  Our paper reviews the planned space-based gamma-ray telescope GAMMA-400 and
evaluates in details its opportunities in the field of dark matter (DM)
indirect searches. We estimated GAMMA-400 mean sensitivity to the diphoton DM
annihilation cross section in the Galactic center for DM particle masses in the
range of 1-500 GeV. We obtained the sensitivity gain at least by 1.2-1.5 times
(depending on DM particle mass) with respect to the expected constraints from
12 years of observations by Fermi-LAT for the case of Einasto DM density
profile. The joint analysis of the data from both telescopes may yield the gain
up to 1.8-2.3 times. Thus the sensitivity reaches the level of annihilation
cross section $\langle \sigma v
\rangle_{\gamma\gamma}(m_\chi=100~\mbox{GeV})\approx 10^{-28}$ cm$^3$/s. This
will allow us to test the hypothesized narrow lines predicted by specific DM
models, particularly the recently proposed pseudo-Goldstone boson DM model. We
also considered the decaying DM - in this case the joint analysis may yield the
sensitivity gain up to 1.1-2.0 times reaching the level of DM lifetime
$\tau_{\gamma\nu}(m_\chi=100~\mbox{GeV}) \approx 2\cdot 10^{29}$ s. We
estimated the GAMMA-400 sensitivity to axion-like particle (ALP) parameters by
a potential observation of the supernova explosion in the Local Group. This is
very sensitive probe of ALPs reaching the level of ALP-photon coupling constant
$g_{a\gamma} \sim 10^{-13}~\mbox{GeV}^{-1}$ for ALP masses $m_a \lesssim 1$
neV. We also calculated the sensitivity to ALPs by constraining the modulations
in the spectra of the Galactic gamma-ray pulsars due to possible ALP-photon
conversion. GAMMA-400 is expected to be more sensitive than the CAST helioscope
for ALP masses $m_a \approx (1-10)$ neV reaching $g_{a\gamma}^{min} \approx
2\cdot 10^{-11}~\mbox{GeV}^{-1}$. Other potentially interesting targets and
candidates are briefly considered too.
