If the universe is expanding will gravitational attraction eventually go to zero?

Question

Let's assume that we prove that dark matter exists (after all, only about 4 percent of the entire universal mass is atoms, and 22% dark matter, 74% dark energy (I think I got the numbers right)).

However, if that is the case, than everything would technically pull on everything, right? But if the universe is continuously expanding, but mass cannot be created or destroyed, unless it is from or to energy, than everything pulls on each other, but as time passes it would be weaker and weaker.

1. So my question is, can it ever reach a time when gravitation reaches zero?

2. Or if mass can be created from the expansion of the universe, than does that mean since it is expanding that there is no change in gravitation?

3. Also, how is the Hubble Constant calculated?

Answer 1

I describe how to calculate the Hubble parameter in How does the Hubble parameter change with the age of the universe?. You should have a quick read through this as it's relevant to the rest of your question.

We know the universe is expanding. We describe its size by a parameter called the scale factor, $a$. The rate of expansion is the rate of change of $a$ with time, which we write as $\dot{a}$.

Our everyday experience of gravity is that it accelerates things i.e. it speeds them up or slows them down. If you drop a ball gravity accelerates it downwards, and if you throw the ball up gravity slows it. In the context of an expanding universe the corresponding quantity is the rate of change of $\dot{a}$ with time, which we write as $\ddot{a}$. If $\ddot{a} \lt 0$ that means the expansion rate is slowing down, while if $\ddot{a} \gt 0$ that means the expansion rate is speeding up. So when you ask if gravitation will ever be zero, I take this to mean that $\ddot{a} = 0$ i.e. the expansion of the universe is neither slowing down nor speeding up.

The equation for $\ddot{a}$ comes from the Friedmann equations. For a flat universe like ours, and assuming the pressure is zero, $\ddot{a}$ is given by:

$$ \frac{\ddot{a}}{a} = -\frac{4\pi G}{3}\rho + \frac{c^2}{3}\Lambda \tag{1} $$

where $\rho$ is the density of the stuff in the universe and $\Lambda$ is the cosmological constant i.e. the dark energy. Note that the density $\rho$ decreases with time as the universe expands because the same amount of matter occupies a bigger volume of space. However the cosmological constant $\Lambda$ does not change with time.

So is there a time when $\ddot{a} = 0$? If we take equation (1) and set $\ddot{a} = 0$ we get:

$$ \frac{4\pi G}{3}\rho = \frac{c^2}{3}\Lambda $$

or rearranging gives us:

$$ \rho = \frac{c^2}{4\pi G}\Lambda $$

and this value of $\rho$ happened about 5 billion years ago at the point where the rate of expansion changed from slowing to accelerating. This is the point of inflection in the graph of $a$ versus time:

So there was a moment about 5 billion years ago when the net gravity in the universe was effectively zero. This moment will never come again because dark energy is now accelerating the expansion.

Answer 2

However, if that is the case, than everything would technically pull on everything, right?

No. A gravitational field is a place where space is "neither homogeneous nor isotropic". You can See Einstein talking about that here. And the FLRW metric "starts with the assumption of homogeneity and isotropy of space". I'm confident that this is correct because the universe didn't contract when it was small and dense. If it did, we wouldn't be here. So a gravitational field is a place where space is inhomogeneous, but in the large scale universe space is homogeneous, so on the large scale, when it comes to the universe, there is no overall gravitational field. So everything doesn't pull on everything else. Instead concentrations of energy in the guise of matter pull on other concentrations of energy in the guise of matter, and these aren't everything.

But if the universe is continuously expanding, but mass cannot be created or destroyed, unless it is from or to energy, than everything pulls on each other, but as time passes it would be weaker and weaker. So my question is, can it ever reach a time when gravitation reaches zero?

Does not parse! The gravitation was zero when the universe was small and dense, and it's zero now. A gravitational field is a place where space is inhomogenous, and as a result of this the motion of light and matter falls down. But it isn't a place where "space falls down". The universe isn't a place that's contracting because of gravity, and never ever was. The expansion of the universe has got a lot to do with general relativity, but not gravity. Why don't you ask another question about the expansion of the universe?

Or if mass can be created from the expansion of the universe, than does that mean since it is expanding that there is no change in gravitation?

Yes. On the large scale space is homogeneous, whilst a gravitational field is a place where space is inhomogeneous. So on the large scale, when it comes to the universe, there is no overall gravitational field. There is no change from zero.