Early Dark Energy Models Research Articles

Clustering and halo abundances in early dark energy cosmological models

ABSTRACT Cold Dark Matter with cosmological constant (ΛCDM) cosmological models with early dark energy (EDE) have been proposed to resolve tensions between the Hubble constant $H_0=100\, h$ km ṡ−1Ṁpc−1 measured locally, giving h ≈ 0.73, and H0 deduced from Planck cosmic microwave background (CMB) and other early-Universe measurements plus ΛCDM, giving h ≈ 0.67. EDE models do this by adding a scalar field that temporarily adds dark energy equal to about 10 per cent of the cosmological energy density at the end of the radiation-dominated era at redshift z ∼ 3500. Here, we compare linear and non-linear predictions of a Planck-normalized ΛCDM model including EDE giving h = 0.728 with those of standard Planck-normalized ΛCDM with h = 0.678. We find that non-linear evolution reduces the differences between power spectra of fluctuations at low redshifts. As a result, at z = 0 the halo mass functions on galactic scales are nearly the same, with differences only 1–2 per cent. However, the differences dramatically increase at high redshifts. The EDE model predicts 50 per cent more massive clusters at z = 1 and twice more galaxy-mass haloes at z = 4. Even greater increases in abundances of galaxy-mass haloes at higher redshifts may make it easier to reionize the universe with EDE. Predicted galaxy abundances and clustering will soon be tested by the James Webb Space Telescope (JWST) observations. Positions of baryonic acoustic oscillations (BAOs) and correlation functions differ by about 2 per cent between the models – an effect that is not washed out by non-linearities. Both standard ΛCDM and the EDE model studied here agree well with presently available acoustic-scale observations, but the Dark Energy Spectroscopic Instrument and Euclid measurements will provide stringent new tests.

Sources of H0 -tension in dark energy scenarios

By focusing on the simple $w\neq-1$ extension to $\Lambda$CDM, we assess which epoch(s) possibly source the $H_0$-tension. We consider Cosmic Microwave Background (CMB) data in three possible ways: $i)$ complete CMB data; $ii)$ excluding the $l<30$ temperature and polarization likelihoods; $iii)$ imposing early universe priors, that disentangle early and late time physics. Through a joint analysis with low-redshift supernovae type-Ia and gravitationally lensed time delay datasets, {and neglecting galaxy clustering Baryonic Acoustic Oscillation (BAO) data}, we find that the inclusion of early universe CMB priors is consistent with the local estimate of $H_0$ while excluding the low-$l$+lowE likelihoods mildly relaxes the tension. This is in contrast to joint analyses with the complete CMB data. Our simple implementation of contrasting the effect of different CMB priors on the $H_0$ estimate shows that the early universe information from the CMB data when decoupled from late-times physics could be in agreement with a higher value of $H_0$. {We also find no evidence for the early dark energy model using only the early universe physics within the CMB data. Finally using the BAO data in different redshift ranges to perform inverse distance ladder analysis, we find that the early universe modifications, while being perfectly capable of alleviating the $H_0$-tension when including the BAO galaxy clustering data, would be at odds with the Ly-$\alpha$ BAO data due to the difference in $r_{\rm d}\, vs.\, H_0$ correlation between the two BAO datasets.} We therefore infer and speculate that source for the $H_0$-tension between CMB and local estimates could possibly originate in the modeling of late-time physics within the CMB analysis. This in turn recasts the $H_0$-tension as an effect of late-time physics in CMB, instead of the current early-time CMB vs. local late-time physics perspective.

Exploring an early dark energy solution to the Hubble tension with Planck and SPTPol data

