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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

The first Hubble diagram and cosmological constraints using superluminous supernovae

In this work, we present the first Hubble diagram of superluminous supernovae (SLSNe) out to a redshift of two, together with constraints on the matter density, Ω M , and the dark energy equation-of-state parameter, w(≡p/ρ). We build a sample of 20 cosmologically useful SLSNe I based on light curve and spectroscopy quality cuts. We confirm the robustness of the peak–decline SLSN I standardization relation with a larger data set and improved fitting techniques than previous works. We then solve the SLSN model based on the above standardization via minimization of the χ2 computed from a covariance matrix that includes statistical and systematic uncertainties. For a spatially flat Λ cold dark matter (ΛCDM) cosmological model, we find $\Omega _{\rm M}=0.38^{+0.24}_{-0.19}$, with an rms of 0.27 mag for the residuals of the distance moduli. For a w 0 w a CDM cosmological model, the addition of SLSNe I to a ‘baseline’ measurement consisting of Planck temperature together with Type Ia supernovae, results in a small improvement in the constraints of w 0 and wa of 4 per cent. We present simulations of future surveys with 868 and 492 SLSNe I (depending on the configuration used) and show that such a sample can deliver cosmological constraints in a flat ΛCDM model with the same precision (considering only statistical uncertainties) as current surveys that use Type Ia supernovae, while providing a factor of 2–3 improvement in the precision of the constraints on the time variation of dark energy, w 0 and w a . This paper represents the proof of concept for superluminous supernova cosmology, and demonstrates they can provide an independent test of cosmology in the high-redshift (z > 1) universe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Hubble Space Telescope Captures UGC 12591: bulge/disc properties, star formation and ‘missing baryons’ census in a very massive and fast-spinning hybrid galaxy

We present Hubble Space Telescope (HST) observations of the nearby, massive, highly rotating hybrid galaxy UGC 12591, along with observations in the UV to FIRbands. HST data in V, I, and H bands is used to disentangle the structural components. Surface photometry shows a dominance of the bulge over the disc with an H-band B/D ratio of $69{{\,\rm per\,cent}}$. The spectral energy distribution (SED) fitting reveals an extremely low global star formation rate (SFR) of $\rm \sim 0.1\!-\!0.2\, M_\odot \, yr^{-1}$, exceptionally low for the galaxy’s huge stellar mass of $\rm 1.6\times 10^{11}M_\odot$, implying a strong quenching of its SFR with a star formation efficiency of 3–5 per cent. For at least the past $\rm 10^{8}$ yr, the galaxy has remained in a quiescent state as a sterile, ‘red and dead’ galaxy. UGC 12591 hosts a supermassive black hole (SMBH) of $\rm 6.18\times 10^{8} \, M_\odot$, which is possibly quiescent at present, i.e. we neither see large ($\rm \gt 1 kpc$) radio jets nor the SMBH contributing significantly to the mid-IR SED, ruling out strong radiative feedback of AGN. We obtained a detailed census of all observable baryons with a total mass of $\rm 6.46\times 10^{11} \, M_\odot$ within the virial radius, amounting to a baryonic deficiency of ${\sim }85{{\,\rm per\,cent}}$ relative to the cosmological mean. Only a small fraction of these baryons reside in a warm/hot circumgalactic X-ray halo, while the majority are still unobservable. We discussed various astrophysical scenarios to explain its unusual properties. Our work is a major step forward in understanding the assembly history of such extremely massive, isolated galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

A dark siren measurement of the Hubble constant using gravitational wave events from the first three LIGO/Virgo observing runs and DELVE

