{0}$ from sh0es increase the preference for EDE over $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ to the $\ensuremath{\sim}3.6\ensuremath{\sigma}$ level. After checking the EDE nonlinear matter power spectrum as predicted by standard semi-analytical algorithms via a dedicated set of $N$-body simulations, we test the 1-parameter EDE cosmology against WL data. We find that it does not significantly worsen the fit to the ${S}_{8}$ measurement as compared to $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$, and that current WL observations do not exclude the EDE resolution to the Hubble tension. We also caution against the interpretation of constraints obtained from combining statistically inconsistent datasets within the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmology. In light of the CMB lensing anomalies, we show that the lensing-marginalized CMB data also favor nonzero ${f}_{\mathrm{EDE}}({z}_{c})$ at $\ensuremath{\sim}2\ensuremath{\sigma}$, predicts ${H}_{0}$ in $1.4\ensuremath{\sigma}$ agreement with sh0es and ${S}_{8}$ in $1.5\ensuremath{\sigma}$ and $0.8\ensuremath{\sigma}$ agreement with kids-viking and des respectively. There still exists however a $\ensuremath{\sim}2.5\ensuremath{\sigma}$ tension with the joint results from kids-viking and des. With an eye on Occam's razor, we finally discuss promising extensions of the EDE cosmology that could allow us to fully restore cosmological concordance.

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28 results found

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Abstract: The $\Lambda$CDM model provides a good fit to a large span of cosmological data but harbors areas of phenomenology. With the improvement of the number and the accuracy of observations, discrepancies among key cosmological parameters of the model have emerged. The most statistically significant tension is the $4-6\sigma$ disagreement between predictions of the Hubble constant $H_0$ by early time probes with $\Lambda$CDM model, and a number of late time, model-independent determinations of $H_0$ from local measurements of distances and redshifts. The high precision and consistency of the data at both ends present strong challenges to the possible solution space and demand a hypothesis with enough rigor to explain multiple observations--whether these invoke new physics, unexpected large-scale structures or multiple, unrelated errors. We present a thorough review of the problem, including a discussion of recent Hubble constant estimates and a summary of the proposed theoretical solutions. Some of the models presented are formally successful, improving the fit to the data in light of their additional degrees of freedom, restoring agreement within $1-2\sigma$ between {\it Planck} 2018, using CMB power spectra data, BAO, Pantheon SN data, and R20, the latest SH0ES Team measurement of the Hubble constant ($H_0 = 73.2 \pm 1.3{\rm\,km\,s^{-1}\,Mpc^{-1}}$ at 68\% confidence level). Reduced tension might not simply come from a change in $H_0$ but also from an increase in its uncertainty due to degeneracy with additional physics, pointing to the need for additional probes. While no specific proposal makes a strong case for being highly likely or far better than all others, solutions involving early or dynamical dark energy, neutrino interactions, interacting cosmologies, primordial magnetic fields, and modified gravity provide the best options until a better alternative comes along.[Abridged]

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Topics: Hubble's law (54%), Dark energy (53%), Planck (52%) ... show more

138 Citations

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Abstract: We revisit the impact of early dark energy (EDE) on galaxy clustering using BOSS galaxy power spectra, analyzed using the effective field theory (EFT) of large-scale structure (LSS), and anisotropies of the cosmic microwave background (CMB) from Planck. Recent studies found that these data place stringent constraints on the maximum abundance of EDE allowed in the Universe. We argue here that their conclusions are a consequence of their choice of priors on the EDE parameter space, rather than any disagreement between the data and the model. For example, when considering EFT-LSS, CMB, and high-redshift supernovae data we find the EDE and $\Lambda$CDM models can provide statistically indistinguishable fits ($\Delta \chi^2 = 0.12$) with a relatively large value for the maximum fraction of energy density in the EDE ($f_{\rm ede} = 0.09$) and Hubble constant ($H_0 = 71$ km/s/Mpc) in the EDE model. Moreover, we demonstrate that the constraining power added from the inclusion of EFT-LSS traces to the potential tension between the power-spectrum amplitudes $A_s$ derived from BOSS and from Planck that arises even within the context of $\Lambda$CDM. Until this is better understood, caution should be used when interpreting EFT-BOSS+Planck constraints to models beyond $\Lambda$CDM. These findings suggest that EDE still provides a potential resolution to the Hubble tension and that it is worthwhile to test the predictions of EDE with future data-sets and further study its theoretical possibilities.