A promising idea to resolve the long standing Hubble tension is to postulate a new subdominant dark-energy-like component in the pre-recombination Universe which is traditionally termed as the Early Dark Energy (EDE). However, as shown in Refs. \cite{Hill:2020osr,Ivanov:2020ril} the cosmic microwave background (CMB) and large-scale structure (LSS) data impose tight constraints on this proposal. Here, we revisit these strong bounds considering the Planck CMB temperature anisotropy data at large angular scales and the SPTPol polarization and lensing measurements. As advocated in Ref. \cite{Chudaykin:2020acu}, this combined data approach predicts the CMB lensing effect consistent with the $\Lambda$CDM expectation and allows one to efficiently probe both large and small angular scales. Combining Planck and SPTPol CMB data with the full-shape BOSS likelihood and information from photometric LSS surveys in the EDE analysis we found for the Hubble constant $H_0=69.79\pm0.99\,{\rm km\,s^{-1}Mpc^{-1}}$ and for the EDE fraction $f_{\rm EDE}<0.094\,(2\sigma)$. These bounds obtained without including a local distance ladder measurement of $H_0$ (SH0ES) alleviate the Hubble tension to a $2.5\sigma$ level. Including further the SH0ES data we obtain $H_0=71.81\pm1.19\,{\rm km\,s^{-1}Mpc^{-1}}$ and $f_{\rm EDE}=0.088\pm0.034$ in full accordance with SH0ES. We also found that a higher value of $H_0$ does not significantly deteriorate the fit to the LSS data. Overall, the EDE scenario is (though weakly) favoured over $\Lambda$CDM even after accounting for unconstrained directions in the cosmological parameter space. We conclude that the large-scale Planck temperature and SPTPol polarization measurements along with LSS data do not rule out the EDE model as a resolution of the Hubble tension. This paper underlines the importance of the CMB lensing effect for robust constraints on the EDE scenario.

Early modified gravity in light of the H0 tension and LSS data

We present a model of Early Modified Gravity (EMG) consisting in a scalar field $\sigma$ with a non-minimal coupling to the Ricci curvature of the type $M^2_{\rm pl}+\xi \sigma^2$ plus a cosmological constant and a small effective mass and demonstrate its ability to alleviate the $H_0$ tension while providing a good fit to Cosmic Microwave Background (CMB) anisotropies and Baryon Acoustic Oscillations (BAO) data. In this model the scalar field, frozen deep in the radiation era, grows around the redshift of matter-radiation equality because of the coupling to non-relativistic matter. The small effective mass, which we consider here as induced by a quartic potential, then damps the scalar field into coherent oscillations around its minimum at $\sigma=0$, leading to a weaker gravitational strength at early times and naturally recovering the consistency with laboratory and Solar System tests of gravity. We analyze the capability of EMG with positive $\xi$ to fit current cosmological observations and compare our results to the case without an effective mass and to the popular early dark energy models with $\xi=0$. We show that EMG with a quartic coupling of the order of $\lambda\sim\mathcal{O}({\rm eV}^4/M_{\rm pl}^4)$ can substantially alleviate the $H_0$ tension also when the full shape of the matter power spectrum is included in the fit in addition to CMB and Supernovae (SN) data.

Early dark energy in k -essence

Early dark energy (EDE) that becomes subdominant around the epoch of matter-radiation equality can be used to ease the Hubble tension. However, there is the theoretical problem of why the energy scale of EDE is in coincidence with that of matter-radiation equality when their physics are completely unrelated. Sakstein and Trodden [Phys. Rev. Lett. 124, 161301 (2020)] proposed a mechanism to solve this coincidence problem with $\mathcal{O}(\mathrm{eV})$-mass neutrino. In this paper, in order to solve the coincidence problem, we propose a new scenario for EDE in which the onset and ending of EDE are triggered by the radiation-matter transition. The specific example we study is a $k$-essence model. The cosmic evolution equations can be recast into a two-dimensional dynamical system, and its main properties are analyzed. Our results suggest that $k$-essence seems unable to realize the new scenario for EDE. However, an EDE model with a different scenario is realized in $k$-essence. In this model, the ending of EDE can be triggered by the radiation-matter transition, while the onset depends on the initial conditions of the scalar field. Therefore, the obtained model can only be used to solve half of the coincidence problem. The full resolution in the framework of our initial proposed scenario is worthy of more research.