The current and next observation seasons will detect hundreds of gravitational waves (GWs) from compact binary systems coalescence at cosmological distances. When combined with independent electromagnetic measurements, the source redshift will be known, and we will be able to obtain precise measurements of the Hubble constant H_0 via the distance–redshift relation. However, most observed mergers are not expected to have electromagnetic counterparts, which prevents a direct redshift measurement. In this scenario, one possibility is to use the dark sirens method that statistically marginalizes over all the potential host galaxies within the GW location volume to provide a probabilistic source redshift. Here we presented H_0 measurements using two new dark sirens compared to previous analyses using DECam data: GW190924|$\_$|021846 and GW200202|$\_$|154313. The photometric redshifts of the possible host galaxies of these two events are acquired from the DECam Local Volume Exploration Survey (DELVE) carried out on the Blanco telescope at Cerro Tololo. The combination of the H_0 posterior from GW190924|$\_$|021846 and GW200202|$\_$|154313 together with the bright siren GW170817 leads to |$H_{0} = 68.84^{+15.51}_{-7.74}\, \rm {km\, s^{-1}\, Mpc^{-1}}$|⁠. Including these two dark sirens improves the 68 per cent confidence interval (CI) by 7 per cent over GW170817 alone. This demonstrates that the addition of well-localized dark sirens in such analysis improves the precision of cosmological measurements. Using a sample containing 10 well-localized dark sirens observed during the third LIGO/Virgo observation run, without the inclusion of GW170817, we determine a measurement of |$H_{0} = 76.00^{+17.64}_{-13.45}\, \rm {km\, s^{-1}\, Mpc^{-1}}$|⁠.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

The Dark Energy Survey Supernova Program: an updated measurement of the Hubble constant using the inverse distance ladder

We measure the current expansion rate of the Universe, Hubble’s constant $H_0$, by calibrating the absolute magnitudes of supernovae to distances measured by baryon acoustic oscillations (BAO). This ‘inverse distance ladder’ technique provides an alternative to calibrating supernovae using nearby absolute distance measurements, replacing the calibration with a high-redshift anchor. We use the recent release of 1829 supernovae from the Dark Energy Survey spanning $0.01\lt z\lt 1.13$ anchored to the recent baryon acoustic oscillation measurements from Dark Energy Spectroscopic Instrument (DESI) spanning $0.30 \lt z_{\mathrm{eff}}\lt 2.33$. To trace cosmology to $z=0$, we use the third-, fourth-, and fifth-order cosmographic models, which, by design, are agnostic about the energy content and expansion history of the universe. With the inclusion of the higher redshift DESI-BAO data, the third-order model is a poor fit to both data sets, with the fourth-order model being preferred by the Akaike Information Criterion. Using the fourth-order cosmographic model, we find $H_0=67.19^{+0.66}_{-0.64}\mathrm{~km} \mathrm{~s}^{-1} \mathrm{~Mpc}^{-1}$, in agreement with the value found by Planck without the need to assume Flat-$\Lambda$CDM. However, the best-fitting expansion history differs from that of Planck, providing continued motivation to investigate these tensions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Correcting for Selection Biases in the Determination of the Hubble Constant from Time-Delay Cosmography

The time delay between multiple images of strongly lensed quasars has been used to infer the Hubble constant. The primary systematic uncertainty for time-delay cosmography is the mass-sheet transform (MST), which preserves the lensing observables while altering the inferred ⁠H 0 . The TDCOSMO collaboration used velocity dispersion measurements of lensed quasars and lensed galaxies to infer that mass sheets are present, which decrease the inferred H 0 by 8 per cent. Here, we test the assumption that the density profiles of galaxy–galaxy and galaxy–quasar lenses are the same. We use a composite star-plus-dark-matter mass profile for the parent deflector population and model the selection function for galaxy–galaxy and galaxy–quasar lenses. We find that a power-law density profile with an MST is a good approximation to a two-component mass profile around the Einstein radius, but we find that galaxy–galaxy lenses have systematically higher mass-sheet components than galaxy–quasar lenses. For individual systems, λ int correlates with the ratio of the half-light radius and Einstein radius of the lens. By propagating these results through the TDCOSMO hierarchical inference code, we find that H 0 is lowered by a further 3 per cent. Using a more recent measurement of velocity dispersions and our fiducial model for selection biases, we infer H 0 = 66 ± 4 (stat) ± 1 (model sys) ± 2 (measurement sys) km s -1 Mpc -1 for the TDCOSMO plus SLACS data set. The first residual systematic error is due to plausible alternative choices in modelling the selection function, and the second is an estimate of the remaining systematic error in the measurement of velocity dispersions for SLACS lenses. Accurate time-delay cosmography requires precise velocity dispersion measurements and accurate calibration of selection biases.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Testing light-traces-mass in Hubble Frontier Fields Cluster MACS-J0416.1-2403