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Topics: Planck (53%), Dark energy (53%), Hubble's law (52%) ... show more

35 Citations

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Abstract: The mismatch between the locally measured expansion rate of the universe and the one inferred from the cosmic microwave background measurements by Planck in the context of the standard ΛCDM, known as the Hubble tension, has become one of the most pressing problems in cosmology. A large number of amendments to the ΛCDM model have been proposed in order to solve this tension. Many of them introduce new physics, such as early dark energy, modifications of the standard model neutrino sector, extra radiation, primordial magnetic fields or varying fundamental constants, with the aim of reducing the sound horizon at recombination r⋆. We demonstrate here that any model which only reduces r⋆ can never fully resolve the Hubble tension while remaining consistent with other cosmological datasets. We show explicitly that models which achieve a higher Hubble constant with lower values of matter density Ωmh2 run into tension with the observations of baryon acoustic oscillations, while models with larger Ωmh2 develop tension with galaxy weak lensing data. It is generally accepted that the Universe is dominated by dark energy but the different methods to measure the Hubble constant disagree, giving origin to what is known as the "Hubble tension”. The authors demonstrate that the sole reduction of the sound horizon is not sufficient to fully resolve the Hubble tension.

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Topics: Dark energy (65%), Hubble's law (65%), Baryon acoustic oscillations (60%) ... show more

32 Citations

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Sunny Vagnozzi, Eleonora Di Valentino, Stefano Gariazzo, Alessandro Melchiorri +2 more•Institutions (1)

Abstract: The concordance of the $\Lambda$CDM cosmological model in light of current observations has been the subject of an intense debate in recent months. The 2018 Planck Cosmic Microwave Background (CMB) temperature anisotropy power spectrum measurements appear at face value to favour a spatially closed Universe with curvature parameter $\Omega_K<0$. This preference disappears if Baryon Acoustic Oscillation (BAO) measurements are combined with Planck data to break the geometrical degeneracy, although the reliability of this combination has been questioned due to the strong tension present between the two datasets when assuming a curved Universe. Here, we approach this issue from yet another point of view, using measurements of the full-shape (FS) galaxy power spectrum, $P(k)$, from the Baryon Oscillation Spectroscopic Survey DR12 CMASS sample. By combining Planck data with FS measurements, we break the geometrical degeneracy and find $\Omega_K=0.0023 \pm 0.0028$. This constrains the Universe to be spatially flat to sub-percent precision, in excellent agreement with results obtained using BAO measurements. However, as with BAO, the overall increase in the best-fit $\chi^2$ suggests a similar level of tension between Planck and $P(k)$ under the assumption of a curved Universe. While the debate on spatial curvature and the concordance between cosmological datasets remains open, our results provide new perspectives on the issue, highlighting the crucial role of FS measurements in the era of precision cosmology.

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Topics: Cosmic microwave background (59%), Planck (57%), Universe (56%) ... show more

31 Citations

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Abstract: The mismatch between the locally measured expansion rate of the universe and the one inferred from the cosmic microwave background measurements by Planck in the context of the standard $\Lambda$CDM, known as the Hubble tension, has become one of the most pressing problems in cosmology. A large number of amendments to the $\Lambda$CDM model have been proposed in order to solve this tension. Many of them introduce new physics, such as early dark energy, modifications of the standard model neutrino sector, extra radiation, primordial magnetic fields or varying fundamental constants, with the aim of reducing the sound horizon at recombination $r_{\star}$. We demonstrate here that any model which only reduces $r_{\star}$ can never fully resolve the Hubble tension while remaining consistent with other cosmological datasets. We show explicitly that models which achieve a higher Hubble constant with lower values of matter density $\Omega_m h^2$ run into tension with the observations of baryon acoustic oscillations, while models with larger $\Omega_mh^2$ develop tension with galaxy weak lensing data.

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Topics: Dark energy (61%), Hubble's law (59%), Baryon acoustic oscillations (57%) ... show more

28 Citations

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153 results found

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Abstract: The Gibbs sampler, the algorithm of Metropolis and similar iterative simulation methods are potentially very helpful for summarizing multivariate distributions. Used naively, however, iterative simulation can give misleading answers. Our methods are simple and generally applicable to the output of any iterative simulation; they are designed for researchers primarily interested in the science underlying the data and models they are analyzing, rather than for researchers interested in the probability theory underlying the iterative simulations themselves. Our recommended strategy is to use several independent sequences, with starting points sampled from an overdispersed distribution. At each step of the iterative simulation, we obtain, for each univariate estimand of interest, a distributional estimate and an estimate of how much sharper the distributional estimate might become if the simulations were continued indefinitely. Because our focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normality after transformations and marginalization, we derive our results as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations. The methods are illustrated on a random-effects mixture model applied to experimental measurements of reaction times of normal and schizophrenic patients.

