A quick estimation of the number of human-like intelligent civilizations in our universe might go as follows. There are about (the word “about” will be omitted below, but should be assigned to every number) 200 billion stars in our galaxy, and there are 200 billion galaxies in the space from which the light has been able to reach us since the Big Bang 14 billion years ago. So there are 1022 stars.
If each star has one planet in average, and if 1/100 of the stars and planets have the required properties as defined below, the number of planets suitable for hosting an intelligent civilization like ours is as follows: out of 1022 stars, 1020 stars are the same type as our sun, 1018 stars are also far enough from the wild events like novae explosions and from the central black hole of their galaxy, 1016 stars also have a roughly Earth-size planet in the star’s habitable zone (acceptable irradiance), 1014 stars have further a bigger planet on an outer orbit to protect the Earth-size planet from asteroids, 1012 Earth-size planets revolve around their stars with suitable eccentricity, 1010 Earth-size planets also have a suitable rotation around their axis (frequency and direction), 108 Earth-size planets also have plate tectonics, 106 Earth-size planets also have a crust with a suitable chemical composition, 104 Earth-size planets also have a water ocean, 102 Earth-size planets also have a moon stabilizing their rotation axis while ensuring cyclic ocean tides, 100 Earth-size planets also have a suitable atmosphere (composition and pressure).
The above rough estimation has provided 1 civilization like ours in the whole observable universe ever – the deduced single civilization corresponds to us!
We might have chosen different properties and values; however, all estimations provide very low probabilities for the existence of observers like us. The classical Drake equation, as well as cosmologists’ assessments, usually leads to a conclusion that we are alone1,2,3. Even if there were one more civilization, it would most probably be located 10 billion light years away, so that its signals, even if employing energy sources as strong as the whole star, could hardly be detected by us. And even if 10,000 civilizations had evolved on different planets since the Big Bang, they would not exist simultaneously; planet’s life takes 10 billion years (Earth is 4.5 billion now and will be engulfed by the expanding Sun within 5.5 billion years), and if an intelligent civilization lasts 1 million years (optimistically) or less (covering 1/10,000 or less of its planet's existence), each of said 10,000 civilizations would be alone in its time.
Although there are, according to today’s physics, innumerable parallel universes, in which innumerable intelligent civilizations exist, and in which even we ourselves appear in many variations and also in our exact copies – still we are alone in this specific universe of ours which presently spreads around us to a distance of 30 billion light years. We should not be special according to the Copernican principle, but in our universe we probably are.
2Max Tegmark, Our Mathematical Universe, Vintage Books, 2015, p. 397