Here, we reconstruct the projected mass distribution of a massive merging Hubble Frontier Fields cluster MACSJ0416 using the genetic algorithm based free-form technique called Grale. The reconstructions are constrained by 149 lensed images identified by Jauzac et al. using HFF data. No information about cluster galaxies or light is used, which makes our reconstruction unique in this regard. Using visual inspection of the maps, as well as galaxy-mass correlation functions we conclude that overall light does follow mass. Furthermore, the fact that brighter galaxies are more strongly clustered with mass is an important confirmation of the standard biasing scenario in galaxy clusters. On the smallest scales, approximately less than a few arcseconds, the resolution afforded by 149 images is still not sufficient to confirm or rule out galaxy-mass offsets of the kind observed in ACO 3827. We also compare the mass maps of MACSJ0416 obtained by three different groups: Grale, and two parametric Lenstool reconstructions from the CATS and Sharon/Johnson teams. Overall, the three agree well; one interesting discrepancy between Grale and Lenstool galaxy-mass correlation functions occurs on scales of tens of kpc and may suggest that cluster galaxies are more biased tracers of mass than parametric methods generally assume.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Quantifying substructures in Hubble Frontier Field clusters: comparison with ΛCDM simulations

The Hubble Frontier Fields (HFF) are six clusters of galaxies, all showing indications of recent mergers, which have recently been observed for lensed images. As such they are the natural laboratories to study the merging history of galaxy clusters. In this work, we explore the 2D power spectrum of the mass distribution $P_{\rm M}(k)$ as a measure of substructure. We compare $P_{\rm M}(k)$ of these clusters (obtained using strong gravitational lensing) to that of $\Lambda$CDM simulated clusters of similar mass. In order to compute lensing $P_{\rm M}(k)$, we produced free-form lensing mass reconstructions of HFF clusters, without any light traces mass (LTM) assumption. Moreover, the inferred power at small scales tends to be larger if (i)~the cluster is at lower redshift, and/or (ii)~there are deeper observations and hence more lensed images. In contrast, lens reconstructions assuming LTM show higher power at small scales even with fewer lensed images; it appears the small scale power in the LTM reconstructions is dominated by light information, rather than the lensing data. The average lensing derived $P_{\rm M}(k)$ shows lower power at small scales as compared to that of simulated clusters at redshift zero, both dark-matter only and hydrodynamical. The possible reasons are: (i)~the available strong lensing data are limited in their effective spatial resolution on the mass distribution, (ii)~HFF clusters have yet to build the small scale power they would have at $z\sim 0$, or (iii)~simulations are somehow overestimating the small scale power.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

A Hubble Space Telescope survey for novae in M87 – III. Are novae good standard candles 15 d after maximum brightness?

Ten weeks of daily imaging of the giant elliptical galaxy M87 with the Hubble Space Telescope (HST) has yielded 41 nova light curves of unprecedented quality for extragalactic cataclysmic variables. We have recently used these light curves to demonstrate that the observational scatter in the so-called maximum-magnitude rate of decline (MMRD) relation for classical novae is so large as to render the nova-MMRD useless as a standard candle. Here in this paper, we demonstrate that a modified Buscombe–de Vaucouleurs hypothesis, namely that novae with decline times t2 > 10 d converge to nearly the same absolute magnitude about two weeks after maximum light in a giant elliptical galaxy, is supported by our M87 nova data. For 13 novae with daily sampled light curves, well determined times of maximum light in both the F606W and F814W filters, and decline times t 2 > 10 d we find that M87 novae display M606W,15 = -6.37 ± 0.46 and M814W,15 = -6.11 ± 0.43. If very fast novae with decline times t 2 < 10 d are excluded, the distances to novae in elliptical galaxies with stellar binary populations similar to those of M87 should be determinable with 1σ accuracies of ± 20 percent with the above calibrations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

