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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Weak lensing in DES Y3: redshift distributions, shape catalogue, and mass mapping

The size of galaxy surveys have rapidly escalated with time, growing from thousands of galaxies of the first pioneering surveys to current and future surveys (DES, KiDS, HSC, LSST, Euclid, WFIRST), which map (or plan to map) a few hundreds millions of galaxies. These ambitious programs have the potential to answer many open questions in Cosmology (or, depending on their results, to open new exciting scenarios, involving new physics beyond the standard cosmological model and the standard model of particle physics). In particular, this thesis focuses on the first three years of data from the Dark Energy Survey (DES Y3), which comprises 100 million galaxies observed in 5 different optical bands over 5000 square degrees of the southern hemisphere. DES and the data set used in this thesis are discussed in detail in Chapter 3, which together with Chapter 1 and 2 constitutes Part I of this thesis. The scientifically positive outcome of DES and other photometric galaxy surveys goes h and in h and with a supreme understanding of the data, of the observational systematics affecting the measurements, and of the limits of the theoretical modelling of the observables. One of the main challenge of galaxy photometric surveys like DES is to correctly estimate the distance to the galaxies. Photometric surveys observe the galaxies in a limited number of broad optical bands, and the estimate of their \textit{redshifts} is somewhat uncertain, which constitutes one of the main limiting factor of their cosmological analyses. Part II and its Chapter 4 are devoted to a new auxiliary technique recently developed that allows to infer (or calibrate) redshift distributions exploiting cross-correlation with small reference samples with secure redshifts. The so called ``clustering-redshift'' method is discussed in depth, as well as its role in the overall DES Y3 redshift calibration strategy. Part III and Chapter 5 are devoted to another key aspect of photometric surveys, that enables the stu dy of weak gravitational lensing: the shape catalogue. The official DES Y3 shape catalogue is presented, together with all the systematic tests performed to validate it such that it can be considered science-ready. Last, part IV focuses on how to use weak gravitational lensing and the DES Y3 shape catalogue to create weak lensing mass maps, i.e., maps of the mass distribution of the Universe. Chapter 6 discusses different map making techniques, whereas Chapter 7 presents a simulated cosmological analysis using the high order moments of the mass maps.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Calibration and Commissioning of the LSST

Understanding the nature of dark energy and dark matter remains one of the fundamental questions in physics today; impacting our understanding of particle physics, cosmology, and possibly theories of gravity. Given the scale and complexity of the next generation of cosmology experiments (e.g., the Rubin Observatory, the Euclid satellite mission, and the Roman space telescope) we are entering an era where statistical noise no longer determines the accuracy to which we can measure cosmological parameters. Our ability to control and correct for systematics will ultimately determine the scientific impact of these experiments. This award addressed the challenge of how we determine what limits the accuracy of our cosmological measures, what techniques are appropriate for measuring and calibrating the properties of galaxies to best constrain cosmological models, how to develop statistical techniques that are insensitive to systematic errors, and how to optimize survey strategies in order to minimize systematics while maximizing the speed at which an experiment can achieve its science objectives. In this final technical report for award DE-SC0011635 we describe a set of open-source frameworks that simulate the characteristics and properties of current and planned cosmology surveys and the application of these frameworks to the development of new methodologies for estimating the properties and distances to galaxies that are robust to noisy and incomplete data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Milky Way Satellite Census. I. The Observational Selection Function for Milky Way Satellites in DES Y3 and Pan-STARRS DR1

We report the results of a systematic search for ultra-faint Milky Way satellite galaxies using data from the Dark Energy Survey (DES) and Pan-STARRS1 (PS1). Together, DES and PS1 provide multi-band photometry in optical/near-infrared wavelengths over ~80% of the sky. Our search for satellite galaxies targets ~25,000 deg$^2$ of the high-Galactic-latitude sky reaching a 10$\sigma$ point-source depth of $\gtrsim$ 22.5 mag in the $g$ and $r$ bands. While satellite galaxy searches have been performed independently on DES and PS1 before, this is the first time that a self-consistent search is performed across both data sets. We do not detect any new high-significance satellite galaxy candidates, while recovering the majority of satellites previously detected in surveys of comparable depth. We characterize the sensitivity of our search using a large set of simulated satellites injected into the survey data. We use these simulations to derive both analytic and machine-learning models that accurately predict the detectability of Milky Way satellites as a function of their distance, size, luminosity, and location on the sky. To demonstrate the utility of this observational selection function, we calculate the luminosity function of Milky Way satellite galaxies, assuming that the known population of satellite galaxies is representative of the underlying distribution. We provide access to our observational selection function to facilitate comparisons with cosmological models of galaxy formation and evolution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Difficulties with late-time solutions for the Hubble tension

