The intergalactic electromagnetic cascade solution for the anomalies from $\gamma$-ray blazar observations

Recent progress in very high energy (VHE, E >100 GeV) $\gamma$-ray observations, together with advances in the extragalactic background light (EBL) modelling, allows to search for new phenomena such as $\gamma$-axion-like particle ($\gamma \rightarrow$ ALP) oscillation and to explore the extragalactic magnetic field (EGMF) strength and structure. These studies are usually performed by searching for some deviation from the so-called absorption-only model, that accounts for only primary photon absorption on the EBL and adiabatic losses. In fact, there exist several indications that the absorption-only model is incomplete. We present and discuss the intergalactic electromagnetic cascade model (IECM) --- the simplest model that allows to coherently explain all known anomalies. This model has a number of robust signatures that could be searched for with present and future instruments. The IECM model may serve as a new background template, allowing to make future searches for $\gamma \rightarrow$ ALP oscillation more robust. A detailed account of our calculations is available in astro-ph/1609.01013v2 (A\&A,in print).