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One of the frontiers for advancing what is known about dark matter lies in using strong gravitational lenses to characterize the population of the smallest dark matter haloes. There is a large volume of information in strong gravitational lens images – the question we seek to answer is to what extent we can refine this information. To this end, we forecast the detectability of a mixed warm and cold dark matter scenario using the anomalous flux ratio method from strong gravitational lensed images. The halo mass function of the mixed dark matter scenario is suppressed relative to cold dark matter but still predicts numerous low-mass dark matter haloes relative to warm dark matter. Since the strong lensing signal receives a contribution from a range of dark matter halo masses and since the signal is sensitive to the specific configuration of dark matter haloes, not just the halo mass function, degeneracies between different forms of suppression in the halo mass function, relative to cold dark matter, can arise. We find that, with a set of lenses with different configurations of the main deflector and hence different sensitivities to different mass ranges of the halo mass function, the different forms of suppression of the halo mass function between the warm dark matter model and the mixed dark matter model can be distinguished with 40 lenses with Bayesian odds of 30:1.

 

Dark matter could comprise, at least in part, primordial black holes (PBHs). To test this hypothesis, we present an approach to constrain the PBH mass (MPBH) and mass fraction (fPBH) from the flux ratios of quadruply imaged quasars. Our approach uses an approximate Bayesian computation forward modelling technique to directly sample the posterior distribution of MPBH and fPBH, while marginalizing over the subhalo mass function amplitude, spatial distribution, and the size of the lensed source. We apply our method to 11 quadruply imaged quasars and derive a new constraint on the intermediate-mass area of PBH parameter space 104 M⊙ < MPBH < 106 M⊙. We obtain an upper limit fPBH < 0.17 (95 per cent confidence limit). This constraint is independent of all other previously published limits.

 

The gravitationally lensed supernova Refsdal appeared in multiple images produced through gravitational lensing by a massive foreground galaxy cluster. After the supernova appeared in 2014, lens models of the galaxy cluster predicted that an additional image of the supernova would appear in 2015, which was subsequently observed. We use the time delays between the images to perform a blinded measurement of the expansion rate of the Universe, quantified by the Hubble constant (H₀). Using eight cluster lens models, we infer$H_0={64.8}_{-4.3}^{+4.4}\text{ kilometers per second per megaparsec}$. Using the two models most consistent with the observations, we find$H_0={66.6}_{-3.3}^{+4.1}\text{ kilometers per second per megaparsec}$. The observations are best reproduced by models that assign dark-matter halos to individual galaxies and the overall cluster.

 

The primordial matter power spectrum quantifies fluctuations in the distribution of dark matter immediately following inflation. Over cosmic time, overdense regions of the primordial density field grow and collapse into dark matter haloes, whose abundance and density profiles retain memory of the initial conditions. By analysing the image magnifications in 11 strongly lensed and quadruply imaged quasars, we infer the abundance and concentrations of low-mass haloes, and cast the measurement in terms of the amplitude of the primordial matter power spectrum. We anchor the power spectrum on large scales, isolating the effect of small-scale deviations from the Lambda cold dark matter (ΛCDM) prediction. Assuming an analytic model for the power spectrum and accounting for several sources of potential systematic uncertainty, including three different models for the halo mass function, we obtain correlated inferences of $\log _{10}\left(P / P_{\Lambda \rm {CDM}}\right)$, the power spectrum amplitude relative to the predictions of the concordance cosmological model, of $0.0_{-0.4}^{+0.5}$, $0.1_{-0.6}^{+0.7}$, and $0.2_{-0.9}^{+1.0}$ at k = 10, 25, and 50 $\rm {Mpc^{-1}}$ at $68 {{\ \rm per\ cent}}$ confidence, consistent with CDM and single-field slow-roll inflation.

 

In late 2014, four images of supernova (SN) “Refsdal,” the first known example of a strongly lensed SN with multiple resolved images, were detected in the MACS J1149 galaxy-cluster field. Following the images’ discovery, the SN was predicted to reappear within hundreds of days at a new position ∼8″ away in the field. The observed reappearance in late 2015 makes it possible to carry out Refsdal’s original proposal to use a multiply imaged SN to measure the Hubble constantH₀, since the time delay between appearances should vary inversely withH₀. Moreover, the position, brightness, and timing of the reappearance enable a novel test of the blind predictions of galaxy-cluster models, which are typically constrained only by the positions of multiply imaged galaxies. We have developed a new photometry pipeline that usesDOLPHOTto measure the fluxes of the five images of SN Refsdal from difference images. We apply four separate techniques to perform a blind measurement of the relative time delays and magnification ratios between the last image SX and the earlier images S1–S4. We measure the relative time delay of SX–S1 to be${\displaystyle {376.0}_{-5.5}^{+5.6}}$days and the relative magnification to be${\displaystyle {0.30}_{-0.3}^{+0.5}}$. This corresponds to a 1.5% precision on the time delay and 17% precision for the magnification ratios and includes uncertainties due to millilensing and microlensing. In an accompanying paper, we place initial and blind constraints on the value of the Hubble constant.