We explore the notion that cosmological models that modify the late-time expansion history cannot simultaneously fit the SH0ES Collaboration’s measurements of the Hubble constant, Dark Energy Spectroscopic Instrument baryon acoustic oscillations data, and type Ia supernova distances. Adopting a few simple phenomenological models, we quantitatively demonstrate that a satisfactory fit with a model with late-time expansion history can only be achieved if one of the following is true: (1) there is a sharp step in the absolute magnitude of type Ia supernovae at very low redshift, 𝑧 ∼0.01, or (2) the distance duality relation, 𝑑 𝐿 ⁡(𝑧) =(1+𝑧) 2 ⁢𝑑 𝐴 ⁡(𝑧), is broken. Both solutions are trivial in that they effectively decouple the calibrated type Ia supernovae measurements from other data, and this qualitatively agrees with previous work built on studying specific dark-energy models. We also identify a less effective class of late-time solutions with a transition at 𝑧 ≃0.15 that lead to a more modest improvement in fit to the data than models with a very low-𝑧 transition. Our conclusions are largely unchanged when we include surface brightness fluctuation distance measurements, with their current systematic uncertainties, to our analysis. Here, we finally illustrate our findings by studying a physical model which, when equipped with the ability to smoothly change the absolute magnitude of type Ia supernovae, partially resolves the Hubble tension.

Cosmological parameters↗
DOE OSTI2017

New Fitting Formula for Cosmic Nonlinear Density Distribution

We have measured the probability distribution function (PDF) of a cosmic matter density field from a suite of N-body simulations. We propose the generalized normal distribution of version 2 (N{sub v2}) as an alternative fitting formula to the well-known log-normal distribution. We find that N{sub v2} provides a significantly better fit than that of the log-normal distribution for all smoothing radii (2, 5, 10, 25 [Mpc h {sup −1}]) that we studied. The improvement is substantial in the underdense regions. The development of non-Gaussianities in the cosmic matter density field is captured by continuous evolution of the skewness and shift parameters of the N{sub v2} distribution. We present the redshift evolution of these parameters for aforementioned smoothing radii and various background cosmology models. All the PDFs measured from large and high-resolution N-body simulations that we use in this study can be obtained from the web site https://astro.kias.re.kr/jhshin.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1984

Fine-scale anisotropy of the cosmic microwave background in a universe dominated by cold dark matter

The fine-scale anisotropy of the cosmic microwave background radiation has been studied in cosmological models with a scale-invariant primordial adiabatic density fluctuation spectrum dominated by cold, weakly interacting particles. Normalization of the present fluctuation spectrum to the observed galaxy distribution results in excessive temperature anisotropy when compared to a recent upper limit on 4.5 arcmin unless the density parameter exceeds 0.4. When this result is combined with the requirement that the universe be at least 13 billion years old, it is found that if the cosmological constant is zero, then the density parameter is between roughly 0.4 and 1 and the Hubble constant is between roughly 60 km/s/Mpc and 50 km/s/Mpc.

