Why does Dark Energy have to exist?

Newton's law of gravitation is only an approximation and has been replaced by Einstein's General Relativity (GR) which explains gravity as a curvature of space-time as the result of the presence of mass and energy.

The key is whether Einstein's much deeper theory can explain the expansion of the universe and how that would relate to dark energy. It turns out the GR can explain it, and the interesting consequence is that it does require 'dark energy' (although it doesn't specify what it is) so it has a natural explanation for the expansion of the universe.

The key idea is that there are 'curvature' terms in GR that are related to the various forms of energy that can produce gravity (rest mass, momentum, pressure). So every curvature term must be related to some sort of energy. When Einstein first formulated GR, he believed that the universe was static so he added an extra curvature term (proportional to the 'cosmological constant') that basically represented the expansion of the metric (space) to counteract the contraction of gravity, keeping the universe neither expanding or contracting. He later decided that it was a big blunder, but that term now can be used for explaining the expansion of the universe. When Einstein formulated GR, he simply added that term to the curvature side of the equation with no corresponding addition of any term in the energy side of the equation - he thought this was just an innate property of the universe. Turns out that is you assume the existence of a 'dark' energy, you can add that dark energy to the energy side of his equation and that will serve as the energy source for the expansion term. The bottom line is the dark energy produces a kind of negative pressure (negative pressure really does exist but it would take too long to explain it). Positive pressure in Einstein's equation produce a contracting form of gravity, negative pressure produces an expanding form of gravity.

So, in some sense you are right. Inverse square law doesn't really hold true if you include the expansion of the universe, but it can be fully explained by Einstein's GR with dark energy.

"Why does Dark Energy have to exist?"

Because we would like to find out if there is "stuff" disguised as the cosmological constant. The cosmological constant is non-zero, so IF Dark Energy is the cosmological constant, then it must exist to describe the Universe displayed.

"But couldn't it simply be that we don't understand exactly how gravity works at very long distances and very low levels?"

No we pretty much do. As the cosmological constant, which is NOT constant over the history displayed: inflation, then stagnation, then acceleration. Dark Energy is just another name for what is allowing relaxation of *global* curvature.

"What if gravity is quantized, and the math doesn't work the way we expect at galactic distances? Resulting in the inverse square law not being strictly accurate at very long distances?"

No, quantization of gravity would agree with GR at large scales, but have something different at small scales.

"How much would our current understanding of the inverse square law of gravity need to be adjusted to explain what we're observing without invoking a completely unknown 'Dark Energy'? Is it a tiny correction, or a large one?"

It fails to describe the Universe displayed, not based on distance, but based on *age*. Expansion occurs between *now* and *then*, not distance. That you can invoke the speed of light to get to a distance, is simply blinding you from the facts.

[EDIT:

Neb, Einsteins "Big Blunder" was putting in a value of the cosmological constant that stopped the "natural" expansion described by GR, with no cosmological constant term. He acceded to the popular belief that the Universe was static. Hubble later showed that this was not the case. We still need a cosmological "constant" (or Dark Energy as an actor) to get the *correct* rate of acceleration.

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Newton's third regulation states that for each action there is an equivalent and opposite reaction. as a result, employing this tried and examined concept and because we've rely and power, there must be dark rely and dark power. of direction, we've not got the technologies to work out then or create them yet yet there became right into a time whilst we could no longer do with anti-rely the two yet that has now been created. i think of you're over simplifying issues somewhat yet confident, you have the undemanding gist of how issues artwork on the topic of dark rely and power.

See friend, actually the inverse square law was used by Newton to derive Newton's Law of Gravitation. And as you have already said "Newton's laws of motion were found to be incomplete because they didn't give the right answers for objects in strong gravitational fields" Einstein gave his theories. So making changes in inverse square law wouldnt help. The Universe is expanding. The more far away an object is, the more it seems to be moving with greater speed farther away. This was concluded by observing the wavelengths of light coming from a galaxy over a period of time. They observed Red Shift to be taking place (by the help of mechanism of Doppler Effect). But after some time they observed tiny ripples in the background of cosmic microwaves, which cant be accounted only on behalf of the present gravitational force, so they(scientists) said that there exists something known as Dark Energy so as to produce this much of required gravitation. If speaking in scientific language, then "Measurements of cosmic microwave background (CMB) anisotropies, most recently by the WMAP spacecraft, indicate that the universe is close to flat. For the shape of the universe to be flat, the mass/energy density of the universe must be equal to a certain critical density. The total amount of matter in the universe (including baryons and dark matter), as measured by the CMB, accounts for only about 30% of the critical density. This implies the existence of an additional form of energy to account for the remaining 70%.[10] The WMAP five-year analysis estimate a universe made up of 74% dark energy, 22% dark matter, and 4% ordinary matter.[13] More recently, the WMAP seven-year analysis gave an estimate of 72.8% dark energy, 22.7% dark matter and 4.6% ordinary matter.[2]" i got this from Wiki. Also till now maths is doing fine with gravitation except at some instances(singularity), so not to blame maths...

Hope it helps.