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  1. 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.

    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.

  3. 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 cosmologicalmore »distance.« less
  4. 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 constrainmore »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.« less
  5. ABSTRACT Core formation and runaway core collapse in models with self-interacting dark matter (SIDM) significantly alter the central density profiles of collapsed haloes. Using a forward modelling inference framework with simulated data-sets, we demonstrate that flux ratios in quadruple image strong gravitational lenses can detect the unique structural properties of SIDM haloes, and statistically constrain the amplitude and velocity dependence of the interaction cross-section in haloes with masses between 106 and 1010 M⊙. Measurements on these scales probe self-interactions at velocities below $30 \ \rm {km} \ \rm {s^{-1}}$, a relatively unexplored regime of parameter space, complimenting constraints at higher velocities from galaxies and clusters. We cast constraints on the amplitude and velocity dependence of the interaction cross-section in terms of σ20, the cross-section amplitude at $20 \ \rm {km} \ \rm {s^{-1}}$. With 50 lenses, a sample size available in the near future, and flux ratios measured from spatially compact mid-IR emission around the background quasar, we forecast $\sigma _{20} \lt 11\rm {\small {--}}23 \ \rm {cm^2} \rm {g^{-1}}$ at $95 {{\ \rm per\ cent}}$ CI, depending on the amplitude of the subhalo mass function, and assuming cold dark matter (CDM). Alternatively, if $\sigma _{20} = 19.2 \ \rmmore »{cm^2}\rm {g^{-1}}$ we can rule out CDM with a likelihood ratio of 20:1, assuming an amplitude of the subhalo mass function that results from doubly efficient tidal disruption in the Milky Way relative to massive elliptical galaxies. These results demonstrate that strong lensing of compact, unresolved sources can constrain SIDM structure on sub-galactic scales across cosmological distances, and the evolution of SIDM density profiles over several Gyr of cosmic time.« less