Vittorio, N.↗
DOE OSTI2022

Dark Energy Survey Year 3 results: Cosmological constraints from galaxy clustering and galaxy-galaxy lensing using the MagLim lens sample

The cosmological information extracted from photometric surveys is most robust when multiple probes of the large scale structure of the Universe are used. Two of the most sensitive probes are the clustering of galaxies and the tangential shear of background galaxy shapes produced by those foreground galaxies, so-called galaxy-galaxy lensing. Combining the measurements of these two two-point functions leads to cosmological constraints that are independent of the way galaxies trace matter (the galaxy bias factor). The optimal choice of foreground, or lens, galaxies is governed by the joint, but conflicting requirements to obtain accurate redshift information and large statistics. We present cosmological results from the full 5000 deg 2 of the Dark Energy Survey’s first three years of observations (Y3) combining those two-point functions, using for the first time a magnitude-limited lens sample (MagLim) of 11 million galaxies, especially selected to optimize such combination, and 100 million background shapes. We consider two flat cosmological models, the Standard Model with dark energy and cold dark matter ( Λ CDM ) a variation with a free parameter for the dark energy equation of state ( w CDM ). Both models are marginalized over 25 astrophysical and systematic nuisance parameters. In Λ CDM we obtain for the matter density Ω m = 0.320 - 0.034 + 0.041 and for the clustering amplitude S 8 ≡ σ 8 ( Ω m / 0.3 ) 0.5 = 0.778 - 0.031 + 0.037 , at 68% C.L. The latter is only 1 σ smaller than the prediction in this model informed by measurements of the cosmic microwave background by the Planck satellite. In w CDM we find Ω m = 0.32 - 0.046 + 0.044 , S 8 = 0.777 - 0.051 + 0.049 and dark energy equation of state w = - 1.031 - 0.379 + 0.218 . We find that including smaller scales, while marginalizing over nonlinear galaxy bias, improves the constraining power in the Ω m - S 8 plane by 31% and in the Ω m - w plane by 41% while yielding consistent cosmological parameters from those in the linear bias case. These results are combined with those from cosmic shear in a companion paper to present full DES-Y3 constraints from the three two-point functions ( 3 × 2 pt ).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Probing New physics with high-redshift quasars: axions and non-standard cosmology

The Hubble diagram of quasars, as candidates to “standardizable” candles, has been used to measure the expansion history of the Universe at late times, up to very high redshifts ( z ~ 7). It has been shown that this history, as inferred from the quasar dataset, deviates at ≳ 3 σ level from the concordance (ΛCDM) cosmology model preferred by the cosmic microwave background (CMB) and other datasets. In this article, we investigate whether new physics beyond ΛCDM (BΛCDM) or beyond the Standard Model (BSM) could make the quasar data consistent with the concordance model. We first show that an effective redshift-dependent relation between the quasar UV and X-ray luminosities, complementing previous phenomenological work in the literature, can potentially remedy the discrepancy. Such a redshift dependence can be realized in a BSM model with axion-photon conversion in the intergalactic medium (IGM), although the preferred parameter space is in tension with various other astrophysical constraints on axions, at a level depending on the specific assumptions made regarding the IGM magnetic field. We briefly discuss a variation of the axion model that could evade these astrophysical constraints. On the other hand, we show that models beyond ΛCDM such as one with a varying dark energy equation of state ( w CDM) or the phenomenological cosmographic model with a polynomial expansion of the luminosity distance, cannot alleviate the tension. The code for our analysis, based on emcee [1] and corner.py [2], is publicly available at github.com/ChenSun-Phys/high_z_candles.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Cosmological constraints from the DESI DR1 joint power spectrum and bispectrum analysis

We derive cosmological parameter constraints from the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) galaxy clustering data, based on a joint full-shape analysis of the power spectrum multipoles and the bispectrum monopole using the ShapeFit framework. This is the follow-up of our previous work, in which we obtained for the first time constraints on the ShapeFit parameters using the bispectrum of DESI DR1. Here we present the first ShapeFit cosmological inference results using the bispectrum of DESI DR1. We recover values for the matter density parameter and Hubble constant of respectively $Ω_m=0.310\pm0.012$ and $H_0=[68.92\pm0.97]\,\mathrm{km\, s^{-1} Mpc^{-1}}$, consistent with previous results from the full DESI DR1 dataset that did not use the bispectrum signal. The inclusion of the bispectrum significantly tightens the constraints on the amplitude of fluctuations, reducing the error-bars in $\ln(A_s\times10^{10})$ by approximately 20%, compared to using the power spectrum alone. We also explore extended cosmological models by performing fits for the evolving dark energy equation of state $w_0w_a$, and the sum of neutrino masses $\sum m_ν$. In these cases, we obtain constraints slightly larger than the ones from previous works from the DESI collaboration, due to not combining the full-shape results with other probes in all tracers. We find no strong evidence of deviations from standard $Λ$CDM, with the dark energy equation-of-state remaining within 2$σ$ from a cosmological constant $Λ$, and the neutrino mass being consistent with the normal hierarchy, $\sum m_ν<0.1\,[eV]$ at 95% confidence limit. These constraints are broadly consistent with other DESI DR1 analyses, thus validating the robustness of the ShapeFit compression approach and the inclusion of the bispectrum for cosmological inference.

