{'fraction_non_alphanumeric': 0.019250253292806486, 'fraction_numerical': 0.00303951367781155, 'mean_word_length': 5.457516339869281, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Testing ΛCDM with Gravitational Lensing Constraints on Small-Scale Structure

This paper primarily addresses the question of whether recent lensing observations probing the small-scale structure in the universe are consistent with the ΛCDM model. A conservative approach is taken, in which only the most difficult to explain cases of image flux anomalies in strong lenses are considered. Numerical simulations are performed to compare predictions for the ΛCDM small-scale mass function with observed flux ratios. By simulating several representative cases, it is found that all the cusp caustic lens anomalies and the disagreements between monochromatic flux ratios and simple lens models can be explained without any substructure in the primary lenses' dark matter halos. Intergalactic ΛCDM halos are enough to naturally explain these cases. However, thus far, spectroscopic gravitational lensing observations require more small-mass halos (~106 M☉) than are expected in the ΛCDM model.