Testing H0 in acoustic dark energy models with Planck and ACT polarization data

The canonical acoustic dark energy model (cADE), which is based on a scalar field with a canonical kinetic term that rapidly converts potential to kinetic energy around matter radiation equality, alleviates the Hubble tension found in $\Lambda$CDM. We show that it successfully passes new consistency tests in the CMB damping tail provided by the ACT data, while being increasingly constrained and distinguished from alternate mechanisms by the improved CMB acoustic polarization data from Planck. The best fit cADE model to a suite of cosmological observations, including the SH0ES $H_0$ measurement, has $H_0=70.25$ compared with $68.23$ (km s$^{-1}$ Mpc$^{-1}$) in $\Lambda$CDM and a finite cADE component is preferred at the $2.8\sigma$ level. The ability to raise $H_0$ is now mainly constrained by the improved Planck acoustic polarization data, which also plays a crucial role in distinguishing cADE from the wider class of early dark energy models. ACT and Planck TE polarization data are currently mildly discrepant in normalization and drive correspondingly different preferences in parameters. Improved constraints on intermediate scale polarization approaching the cosmic variance limit will be an incisive test of the acoustic dynamics of these models and their alternatives.

Planck 2018 constraints on anisotropic birefringence and its cross-correlation with CMB anisotropy

Parity-violating extensions of standard electromagnetism produce cosmic birefringence, the in vacuo rotation of the linear polarisation direction of a photon during propagation. We employ Planck 2018 CMB polarised data to constrain anisotropic birefringence, modeled by its angular power spectrum Cℓα α, and the cross-correlation with CMB temperature maps, Cℓα T, at scales larger than ∼15 degrees. We present joint limits on the scale invariant quantity, Aα α ≡ ℓ (ℓ +1) Cℓα α / 2 π, and on the analogous amplitude for the cross-correlation, Aα T ≡ ℓ (ℓ +1) Cℓα T / 2 π. We find no evidence of birefringence within the error budget and obtain Aα α < 0.104 [deg^2] and Aα T=1.50+2.41−4.10 [\\muK\\cdotdeg] both at 95 % C.L.. The latter bound appears competitive in constraining a few early dark energy models recently proposed to alleviate the H0 tension. Slicing the joint likelihood at 0Aα T=, the bound on Aα α becomes tighter at Aα α < 0.085 [deg^2] at 95% C.L.. In addition we recast the constraints on Aα α as a bound on the amplitude of primordial magnetic fields responsible for Faraday rotation, finding B1 Mpc < 26.9 nG and B1 Mpc < 24.3 nG at 95% C.L. for the marginalised and sliced case respectively.

Unified framework for early dark energy from α -attractors

One of the most appealing approaches to ease the Hubble tension is the inclusion of an early dark energy (EDE) component that adds energy to the Universe in a narrow redshift window around the time of recombination and dilutes faster than radiation afterwards. In this paper, we analyze EDE in the framework of $\alpha$-attractor models. As well known, the success in alleviating the Hubble tension crucially depends on the shape of the energy injection. We show how different types of energy injections can be easily obtained, thanks to the freedom in choosing the functional form of the potential inspired by $\alpha$-attractor models. To confirm our intuition we perform an MCMC analysis for three representative cases and find indeed that $H_0$ is significantly larger than in $\Lambda$CDM like in other EDE models. Unlike axion-driven EDE models with super Planckian decay constant, the curvature of EDE models required by the data is natural in the context of recent theoretical developments in $\alpha$-attractors.

A novel early dark energy model

We present a theoretical study of an early dark energy (EDE) model. The equation of state ω(z) evolves during the thermal history in a framework of a Friedmann-Lemaitre-Robertson-Walker Universe, following an effective parametrization that is a function of redshift z. We explore the evolution of the system from the radiation domination era to the late times, allowing the EDE model to have a non-negligible contribution at high redshift (as opposed to the cosmological constant that only plays a role once the structure is formed) with a very little input to the Big Bang Nucleosynthesis, and to do so, the equation of state mimics the radiation behaviour, but being subdominant in terms of its energy density. At late times, the equation of state of the dark energy model asymptotically tends to the fiducial value of the De Sitter domination epoch, providing an explanation for the accelerated expansion of the Universe at late times, emulating the effect of the cosmological constant. The proposed model has three free parameters, that we constrain using SNIa luminosity distances, along with the CMB shift parameter and the deceleration parameter calculated at the time of dark energy - matter equality. With full knowledge of the best fit for our model, we calculate different observables and compare these predictions with the standardΛCDM model. Besides the general consent of the community with the cosmological constant, there is no fundamental reason to choose that particular candidate as dark energy. Here, we open the opportunity to consider a more dynamical model, that also accounts for the late accelerated expansion of the Universe.