First Cosmological Results using Type Ia Supernovae from the Dark Energy Survey: Measurement of the Hubble Constant

We present an improved measurement of the Hubble constant (H_0) using the ‘inverse distance ladder’ method, which adds the information from 207 Type Ia supernovae (SNe Ia) from the Dark Energy Survey (DES) at redshift 0.018 < z < 0.85 to existing distance measurements of 122 low-redshift (z < 0.07) SNe Ia (Low-z) and measurements of Baryon Acoustic Oscillations (BAOs). Whereas traditional measurements of H_0 with SNe Ia use a distance ladder of parallax and Cepheid variable stars, the inverse distance ladder relies on absolute distance measurements from the BAOs to calibrate the intrinsic magnitude of the SNe Ia. We find H_0 = 67.8 ± 1.3 km s^−1 Mpc^−1 (statistical and systematic uncertainties, 68 per cent confidence). Our measurement makes minimal assumptions about the underlying cosmological model, and our analysis was blinded to reduce confirmation bias. We examine possible systematic uncertainties and all are below the statistical uncertainties. Our H_0 value is consistent with estimates derived from the Cosmic Microwave Background assuming a ΛCDM universe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Local resolution of the Hubble tension: The impact of screened fifth forces on the cosmic distance ladder

The discrepancy between the values of the Hubble constant H0 derived from the local distance ladder and the cosmic microwave background provides a tantalizing hint of new physics. We explore a potential resolution involving screened fifth forces in the local Universe, which alter the Cepheid calibration of supernova distances. In particular, if the Cepheids with direct distance measurements from parallax or water masers are screened but a significant fraction of those in other galaxies are not, neglecting the difference between their underlying period–luminosity relations biases the local H 0 measurement high. This difference derives from a reduction in the Cepheid pulsation period and possible increase in luminosity under a fifth force. We quantify the internal and environmental gravitational properties of the Riess et al. distance ladder galaxies to assess their degrees of screening under a range of phenomenological models, and propagate this information into the H 0 posterior as a function of fifth force strength. We consider well-studied screening models in scalar–tensor gravity theories such as chameleon, K-mouflage and Vainshtein, along with a recently-proposed mechanism based on baryon–dark matter interactions in which screening is governed by the local dark matter density. We find that a fifth force strength ~5%–30% that of gravity can alleviate the H 0 tension in many scenarios, around the sensitivity level at which tests based on other distance ladder data can constrain this strength. Here, our most successful models achieve consistency with Planck at the ~1.5σ level. Although our analysis is exploratory and based on screening models that are not necessarily realized in full theories, our results demonstrate that new physics-based local resolutions of the H 0 tension are possible, supplementing those already known in the prerecombination era.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Cosmic birefringence test of the Hubble tension

A cosmic pseudo-Nambu-Goldstone boson has been proposed to resolve the four-sigma discrepancy between precision measurements of the expansion rate of the universe. We show this solution may also produce a cosmic birefringence (CB) signal in the polarization of the cosmic microwave background (CMB); observations of the CB power spectrum and cross-correlation with the CMB can independently confirm the presence of this new boson. In this work, we find significant new contributions to the CB signal, and show that future CMB experiments will greatly improve sensitivity to CB and Hubble tension scenarios.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Model independent comparison of supernova and strong lensing cosmography: Implications for the Hubble constant tension

We use supernovae measurements, calibrated by the local determination of the Hubble constant $H_0$ by SH0ES, to interpolate the distance-redshift relation using Gaussian process regression. We then predict, independent of the cosmological model, the distances that are measured with strong lensing time delays to test their mutual agreement. In this work we find excellent agreement between these predictions and the measurements. The agreement holds when we consider only the redshift dependence of the distance-redshift relation, independent of the value of $H_0$. Our results disfavor the possibility that lens mass modeling contributes a 10% bias or uncertainty in the strong lensing analysis, as suggested recently in the literature. In general our analysis strengthens the case that residual systematic errors in both measurements are below the level of the current discrepancy with the CMB determination of $H_0$, and supports the possibility of new physical phenomena on cosmological scales. With additional data our methodology can provide more stringent tests of unaccounted for systematics in the determinations of the distance-redshift relation in the late universe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Hubble constant difference between CMB lensing and BAO measurements

