Here we briefly review possible indirect effects of dark matter (DM) of the Universe. It includes effects in cosmic rays (CR): first of all, the positron excess at ∼ 500 GeV and possible electron-positron excess at 1-1.5 TeV. We tell that the main and least model-dependent constraint on such possible interpretation of CR effects goes from gamma-ray background. Even ordinary e + e − mode of DM decay or annihilation produces prompt photons (FSR) so much that it leads to contradiction with data on cosmic gamma-rays. We present our attempts to possibly avoid gamma-ray constraint. They concern peculiarities of both space distribution of DM and their physics. The latter involves complications of decay/annihilation modes of DM, modifications of Lagrangian of DM-ordinary matter interaction, and inclusion of mode with identical fermions in final state. In this way, no possibilities to suppress were found yet except, possibly, mode with identical fermions. While the case of spatial distribution variation allows achieving consistency between different data. Also we consider stable form of dark matter which can interact with baryons. We show which constraint such DM candidate can get from damping effect in plasma during large scale structure formation in comparison with other existing constraints.

The observed anomalous excess of high-energy cosmic ray (CR) positrons is widely discussed as possible indirect evidence for dark matter (DM). However, any source of cosmic positrons is inevitably the source of gamma radiation. The least model dependent test of CR anomalies interpretation via DM particles decays (or annihilation) is connected with gamma-ray background due to gamma overproduction in such processes. In this work, we impose an observational constraint on gamma ray production from DM. Then, we study the possible suppression of gamma yield in the DM decays into identical final fermions. Such DM particles arise in the multi-component dark atom model. The influence of the interaction vertices on the gamma suppression was also considered. No essential gamma suppression effects are found. However, some minor ones are revealed.