A local resolution of the Hubble tension: The impact of screened fifth forces on the cosmic distance ladder Harry Desmond,1, ∗ Bhuvnesh Jain,2, y and Jeremy Sakstein2, z 1Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK 2Center for Particle Cosmology, Department of Physics and Astronomy, University of Pennsylvania, 209 S. 33rd St., Philadelphia, PA 19104, USA (Dated: April 13, 2020) The discrepancy between the values of the Hubble constant H0 derived from the local distance ladder and the cosmic microwave background provides a tantalising 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 H0 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 H0 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 local dark matter density. We find that a fifth force strength ∼ 5−30% that of gravity can alleviate (though not resolve) the H0 tension in some scenarios, around the sensitivity level at which tests based on other distance ladder data can constrain this strength. Many of our models reduce the tension below 3σ, but reduction below 2σ is unlikely possible while maintaining self-consistency of the distance ladder. Although our analysis is exploratory and based on screening models not necessarily realised in full theories, our results demonstrate that new physics-based local resolutions of the H0 tension are possible, supplementing those already known in the pre-recombination era. I. INTRODUCTION magnitude of the raw discrepancy (derived simply by com- bining errorbars in quadrature) has been growing, and is now The Hubble parameter H0, describing the expansion rate sufficiently large that almost all statistical approaches suggest of the Universe today, is a critical quantity in cosmology. strong disagreement. The second is to argue that one or more Perhaps the most significant discrepancy that currently exists of the H0 pipelines suffer from systematics which have not in the standard cosmological model, ΛCDM, is that when been fully accounted for in the fiducial analyses. This is more measured locally (out to ∼100 Mpc) H0 is found to be ∼74 plausible for the distance ladder measurements than the CMB km s−1 Mpc−1, while high-redshift observations imply ∼67 due to the complexity of the calibrations between rungs of the km s−1 Mpc−1. The current most precise estimates from these ladder and the range of models required to describe the astro- two regimes are 74:03 ± 1:42 km s−1 Mpc−1 from the local physical objects involved, although some fraction of the dis- distance ladder [1–3] (hereafter R16, R18 & R19) and 67:4 ± crepancy could be due to systematics in CMB measurements 0:5 km s−1 Mpc−1 from the cosmic microwave background (e.g. [12]). For the distance ladder, re-analyses have focused (CMB) [4] (hereafter Planck), a tension of 4:4σ. These are on the treatment of outliers in the Cepheid period–luminosity supplemented at low redshift by independent analyses such as relation (PLR) [13, 14], the dependence of supernova lumi- H0LiCOW, which uses time delay distances to low-redshift nosity on the mass and star formation rate of the host galaxy +1:7 −1 −1 [15], the parallaxes of Milky Way Cepheids [16, 17] and the lensed quasars to derive H0 = 73:3−1:8 km s Mpc [5], and at high redshift by galaxy and Lyα measurements of baryon geometric distances to the anchor galaxies [18, 19]. acoustic oscillations calibrated against elemental abundances The final class of solutions to the H0 tension is to postulate from Big Bang nucleosynthesis [6] and the “inverse distance new physics that introduces a difference between the expansion − − arXiv:1907.03778v4 [astro-ph.CO] 10 Apr 2020 1 1 ladder” [7], yielding H0 = 66:98 ± 1:18 km s Mpc and rate inferred locally and at recombination. Although requiring −1 −1 Λ H0 = 67:77 ± 1:30 km s Mpc respectively. a deviation from CDM, and therefore less conventional, this Prospective resolutions to this disagreement fall into one of could naturally explain the fact that a variety of local measure- −1 −1 three classes. The first is to modify the statistical framework to ments cluster around 73 km s Mpc and high-redshift ones −1 −1 refine the measure of the tension (e.g. [8–11]). While a range around 67 km s Mpc . For example, it has been proposed of estimates for the probability of distance ladder and CMB that the Milky Way is near the centre of a statistically under- concordance are derivable from plausible methodologies, the dense region of size potentially several hundred