We apply a tension metric QUDM, the update difference in mean parameters, to understand the source of the difference in the measured Hubble constant H0 inferred with cosmic microwave background lensing measurements from the Planck satellite (H 0 = $67.9$ $^{+1.1}_{–1.3}$ km/s/Mpc) and from the South Pole Telescope (H 0 = $72.0$ $^{+2.1}_{–2.5}$ km/s/Mpc) when both are combined with baryon acoustic oscillation (BAO) measurements with priors on the baryon density (BBN). Q UDM isolates the relevant parameter directions for tension or concordance where the two data sets are both informative, and aids in the identification of subsets of data that source the observed tension. With Q UDM , we uncover that the difference in H 0 is driven by the tension between Planck lensing and BAO+BBN, at probability-to-exceed of 6.6%. Most of this mild tension comes from the galaxy BAO measurements parallel to the line of sight in the redshift range 0.2 < z < 0.75. Here, the redshift dependence of the parallel BAOs pulls both the matter density Ω m and H 0 high in Λ CDM, but these parameter anomalies are usually hidden when the BAO measurements are combined with other cosmological data sets with much stronger Ω m constraints.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Small-scale clumping at recombination and the Hubble tension

Despite the success of the standard ΛCDM model of cosmology, recent data improvements have made tensions emerge between low- and high-redshift observables, most importantly in determinations of the Hubble constant H 0 and the (rescaled) clustering amplitude S 8 . The high-redshift data, from the cosmic microwave background (CMB), crucially relies on recombination physics for its interpretation. In this work, we study how small-scale baryon inhomogeneities (i.e., clumping) can affect recombination and consider whether they can relieve both the H 0 and S 8 tensions. Such small-scale clumping, which may be caused by primordial magnetic fields or baryon isocurvature below kpc scales, enhances the recombination rate even when averaged over larger scales, shifting recombination to earlier times. We introduce a flexible clumping model, parametrized via three spatial zones with free densities and volume fractions, and use it to study the impact of clumping on CMB observables. We find that increasing H 0 decreases both Ω m and S 8 , which alleviates the S 8 tension. On the other hand, the shift in Ω m is disfavored by the low-z baryon-acoustic-oscillations measurements. We find that the clumping parameters that can change the CMB sound horizon enough to explain the H 0 tension also alter the damping tail, so they are disfavored by current Planck 2018 data. We test how the CMB damping-tail information rules out changes to recombination by first removing ℓ > 1000 multipoles in Planck data, where we find that clumping could resolve the H 0 tension. Furthermore, we make predictions for future CMB experiments, as their improved damping-tail precision can better constrain departures from standard recombination. Both the Simons Observatory and CMB-S4 will provide decisive evidence for or against clumping as a resolution to the H 0 tension.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Chameleon early dark energy and the Hubble tension

Early dark energy (EDE) offers a particularly interesting theoretical approach to the Hubble tension, albeit one that introduces its own set of challenges, including a new “why then” problem related to the EDE injection time at matter-radiation equality, and a mild worsening of the large-scale structure (LSS) tension. Both these challenges center on the properties of dark matter, which becomes the dominant component of the Universe at EDE injection and is also responsible for seeding LSS. Driven by this, we present the potential of couplings between EDE and dark matter to address these challenges, focusing on a mechanism similar to chameleon dark energy theories, deeming this chameleon early dark energy (CEDE). We present relevant background and perturbation equations and study the dynamics of the case of a quartic scalar potential and an exponential coupling.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A Step in Understanding the Hubble Tension