Novell-Masot, S. [ICC, Barcelona U.; Geneva U., De↗
DOE OSTI2026

Cosmological constraints from the DESI DR1 joint power spectrum and bispectrum analysis

We derive cosmological parameter constraints from the Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) galaxy clustering data, based on a joint full-shape analysis of the power spectrum multipoles and the bispectrum monopole using the ShapeFit framework. This is the follow-up of our previous work, in which we obtained for the first time constraints on the ShapeFit parameters using the bispectrum of DESI DR1. Here we present the first ShapeFit cosmological inference results using the bispectrum of DESI DR1. We recover values for the matter density parameter and Hubble constant of respectively $Ω_m=0.310\pm0.012$ and $H_0=[68.92\pm0.97]\,\mathrm{km\, s^{-1} Mpc^{-1}}$, consistent with previous results from the full DESI DR1 dataset that did not use the bispectrum signal. The inclusion of the bispectrum significantly tightens the constraints on the amplitude of fluctuations, reducing the error-bars in $\ln(A_s\times10^{10})$ by approximately 20%, compared to using the power spectrum alone. We also explore extended cosmological models by performing fits for the evolving dark energy equation of state $w_0w_a$, and the sum of neutrino masses $\sum m_ν$. In these cases, we obtain constraints slightly larger than the ones from previous works from the DESI collaboration, due to not combining the full-shape results with other probes in all tracers. We find no strong evidence of deviations from standard $Λ$CDM, with the dark energy equation-of-state remaining within 2$σ$ from a cosmological constant $Λ$, and the neutrino mass being consistent with the normal hierarchy, $\sum m_ν<0.1\,[eV]$ at 95% confidence limit. These constraints are broadly consistent with other DESI DR1 analyses, thus validating the robustness of the ShapeFit compression approach and the inclusion of the bispectrum for cosmological inference.

Novell-Masot, S. [ICC, Barcelona U.; Geneva U., De↗
DOE OSTI2019

First Detection of Scale-Dependent Linear Halo Bias in N -Body Simulations with Massive Neutrinos

Using N-body simulations with massive neutrino density perturbations, we detect the scaledependent linear halo bias with high significance. This is the first time that this effect is detected in simulations containing neutrino density perturbations on all scales, confirming the same finding from separate universe simulations. The scale dependence is the result of the additional scale in the system, i.e. the massive neutrino free-streaming length, and it persists even if the bias is defined with respect to the cold dark matter plus baryon (instead of total matter) power spectrum. The separate universe approach provides a good model for the scale-dependent linear bias, and the effect is approximately 0.25f ν and 0.43f ν for halos with bias of 1.7 and 3.5, respectively. While the size of the effect is small, it is not insignificant in terms of f ν and should therefore be included to accurately constrain neutrino mass from clustering statistics of biased tracers. Furthermore, this feature is a distinct signature of free-streaming particles and cannot be mimicked by other components of the standard cosmological model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from the anisotropic power spectrum of the quasar sample between redshift 0.8 and 2.2

