Hubble tension and fifth forces

Fifth forces are ubiquitous in modified theories of gravity. In this paper, we analyze their effect on the Cepheid-calibrated cosmic distance ladder, specifically with respect to the inferred value of the Hubble constant (H0). We consider a variety of effective models where the strength, or amount of screening, of the fifth force is estimated using proxy fields related to the large-scale structure of the Universe. To quantify the level of tension between the local distance ladder and the Planck value for H0, we calculate the probability of obtaining a test result at least as extreme as the observed one, assuming that the model is correct (the p-value). For all models considered, the level of agreement is greater than or similar to 20%, relieving the tension compared to the concordance model, exhibiting an agreement of only 1%. The alleviated discrepancy comes partially at the cost of an increased tension between distance estimates from Cepheids and the tip of the red-giant branch (TRGB). Demanding also that the consistency between Cepheid and TRGB distance estimates is not impaired, some fifth force models can still accommodate the data with a probability greater than or similar to 20%. This provides incentive for more detailed investigations of fundamental theories on which the effective models are based and their effect on the Hubble tension.