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Topics: Bayesian inference (58%), Gibbs sampling (57%), Mixture model (55%) ... show more

12,022 Citations

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Abstract: We discuss the cosmological simulation code GADGET-2, a new massively parallel TreeSPH code, capable of following a collisionless fluid with the N-body method, and an ideal gas by means of smoothed particle hydrodynamics (SPH). Our implementation of SPH manifestly conserves energy and entropy in regions free of dissipation, while allowing for fully adaptive smoothing lengths. Gravitational forces are computed with a hierarchical multipole expansion, which can optionally be applied in the form of a TreePM algorithm, where only short-range forces are computed with the ‘tree’ method while long-range forces are determined with Fourier techniques. Time integration is based on a quasi-symplectic scheme where long-range and short-range forces can be integrated with different time-steps. Individual and adaptive short-range time-steps may also be employed. The domain decomposition used in the parallelization algorithm is based on a space-filling curve, resulting in high flexibility and tree force errors that do not depend on the way the domains are cut. The code is efficient in terms of memory consumption and required communication bandwidth. It has been used to compute the first cosmological N-body simulation with more than 10 10 dark matter particles, reaching a homogeneous spatial dynamic range of 10 5 per dimension in a three-dimensional box. It has also been used to carry out very large cosmological SPH simulations that account for radiative cooling and star formation, reaching total particle numbers of more than 250 million. We present the algorithms used by the code and discuss their accuracy and performance using a number of test problems. GADGET-2 is publicly released to the research community. Ke yw ords: methods: numerical ‐ galaxies: interactions ‐ dark matter.

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Topics: N-body simulation (55%), Smoothed-particle hydrodynamics (54%), Matter power spectrum (51%) ... show more

6,033 Citations

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Abstract: We implement the efficient line-of-sight method to calculate the anisotropy and polarization of the cosmic microwave background for scalar and tensor modes in almost Friedmann-Robertson-Walker models with positive spatial curvature. We present new results for the polarization power spectra in such models.

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Topics: Sachs–Wolfe effect (55%), Cosmic microwave background (55%), Baryon acoustic oscillations (52%) ... show more

3,851 Citations

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Nabila Aghanim^{1}, Yashar Akrami^{2}, Yashar Akrami^{3}, Yashar Akrami^{4} +229 more•Institutions (70)

Abstract: We present cosmological parameter results from the ﬁnal full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to signiﬁcant gains in the precision of other correlated parameters Improved modelling of the small-scale polarization leads to more robust constraints on manyparameters,withresidualmodellinguncertaintiesestimatedtoaﬀectthemonlyatthe05σlevelWeﬁndgoodconsistencywiththestandard spatially-ﬂat6-parameter ΛCDMcosmologyhavingapower-lawspectrumofadiabaticscalarperturbations(denoted“base ΛCDM”inthispaper), from polarization, temperature, and lensing, separately and in combination A combined analysis gives dark matter density Ωch2 = 0120±0001, baryon density Ωbh2 = 00224±00001, scalar spectral index ns = 0965±0004, and optical depth τ = 0054±0007 (in this abstract we quote 68% conﬁdence regions on measured parameters and 95% on upper limits) The angular acoustic scale is measured to 003% precision, with 100θ∗ = 10411±00003Theseresultsareonlyweaklydependentonthecosmologicalmodelandremainstable,withsomewhatincreasederrors, in many commonly considered extensions Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: HubbleconstantH0 = (674±05)kms−1Mpc−1;matterdensityparameterΩm = 0315±0007;andmatterﬂuctuationamplitudeσ8 = 0811±0006 We ﬁnd no compelling evidence for extensions to the base-ΛCDM model Combining with baryon acoustic oscillation (BAO) measurements (and consideringsingle-parameterextensions)weconstraintheeﬀectiveextrarelativisticdegreesoffreedomtobe Neﬀ = 299±017,inagreementwith the Standard Model prediction Neﬀ = 3046, and ﬁnd that the neutrino mass is tightly constrained toPmν < 012 eV The CMB spectra continue to prefer higher lensing amplitudesthan predicted in base ΛCDM at over 2σ, which pulls some parameters that aﬀect thelensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAOdataThejointconstraintwithBAOmeasurementsonspatialcurvatureisconsistentwithaﬂatuniverse, ΩK = 0001±0002Alsocombining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w0 = −103±003, consistent with a cosmological constant We ﬁnd no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r0002 < 006 Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations The Planck base-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey’s combined-probe results including galaxy clustering (which prefers lower ﬂuctuation amplitudes or matter density parameters), and in signiﬁcant, 36σ, tension with local measurements of the Hubble constant (which prefer a higher value) Simple model extensions that can partially resolve these tensions are not favoured by the Planck data

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Topics: Baryon acoustic oscillations (62%), Planck (58%), Dark energy (58%) ... show more

3,432 Citations