As cosmological data have improved, tensions have arisen. One such tension is the difference between the locally measured Hubble constant H 0 and the value inferred from the cosmic microwave background (CMB). Interacting radiation has been suggested as a solution, but studies show that conventional models are precluded by high-ℓ CMB polarization data. It seems at least plausible that a solution may be provided by related models that distinguish between high- and low-ℓ multipoles. When interactions of strongly-coupled radiation are mediated by a force-carrier that becomes non-relativistic, the dark radiation undergoes a "step" in which its relative energy density increases as the mediator deposits its entropy into the lighter species. If this transition occurs while CMB-observable modes are inside the horizon, high- and low-ℓ peaks are impacted differently, corresponding to modes that enter the horizon before or after the step. Here, these dynamics are naturally packaged into the simplest supersymmetric theory, the Wess-Zumino model, with the mass of the scalar mediator near the eV-scale. We investigate the cosmological signatures of such "Wess-Zumino Dark Radiation" (WZDR) and find that it provides an improved fit to the CMB alone, favoring larger values of H 0 . If supernovae measurements from the SH0ES collaboration are also included in the analysis, the inferred value of H 0 is yet larger, but the preference for dark radiation and the location of the transition is left nearly unchanged. Utilizing a standardized set of measures, we compare to other models and find that WZDR is among the most successful at addressing the H 0 tension and the best of those with a Lagrangian formulation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Early dark sector, the Hubble tension, and the swampland

We consider the interplay of the Early Dark Energy (EDE) model, the Swampland Distance Conjecture (SDC), and cosmological parameter tensions. EDE is a proposed resolution of the Hubble tension relying upon a near-Planckian scalar field excursion, while the SDC predicts an exponential sensitivity of masses of other fields to such an excursion, m ∝ e –c |ΔΦ|/Mpl with c ~ 0(1). Meanwhile, EDE is in tension with large-scale structure (LSS) data, due to shifts in the standard ΛCDM parameters necessary to fit the cosmic microwave background (CMB). One might hope that a proper treatment of the model, e.g., accounting for the SDC, may ameliorate the tension with LSS. Motivated by these considerations, we introduce the Early Dark Sector (EDS) model, wherein the mass of dark matter is exponentially sensitive to super-Planckian field excursions of the EDE scalar. The EDS model exhibits new phenomenology in both the early and late universe, the latter due to an EDE-mediated dark matter self-interaction. This dark matter-philic "fifth force", while constrained to be small, remains active in the late universe and is not screened in virialized halos. We find that the new interaction with dark matter partially resolves the LSS tension. However, the marginalized posteriors are nonetheless consistent with f EDE = 0 at 95% CL once the Dark Energy Survey Year 3 measurement of S 8 is included. We study constraints on the model from Atacama Cosmology Telescope data, and find a factor of two improvement on the error bar on the SDC parameter c, along with an increased preference for the EDE component. Here, we discuss the implications of these constraints for the SDC, and find the tightest observational constraints to date on a swampland parameter, suggesting that an EDE description of cosmological data is in tension with the SDC.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Role of the Hubble scale in the weak lensing versus CMB tension

Here, we explore a reparametrization of the lensing amplitude tension between weak lensing (WL) and cosmic microwave background (CMB) data and its implications for a joint resolution with the Hubble tension. Specifically, we focus on the lensing amplitude over a scale of 12 Mpc in absolute distance units using a derived parameter S 12 and show its constraints from recent surveys in comparison with Planck 2018. In WL alone, we find that the absolute distance convention correlates S 12 with H 0 . Accounting for this correlation in the 3D space S 12 ×w m ×ℎ reproduces the usual levels of 2~3⁢σ tension inferred from S 8 ×Ω m . Additionally, we derive scaling relations in the S 8 ×ℎ and S 12 ×ℎ planes that are allowed by Λ⁢CDM and extrapolate target scalings needed to solve the H 0 and lensing-amplitude tensions jointly in a hypothetical beyond-Λ⁢CDM model. As a test example, we quantify how the early dark energy scenario compares with these target scalings. Useful fitting formulas for S 8 and S 12 as a function of other cosmological parameters in Λ⁢CDM are provided, with 1% precision.

79 ASTRONOMY AND ASTROPHYSICS↗