Mpc, which would generate streaming velocities away from us and hence bias local measurements of H0 high [20, 21]. The CMB mea- surements are also sensitive to the physics of recombination, ∗ [email protected] y which may be modified to alter the H0 constraint [22, 23]. [email protected] Alternatively, an increase in the number of relativistic degrees z [email protected] 2 Fully Unscreened Envelope Unscreened Screened (MW, N4258) SN Distance Calibrator FIG. 1. Left: The distance ladder. Each vertical segment represents a rung, as indicated at the very top. Distances to objects in the upper part are calibrated by means of the lower indicator. A fiducial screening status of each rung is shown under the distance axis: a rung is labelled as unscreened when that is the case for at least one indicator. In this work we consider SNe to be screened, although this may not be the case in some models; we consider this further in AppendixB. Right: A schematic representation of the Cepheid period–luminosity relation (PLR) when various parts of a Cepheid are unscreened. The grey solid line shows the Newtonian relation as traced out by the screened Cepheids in the MW and N4258. The red dashed line shows the relation for Cepheids with unscreened envelopes and the blue dotdashed line for both envelope and core unscreened. The distances between the lines indicate that unscreening the core has a larger effect than unscreening the envelope. Assuming an unscreened Cepheid lies on the Newtonian PLR causes its luminos- ity and hence distance to be underestimated, as shown by the vertical line at fixed measured period. This causes the inferred H0 to be biased high. of freedom Neff by ∼0.4–1 (“dark radiation”) could partially post-Newtonian tests of gravity within the Solar System while resolve the tension [24–27]; this is degenerate with a change allowing them to impact astrophysical and cosmological ob- in the effective strength of gravity between the epochs of Big servables, and has now been recognised as a fairly generic Bang Nucleosynthesis and recombination [28]. There is also property of theories with fifth forces [see e.g. 43, 44, 46–50, a significant degeneracy with the systematic lensing power pa- and references therein]. The Universe’s accelerated expansion rameter AL [27], whose measured deviation from unity is not has been hypothesised to arise from new fields in this way understood. A component of dark energy at very high redshift [41, 51], and the low-energy limits of UV complete theories [29–31], an interaction of dark energy [32, 33], an injection of are expected to contain screened fifth forces on a range of energy from scalar fields at recombination [34] or the decay of scales [52–65]. Empirical searches for these are growing in dark matter into dark radiation at the time of matter-radiation sophistication [e.g. 43, 66, 67], with several indications that equality [35–37] or later [38] may also push the CMB value they may in fact be of use in accounting for certain astrophys- upwards. A full high-redshift solution would appear to require ical phenomena [68–72]. an exotic physics scenario however, as none of the commonly- In this paper we develop a framework for propagating gravi- considered extensions to ΛCDM offer an entirely satisfactory tational enhancements due to fifth forces into the distance con- solution [27, 39, 40]. straints on extragalactic Cepheid hosts, and hence H0 when We propose a local resolution to the H0 tension relying SN measurements are included. We implement a range of on theoretically and observationally well-motivated physics phenomenological screening models within this framework— beyond the standard model. Specifically, we describe how in which the degree of screening is set by either environ- a partially screened fifth force naturally leads to an overes- mental or intra-halo gravitational variables—in order to quan- timate of H0 in distance-ladder analyses if the gravitational tify the bias expected in H0 under various scenarios for fifth properties of Cepheids calibrating the period–luminosity re- force behaviour. Some of our screening proxies correspond to lation (principally in the Milky Way and N4258) differ from commonly studied mechanisms including chameleon [73, 74], those of Cepheids in galaxies with Type Ia supernovae (here- symmetron [75], dilaton [76], K-mouflage [77] and Vainshtein after simply “SNe”), which are used to extend the distance [78] screening.