Why does gravitational attraction result in a decelerating universe I read the following statement:

There is matter and energy in the universe, and their mutual gravitational attraction will slow down the expansion of the universe, leading to a monotonically decreasing expansion rate $H(t)$ (the Hubble constant) -- a decelerating universe.

Why does gravitational attraction slow down the expansion of the universe? Intuitively I would think that as the space between matter expands, the gravitational attraction between matter is weaker, so the expansion rate would increase instead of decrease.
 A: To understand this, keep in mind that the galaxies (or, to be more accurate, clusters of galaxies) are in freefall motion. In a Newtonian picture, this means that there is no force on them other than gravity, and in the GR picture their worldlines are timelike geodesics. Meanwhile if we ignore or "switch off" the dark energy component, then the whole of gravitation is mutually attractive. Therefore the gravitational effect between any pair of galaxies is always attractive, which means it will tend to reduce their motion away from each other. The Newtonian intuition gets the sign right here, and the GR calculation makes it all precise in terms of worldlines. So gravitation would always be expected to slow the expansion. Your intuition about the weakening effect as the galaxies move further apart is right, but you should see it as a weakening of the deceleration. Compare with a car which is moving quickly and the driver applies the brakes strongly at first, so the car decelerates. If the driver then gradually releases the brakes, then the deceleration reduces, but it is still deceleration. Here gravity provides the 'brakes' and the reduced effect of gravity as the galaxies get further apart means the 'brakes' are being gradually released. In the absence of any brakes, the expansion rate would be constant.  It would not increase.
Of course, all the above is what you would expect in the absence of dark energy or a cosmological constant.