Combined analysis of Planck and SPTPol data favors the early dark energy models

We study the implications of the Planck temperature power spectrum at low multipoles, 0ℓ<100, and SPTPol data. We show that this combination predicts consistent lensing-induced smoothing of acoustic peaks within ΛCDM cosmology and yields the robust predictions of the cosmological parameters. Combining only the Planck large-scale temperature data and the SPTPol polarization and lensing measurements within ΛCDM model we found substantially lower values of linear matter density perturbation σ8 which bring the late-time parameter S8=σ8√Ωm/0.3=0.763±0.022 into accordance with galaxy clustering and weak lensing measurements. It also raises up the Hubble constant H0=69.68±1.00kms that reduces the Hubble tension to the 2.5σ level. We examine the residual tension in the Early Dark Energy (EDE) model which produces the brief energy injection prior to recombination. We implement both the background and perturbation evolutions of the scalar field which potential scales as V(ϕ)∝ ϕ2n. Including cosmic shear measurements (KiDS, VIKING-450, DES) and local distance-ladder data (SH0ES) to the combined fit we found that EDE completely alleviates the Hubble tension while not degradating the fit to large-scale structure data. The EDE scenario significantly improves the goodness-of-fit by 2.9σ in comparison with the concordance ΛCDM model. The account for the intermediate-redshift data (the supernova dataset and baryon acoustic oscillation data) fits perfectly to our parameter predictions and indicates the preference of EDE over ΛCDM at 3σ.

One-point probability distribution function from spherical collapse: early dark energy versus ΛCDM

ABSTRACT We compute the one-point probability distribution function (PDF) of an initially Gaussian dark matter density field using spherical collapse (SC). We compare the results to other forms available in the literature and also compare the PDFs in the Λ-cold dark matter model with an early dark energy (EDE) model. We find that the skewed lognormal distribution provides the best fit to the non-linear PDF from SC for both cosmologies, from a = 0.1 to 1 and for scales characterized by the comoving width of the Gaussian: σG = 0.5, 1, and 2. To elucidate the effect of cosmology, we examine the linear and non-linear growth rates through test cases. For overdensities, when the two models have the same initial density contrast, the differences due to cosmology are amplified in the non-linear regime, whereas, if the two models have the same linear density contrast today, then the differences in cosmology are damped in the non-linear regime. This behaviour is in contrast with voids, where the non-linear growth becomes ‘self-regulatory’ and is less sensitive to cosmology and initial conditions. To compare the PDFs, we examine the difference of the PDFs and evolution of the width of the PDF. The trends with scale and redshift are as expected. A tertiary aim of this paper was to check if the fitting form for the non-linear density–velocity divergence relation, derived for constant equation of state (w) models by Nadkarni-Ghosh holds for the EDE model. We find that it does with an accuracy of 4 per cent, thus increasing its range of validity.

Constraints on the spacetime dynamics of an early dark energy component

We consider an Early Dark Energy (EDE) cosmological model, and perform an analysis which takes into account both background and perturbation effects via the parameters c2eff and c2vis, representing effective sound speed and viscosity, respectively. By using the latest available data we derive constraints on the amount of dark energy at early times and the present value of the equation of state. Our focus is on the effect that early dark energy has on the Cosmic Microwave Background (CMB) data, including polarization and lensing, in a generalized parameter space including a varying total neutrino mass, and tensor to scalar ratio, besides the 6 standard parameters of the minimal cosmological model. We find that the inclusion of Baryonic Acoustic Oscillations (BAO) data and CMB lensing significantly improves the constraints on the EDE parameters, while other high redshift data like the Quasar Hubble diagram and the Lyman-α forest BAO have instead a negligible impact. We find ΩeDE < 0.0039 and w0 < −0.95 at the 95 % C.L. for EDE accounting for its clustering through the inclusion of perturbation dynamics. This limit becomes weaker ΩeDE < 0.0034 if perturbations are neglected. The constraints on the EDE parameters are remarkably stable even when Σ mν, and r parameters are varied, with weak degeneracies between ΩeDE and r or Σ mν. In general we expect smaller values for the upper limits on the total amount of EDE with an increasing neutrino mass, while with a decreasing value of the tensor to scalar ratio we expect the 2σ upper limits on EDE to increase. We compare this EDE model with a simple wCDM with zero dark energy at early times and we find ∼1–2% different upper limits on total neutrino mass and ∼0.1–0.2% difference on the equation of state at the present time. Perturbation parameters are not constrained with current data sets, and tensions between the CMB derived H0 and σ8 values and those measured with local probes are not eased. This work demonstrates the capability of CMB probes to constrain the total amount of EDE well below the percent level.