 

Time delay cosmography uses the arrival time delays between images in strong gravitational lenses to measure cosmological parameters, in particular the Hubble constant H0. The lens models used in time delay cosmography omit dark matter subhalos and line-of-sight halos because their effects are assumed to be negligible. We explicitly quantify this assumption by analyzing realistic mock lens systems that include full populations of dark matter subhalos and line-of-sight halos, applying the same modeling assumptions used in the literature to infer H0. We base the mock lenses on six quadruply-imaged quasars that have delivered measurements of the Hubble constant, and quantify the additional uncertainties and/or bias on a lens-by-lens basis. We show that omitting dark substructure does not bias inferences of H0. However, perturbations from substructure contribute an additional source of random uncertainty in the inferred value of H0 that scales as the square root of the lensing volume divided by the longest time delay. This additional source of uncertainty, for which we provide a fitting function, ranges from 0.6−2.4%. It may need to be incorporated in the error budget as the precision of cosmographic inferences from single lenses improves, and sets a precision limit on inferences from single lenses. 

Abstract The mass-concentration relation of dark matter halos reflects the assembly history of objects in hierarchical structure formation scenarios, and depends on fundamental quantities in cosmology such as the slope of the primordial matter power-spectrum. This relation is unconstrained by observations on sub-galactic scales. We derive the first measurement of the mass-concentration relation using the image positions and flux ratios from eleven quadruple-image strong gravitational lenses (quads) in the mass range 106 − 1010M⊙, assuming cold dark matter. We model both subhalos and line of sight halos, finite-size background sources, and marginalize over nuisance parameters describing the lens macromodel. We also marginalize over the the logarithmic slope and redshift evolution of the mass-concentration relation, using flat priors that encompass the range of theoretical uncertainty in the literature. At z = 0, we constrain the concentration of 108M⊙ halos $c=12_{-5}^{+6}$ at $68 \%$ CI, and $c=12_{-9}^{+15}$ at $95 \%$ CI. For a 107M⊙ halo, we obtain $68 \%$ ($95 \%$) constraints $c=15_{-8}^{+9}$ ($c=15_{-11}^{+18}$), while for 109M⊙ halos $c=10_{-4}^{+7}$ ($c=10_{-7}^{+14}$). These results are consistent with the theoretical predictions from mass-concentration relations in the literature, and establish strong lensing by galaxies as a powerful probe of halo concentrations on sub-galactic scales across cosmological distance. 

ABSTRACT The free-streaming length of dark matter depends on fundamental dark matter physics, and determines the abundance and concentration of dark matter haloes on sub-galactic scales. Using the image positions and flux ratios from eight quadruply imaged quasars, we constrain the free-streaming length of dark matter and the amplitude of the subhalo mass function (SHMF). We model both main deflector subhaloes and haloes along the line of sight, and account for warm dark matter free-streaming effects on the mass function and mass–concentration relation. By calibrating the scaling of the SHMF with host halo mass and redshift using a suite of simulated haloes, we infer a global normalization for the SHMF. We account for finite-size background sources, and marginalize over the mass profile of the main deflector. Parametrizing dark matter free-streaming through the half-mode mass mhm, we constrain the thermal relic particle mass mDM corresponding to mhm. At $95 \, {\rm per\, cent}$ CI: mhm < 107.8 M⊙ ($m_{\rm {DM}} \gt 5.2 \ \rm {keV}$). We disfavour $m_{\rm {DM}} = 4.0 \,\rm {keV}$ and $m_{\rm {DM}} = 3.0 \,\rm {keV}$ with likelihood ratios of 7:1 and 30:1, respectively, relative to the peak of the posterior distribution. Assuming cold dark matter, we constrain the projected mass in substructure between 106 and 109 M⊙ near lensed images. At $68 \, {\rm per\, cent}$ CI, we infer $2.0{-}6.1 \times 10^{7}\, {{\rm M}_{\odot }}\,\rm {kpc^{-2}}$, corresponding to mean projected mass fraction $\bar{f}_{\rm {sub}} = 0.035_{-0.017}^{+0.021}$. At $95 \, {\rm per\, cent}$ CI, we obtain a lower bound on the projected mass of $0.6 \times 10^{7} \,{{\rm M}_{\odot }}\,\rm {kpc^{-2}}$, corresponding to $\bar{f}_{\rm {sub}} \gt 0.005$. These results agree with the predictions of cold dark matter.