ABSTRACT We measure the clustering of quasars of the final data release (DR16) of eBOSS. The sample contains $343\, 708$ quasars between redshifts 0.8 ≤ z ≤ 2.2 over $4699\, \mathrm{deg}^2$. We calculate the Legendre multipoles (0,2,4) of the anisotropic power spectrum and perform a BAO and a Full-Shape (FS) analysis at the effective redshift zeff = 1.480. The errors include systematic errors that amount to 1/3 of the statistical error. The systematic errors comprise a modelling part studied using a blind N-body mock challenge and observational effects studied with approximate mocks to account for various types of redshift smearing and fibre collisions. For the BAO analysis, we measure the transverse comoving distance DM(zeff)/rdrag = 30.60 ± 0.90 and the Hubble distance DH(zeff)/rdrag = 13.34 ± 0.60. This agrees with the configuration space analysis, and the consensus yields: DM(zeff)/rdrag = 30.69 ± 0.80 and DH(zeff)/rdrag = 13.26 ± 0.55. In the FS analysis, we fit the power spectrum using a model based on Regularised Perturbation Theory, which includes redshift space distortions and the Alcock–Paczynski effect. The results are DM(zeff)/rdrag = 30.68 ± 0.90 and DH(zeff)/rdrag = 13.52 ± 0.51 and we constrain the linear growth rate of structure f(zeff)σ8(zeff) = 0.476 ± 0.047. Our results agree with the configuration space analysis. The consensus analysis of the eBOSS quasar sample yields: DM(zeff)/rdrag = 30.21 ± 0.79, DH(zeff)/rdrag = 3.23 ± 0.47, and f(zeff)σ8(zeff) = 0.462 ± 0.045 and is consistent with a flat ΛCDM cosmological model using Planck results.

Neveux, Richard↗
DOE OSTI2023

Past-completeness of inflationary spacetimes

Here, we discuss the question of whether or not inflationary spacetimes can be geodesically complete in the infinite past. Geodesic completeness is a necessary condition for averting an initial singularity during eternal inflation. It is frequently argued that cosmological models which are expanding sufficiently fast (having average Hubble expansion rate H avg > 0) must be incomplete in null and timelike past directions. This well-known conjecture relies on specific bounds on the integral of the Hubble parameter over a past- directed timelike or null geodesic. As stated, we show this claim is an open issue. We show that the calculation of H avg yields a continuum of results for a given spacetime predicated upon the underlying topological assumptions. We present an improved definition for H avg and introduce an uncountably infinite cohort of cosmological solutions which are geodesically complete despite having H avg > 0. We discuss a standardized definition for inflationary spacetimes as well as quantum (semiclassical) cosmological concerns over physically reasonable scale factors.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Systematic search for tidal features around nearby galaxies: I. Enhanced SDSS imaging of the Local Volume

In hierarchical models of galaxy formation, stellar tidal streams are expected around most, if not all, galaxies. Although these features may provide useful diagnostics of the Λ CDM model, their observational properties remain poorly constrained because they are challenging to detect and interpret and have been studied in detail for only a sparse sampling of galaxy population. More quantitative, systematic approaches are required. We advocate statistical analysis of the counts and properties of such features in archival wide-field imaging surveys for a direct comparison against results from numerical simulations. We aim to study systematically the frequency of occurrence and other observational properties of tidal features around nearby galaxies. The sample we construct will act as a foundational dataset for statistical comparison with cosmological models of galaxy formation. Our approach is based on a visual classification of diffuse features around a volume-limited sample of nearby galaxies, using a post-processing of Sloan Digital Syk Survey (SDSS) imaging optimized for the detection of stellar structure with low surface brightness. At a limiting surface brightness of 28 mag arcsec –2 , 14% of the galaxies in our sample exhibit evidence of diffuse features likely to have arisen from minor merging events. Our technique recovers all previously known streams in our sample and yields a number of new candidates. Consistent with previous studies, coherent arc-like features and shells are the most common type of tidal structures found in this study. Here, we conclude that although some detections are ambiguous and could be corroborated or refuted with deeper imaging, our technique provides a reliable foundation for the statistical analysis of diffuse circumgalactic features in wide-area imaging surveys, and for the identification of targets for follow-up studies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Cool dark sector, concordance, and a low σ 8