Early Dark Energy from Massive Neutrinos as a Natural Resolution of the Hubble Tension

The Hubble tension can be significantly eased if there is an early component of dark energy that becomes active around the time of matter-radiation equality. Early dark energy models suffer from a coincidence problem-the physics of matter-radiation equality and early dark energy are completely disconnected, so some degree of fine-tuning is needed in order for them to occur nearly simultaneously. In this Letter, we propose a natural explanation for this coincidence. If the early dark energy scalar couples to neutrinos then it receives a large injection of energy around the time that neutrinos become nonrelativistic. This is precisely when their temperature is of order of their mass, which, coincidentally, occurs around the time of matter-radiation equality. Neutrino decoupling therefore provides a natural trigger for early dark energy by displacing the field just before matter-radiation equality. We discuss various theoretical aspects of this proposal, potential observational signatures, and future directions for its study.

Is the Hubble tension a hint of AdS phase around recombination?

Anti-de Sitter (AdS) vacua, being theoretically important, might have an unexpected impact on the observable universe. We find that in early dark energy (EDE) scenarios the existence of AdS vacua around recombination can effectively lift the CMB-inferred $H_0$ value. As an example, we study a phenomenological EDE model with an AdS phase starting at the redshift $z\sim2000$ and ending shortly after recombination (hereafter the universe will settle down in a $\Lambda>0$ phase until now), and obtain a best-fit $H_0=72.74$ km/s/Mpc without degrading the CMB fit compared with the standard $\Lambda$CDM model.

Can we distinguish early dark energy from a cosmological constant?

Early dark energy (EDE) models are a class of quintessence dark energy with a dynamically evolving scalar field which display a small but non-negligible amount of dark energy at the epoch of matter-radiation equality. Compared with a cosmological constant, the presence of dark energy at early times changes the cosmic expansion history and consequently the shape of the linear theory power spectrum and potentially other observables. We constrain the cosmological parameters in the EDE cosmology using recent measurements of the cosmic microwave background and baryon acoustic oscillations. The best-fitting models favour no EDE; here we consider extreme examples which are in mild tension with current observations in order to explore the observational consequences of a maximally allowed amount of EDE. We study the non-linear evolution of cosmic structure in EDE cosmologies using large volume N-body simulations. Many large-scale structure statistics are found to be very similar between the $\Lambda$ cold dark matter ($\Lambda$CDM) and EDE models. We find that the most promising way to distinguish EDE from $\Lambda$CDM is to measure the power spectrum on large scales, where differences of up to 15% are expected.

Early dark energy and its interaction with dark matter

We study a class of early dark energy models which has a substantial amount of dark energy in the early epoch of the Universe. We examine the impact of the early dark energy fluctuations on the growth of structure and the cosmic microwave background power spectrum in the linear approximation. Furthermore, we investigate the influence of the interaction between the early dark energy and the dark matter and its effect on the structure growth and cosmic microwave background. We finally constrain the early dark energy model parameters and the coupling between dark sectors by confronting different observations.

Current constraints on early and stressed dark energy models and future 21 cm perspectives

Despite the great progress of current cosmological measurements, the nature of the dominant component of the universe, coined dark energy, is still an open question. Early Dark Energy is a possible candidate which may also alleviate some fine tuning issues of the standard paradigm. Using the latest available cosmological data, we find that the 95% CL upper bound on the early dark energy density parameter is $\Omega_{\textrm{eDE}}$. On the other hand, the dark energy component may be a stressed and inhomogeneous fluid. If this is the case, the effective sound speed and the viscosity parameters are unconstrained by current data. Future omniscope-like $21$cm surveys, combined with present CMB data, could be able to distinguish between standard quintessence scenarios from other possible models with $2\sigma$ significance, assuming a non-negligible early dark energy contribution. The precision achieved on the $\Omega_{\textrm{eDE}}$ parameter from these $21$ cm probes could be below $\mathcal{O} (10\%)$.

