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The major scientific goals of the SRG mission all-sky survey are:

The study of the Large-scale structure of the Universe and measurements of the Dark Energy equation of state; The exploration of the growth and cosmological evolution of supermassive Black holes in the Universe. To fulfill of these goals, SRG will survey the sky in an energy band up to 11 keV with unprecedented sensitivity and angular resolution. In course of the all sky survey SRG will discover about 100 000 galaxy clusters and 3 million AGNs. Galaxy clusters are the largest gravitationally bounded objects in the Universe and are best explored through the study of X-ray emission from the hot intergalactic gas.

The limiting survey sensitivity achieved after 4 years of observations for objects with low surface brightness, ~4x10^-14šergšs^-1šcm^-2, will permit the discovery of all massive galaxy clusters in the observed Universe with masses M ~3.5x10¹⁴šh^-1šMsun (or Tš~š4.5 keV). Moreover one will be able to discover all galaxy clusters with Mš~š2.3x10¹⁴šh^-1šM_sun (or T ~š3.5škeV), situated at redshifts zš~š1, and all galaxy clusters and galaxy groups with Mš~š10¹⁴šh-1šM_sun (or Tš~š2škeV), at redshifts zš~š0.4.

These capabilities will allow one to:

• Obtain Galaxy cluster numbers as a function of redshift N(z) (with resolution δzš=š0.02 up to zš=š2), see fig.2;
• Measure the cosmological evolution of galaxy cluster mass functions and the growth rate of matter distribution nonhomogeneity over the Universe;
• Obtain the power-density spectra of cluster space distribution P(k) at broad distance scales (? from 10 up to 1000šh^-1šMpc);
• Measure baryonic oscillation at power density spectra and determine the position of baryonic peaks with ?1% accuracy.

These will permit the measurement of the Dark Energy equation of state in the Universe - the most significant element of modern cosmology which defines the dynamics of Universe expansion. Also in the course of the SRG survey, the most complete census of Seyfert galaxies, radio galaxies, quasars and blazars in the giant volume of the Universe will be performed.

Fig.2. Number of clusters of galaxies per 20,000 deg², depending on Cosmology model, based on a subset of the ~2,000 most rich clusters of the 50,000 clusters which will be detected by SRG. Solid line ? standard model with ΩM = 0.3, ΩΛ = 0.7, h = 0.73.

These census data will allow one to:

• Define the X-ray luminosity distribution of close galaxies from normal (nonactive) up to the brightest Seyfert galaxies ? a complete picture of star birth and accretion on Black Holes in the local Universe;
• Obtain quasar luminosity function as a function of redshift (up to zš=š7) ? supermassive Black Holes growth history in the nucleus of giant elliptical galaxies;
• Discover a large number of optically-thick (through Compton deflection) galaxy nuclei, unseen in the standard (softer) X-ray band. This permits a study of the evolution of obscured nuclei luminosity and redshift ? revealing the structure of AGNs, and the physics of matter accretion on massive Black Holes;

The observatory, in survey mode, will perform the most complete X-ray luminosity function study for Galactic X-ray sources. In the course of the survey, SRG will monitor X-ray source variability on both short and long temporal scales.

The Observatory would perform:

• A study of coronal events and stellar flares of hundreds of thousands of stars;
• A study of AGNs X-ray variability;
• A search for merging supermassive black holes (together with LISA, gravitational waves);
• A study of GRB afterglow at zš?š10 ? the death of the first stars in the Universe and the star birth history of the Universe;
• A study of Galactic X-ray transients, X-ray binaries etc.

Fig.3 A comparison of the planned eROSITA/SRG survey with existing surveys

In pointing mode, a key task of the SRG mission will be to perform some extra observations as:

• About ~100 of the ?best? galaxy clusters (according to X-ray observations and SZ effect) will be observed to define the Hubble constant evolution with redshift;
• ~1000 galaxy cluster gas temperatures will be measured via their X-ray spectra;
• Several hundred AGNs will be studied for their spectral properties.<>