We investigate a cosmological model in which a fraction of the dark matter is atomic dark matter (ADM). This ADM consists of dark versions of the electron and of the proton, interacting with each other and with dark photons just as their light sector versions do, but interacting with everything else only gravitationally. We find constraints given current cosmic microwave background (CMB) and baryon acoustic oscillation (BAO) data, with and without an H 0 prior, and with and without enforcing a big bang nucleosynthesis consistent helium abundance. We find that, at low dark photon temperature, one can have consistency with BAO and CMB data, with a fraction of dark matter that is ADM (f adm ) as large as ~0.1 . Such a large f adm leads to a suppression of density fluctuations today on scales below about 60 Mpc that may be of relevance to the σ 8 tension. Our work motivates calculation of nonlinear corrections to matter power spectrum predictions in the ADM model. Here, we forecast parameter constraints to come from future ground-based CMB surveys, and find that if ADM is indeed the cause of the σ 8 tension, the influence of the ADM, primarily on CMB lensing, will likely be detectable at high significance.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Constraining ΛCDM cosmological parameters with Einstein Telescope mock data

ABSTRACT We investigate the capability of Einstein Telescope to constrain the cosmological parameters of the non-flat ΛCDM cosmological model. Two types of mock data sets are considered depending on whether or not a short gamma-ray burst is detected, and associated with the gravitational wave emitted by binary neutron stars merger, using the THESEUS satellite. Depending on the mock data set, two statistical estimators are applied: one assumes that the redshift is known, while the other marginalizes over it assuming a specific redshift prior distribution. We demonstrate that (i) using mock catalogues collecting gravitational wave signals emitted by binary neutron stars systems to which a short gamma-ray burst has been associated, Einstein Telescope may achieve an accuracy on the cosmological parameters of $\sigma _{H_0}\approx 0.40$ km s−1 Mpc−1, $\sigma _{\Omega _{k,0}}\approx 0.09$, and $\sigma _{\Omega _{\Lambda ,0}}\approx 0.07$; while (ii) using mock catalogues collecting all gravitational wave signals emitted by binary neutron stars systems for which an electromagnetic counterpart has not been detected, Einstein Telescope may achieve an accuracy on the cosmological parameters of $\sigma _{H_0}\approx 0.04$ km s−1 Mpc−1, $\sigma _{\Omega _{k,0}}\approx 0.01$, and $\sigma _{\Omega _{\Lambda ,0}}\approx 0.01$, once the redshift probability distribution of GW events is known from from population synthesis simulations and/or the measure of the tidal deformability parameter. These results show an improvement of a factor 2–75 with respect to earlier results using complementary data sets.

Califano, Matteo↗
NASA NTRS2011

Signal Processing for a Lunar Array: Minimizing Power Consumption

Motivation for the study is: (1) Lunar Radio Array for low frequency, high redshift Dark Ages/Epoch of Reionization observations (z =6-50, f=30-200 MHz) (2) High precision cosmological measurements of 21 cm H I line fluctuations (3) Probe universe before first star formation and provide information about the Intergalactic Medium and evolution of large scale structures (5) Does the current cosmological model accurately describe the Universe before reionization? Lunar Radio Array is for (1) Radio interferometer based on the far side of the moon (1a) Necessary for precision measurements, (1b) Shielding from earth-based and solar RFI (12) No permanent ionosphere, (2) Minimum collecting area of approximately 1 square km and brightness sensitivity 10 mK (3)Several technologies must be developed before deployment The power needed to process signals from a large array of nonsteerable elements is not prohibitive, even for the Moon, and even in current technology. Two different concepts have been proposed: (1) Dark Ages Radio Interferometer (DALI) (2)( Lunar Array for Radio Cosmology (LARC)

Fourier Transform Spectrometer↗
DOE OSTI2017

Constraints on the production of primordial magnetic seeds in pre-big bang cosmology

We study the amplification of the electromagnetic fluctuations, and the production of 'seeds' for the cosmic magnetic fields, in a class of string cosmology models whose scalar and tensor perturbations reproduce current observations and satisfy known phenomenological constraints. We find that the condition of efficient seeds production can be satisfied and compatible with all constraints only in a restricted region of parameter space, but we show that such a region has significant intersections with the portions of parameter space where the produced background of relic gravitational waves is strong enough to be detectable by aLIGO/Virgo and/or by eLISA.

79 ASTRONOMY AND ASTROPHYSICS↗