Dark energy coupling with electromagnetism as seen from future low-medium redshift probes

Beyond the standard cosmological model the late-time accelerated expansion of the universe can be reproduced by the introduction of an additional dynamical scalar field. In this case, the field is expected to be naturally coupled to the rest of the theory's fields, unless a (still unknown) symmetry suppresses this coupling. Therefore, this would possibly lead to some observational consequences, such as space-time variations of nature's fundamental constants. In this paper we investigate the coupling between a dynamical Dark Energy model and the electromagnetic field, and the corresponding evolution of the fine structure constant ($\alpha$) with respect to the standard local value $\alpha_0$. In particular, we derive joint constraints on two dynamical Dark Energy model parametrizations (the Chevallier-Polarski-Linder and Early Dark Energy model) and on the coupling with electromagnetism $\zeta$, forecasting future low-medium redshift observations. We combine supernovae and weak lensing measurements from the Euclid experiment with high-resolution spectroscopy measurements of fundamental couplings and the redshift drift from the European Extremely Large Telescope, highlighting the contribution of each probe. Moreover, we also consider the case where the field driving the $\alpha$ evolution is not the one responsible for cosmic acceleration and investigate how future observations can constrain this scenario.

Structure formation in inhomogeneous Early Dark Energy models

We study the impact of Early Dark Energy fluctuations in the linear and non-linear regimes of structure formation. In these models the energy density of dark energy is non-negligible at high redshifts and the fluctuations in the dark energy component can have the same order of magnitude of dark matter fluctuations. Since two basic approximations usually taken in the standard scenario of quintessence models, that both dark energy density during the matter dominated period and dark energy fluctuations on small scales are negligible, are not valid in such models, we first study approximate analytical solutions for dark matter and dark energy perturbations in the linear regime. This study is helpful to find consistent initial conditions for the system of equations and to analytically understand the effects of Early Dark Energy and its fluctuations, which are also verified numerically. In the linear regime we compute the matter growth and variation of the gravitational potential associated with the Integrated Sachs-Wolf effect, showing that these observables present important modifications due to Early Dark Energy fluctuations, though making them more similar to the ΛCDM model. We also make use of the Spherical Collapse model to study the influence of Early Dark Energy fluctuations in the nonlinear regime of structure formation, especially on δc parameter, and their contribution to the halo mass, which we show can be of the order of 10%. We finally compute how the number density of halos is modified in comparison to the ΛCDM model and address the problem of how to correct the mass function in order to take into account the contribution of clustered dark energy. We conclude that the inhomogeneous Early Dark Energy models are more similar to the ΛCDM model than its homogeneous counterparts.

Semi-analytic galaxy formation in early dark energy cosmologies

We study the impact of early dark energy (EDE) cosmologies on galaxy properties by coupling high-resolution numerical simulations with semi-analytic modeling (SAM) of galaxy formation and evolution. EDE models are characterized by a non-vanishing high-redshift contribution of dark energy, producing an earlier growth of structures and a modification of large-scale structure evolution. They can be viewed as typical representatives of non-standard dark energy models in which only the expansion history is modified, and hence the impact on galaxy formation is indirect. We show that in EDE cosmologies the predicted space density of galaxies is enhanced at all scales with respect to the standard LCDM scenario, and the corresponding cosmic star formation history and stellar mass density is increased at high-redshift. We compare these results with a set of theoretical predictions obtained with alternative SAMs applied to our reference LCDM simulation, yielding a rough measure of the systematic uncertainty of the models. We find that the modifications in galaxy properties induced by EDE cosmologies are of the same order of magnitude as intra-SAM variations for a standard LCDM realization (unless rather extreme EDE models are considered), suggesting that is difficult to use such predictions alone to disentangle between different cosmological scenarios. However, when independent information on the underlying properties of host dark matter haloes is included, the SAM predictions on galaxy bias may provide important clues on the expansion history and the equation-of-state evolution.