How heavy is the universe? Conflicting answers hint at new physics.

The only thing that has "weight" are stars and planets. And if the modern time-line is close to correct, the majority of mass in the cosmos can not be "weighed".

Weight come from gravity attraction. If stars have been burning for 13 billion years, most mass now, is isolated charge and has no gravitational attraction.

Only dipoles and larger structures are affected by gravity.

How can one measure anything, when we can only see and detect a certain radius(13 billion years) of the whole radius? Surely no one believes that we can see the whole cosmos.

Making sense of our cosmos will always be iffy. Pick any dark area in space. Look at it closely. The farther you look, the denser it gets.

Does that make sense? What if gravity decay was very great at the beginning.......then the most density would be on the rim of the cosmos. Out of sight.

Iffy, iffy, iffy. Astronomy is a guessing game. We can not even determine a base line, to measure the closest star.
 
May 13, 2020
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Given that dark energy and gravity are equal in force and dark energy may be a "push force" of gravity which acts in a thinner and more spread out manner... I would say the weight of the universe is zero.
 
The only thing that has "weight" are stars and planets. And if the modern time-line is close to correct, the majority of mass in the cosmos can not be "weighed".

Weight come from gravity attraction. If stars have been burning for 13 billion years, most mass now, is isolated charge and has no gravitational attraction.

Only dipoles and larger structures are affected by gravity.

How can one measure anything, when we can only see and detect a certain radius(13 billion years) of the whole radius? Surely no one believes that we can see the whole cosmos.

Making sense of our cosmos will always be iffy. Pick any dark area in space. Look at it closely. The farther you look, the denser it gets.

Does that make sense? What if gravity decay was very great at the beginning.......then the most density would be on the rim of the cosmos. Out of sight.

Iffy, iffy, iffy. Astronomy is a guessing game. We can not even determine a base line, to measure the closest star.

As you yourself point out, the title is a jest about gravity locally affecting mass since the researchers want to quantify how much the density of matter clumps up due to that.

Many assertions in your comment doesn't square with cosmology, so maybe it is useful to discuss them?

- Gravity only depends on mass (Newton discovered this), whether from normal or dark matter. Mass has nothing to do with electromagnetic (?) "dipoles" and the amount of mass energy lost in stars due to fusion is something like a percent. Sun will mass approximately the same when it is dead.

- Clumping is observed on all scales starting from the large structures that you correctly mentions and which clumping is the major component of sigma-eight, but also smaller scales down to stars and planets. The dead Sun will affect sigma-eight about as much as today.

- Since the universe expands, the observable radius is much larger than the age, and the age is about 14 billion years. The oldest photons, from the cosmic microwave background, that we see have traveled for 14 billion years but their starting point now lies 46 billion years out [ https://en.wikipedia.org/wiki/Observable_universe ]. The physics and the different measures gets complicated, but this fact is good to know. And the observable radius is, naturally, what we see and can see. We know from cosmic variance (spread in such measures as sigma-eight) that the universe is at least 5 times larger in radius and from its flatness at least 1,000 times larger.

- We have made sense of "100 %" of the universe, since the current cosmology has less than 0.5 % uncertainty and the current cosmology is complete and self consistent. This is a good description of the latest cosmology and what it means:
View: https://www.youtube.com/watch?v=P1Q8tS-9hYo


- If the last sentence still refer to distances, it may be good to know that we have measured the distance to the closest star system (3 stars) since two centuries back [ https://en.wikipedia.org/wiki/Alpha_Centauri#Observational_history ]. The method is in fact a key method in the cosmic distance ladder, which was the first way to measure cosmic distances [ https://en.wikipedia.org/wiki/Cosmic_distance_ladder ].
 
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