I will bite.
"At least space must have some kind of density otherwise space cant curve"
Can you explain firstly why it mentions space and not space-time?
It is implied that time and space is inseparable connected. So if you say space you also say space-time, - except if you mean hairsplitting of course.
Can you explain secondly, mathematically, just using maths, purely in terms of mathematics, the requirement for density in order to define curvature? You do know that the mathematical 'definition' of curvature has nothing to do with density?
There are no difference, but expression.
To know what really happens on a path where the “space-time” is changing, - imaging you could jump between different space-time realities.
Which differences would you see (except that time is different) ?
There must be more differences than only time, and you should know there are.
Let us say you were on board of a spacecraft and sitting inside the kitchen of the spacecraft. Suddenly the spacecraft would jump between different space time realities.
This would cause suddenly different time ticking rates.
If the laws of nature always must be the same, - one second and meter
cannot be comparable the same in 2 different space-time-realities.
If times ticks slower, you can say that 1 second is now “stretchíng”, -
so must then also the length – width – height, - reality.
And opposite, - when a second is comparable faster (“contracted”) as before, - then also all dimensions are also “contracted”.
If you cannot accept this, tell me about the consequence of time dilation.
So before getting lost in expressions, - you must make yourself clear, that we are talking about different space-time-realities, where not
only time
possible can be different.
The expressions, - “Curvature of space” or “Stretching space” - are only expressions for how we under certain circumstances are able to
interpret realities.
For example
When light from a distant object passes close to a galaxy or cluster of galaxies along the line of sight, the image of the background object (here, the quasar) can sometimes be split into two or more separate images (here, A and B). The foreground object is a gravitational lens.
Gravity is stretching time
+ all distances.
Or if you prefer, - (strong) gravity is stretching space time.
Hence light can’t move in a straight line, - but must “bend” from one reality towards another one.
Exactly in the same way it must “bend inwards”, when the universe is losing gravity, - whereby realities (space-time realities) included distances now gets relative / comparable smaller as before, - but still everything always looks the same, - even also time.
This is what the abused expression,- "cosmological redshift" is about.
Redshift are (mainly) time stamps of difference space-time realities, - that fools have turn into religion.
THIS is what the so called (abused expression) dark energy is about, - and shows the greatest stupidity ever invented, because some thought it would be smart to invent a repulsive force.
Maybe because such fools do not like extreme speed, (properly a socialist invention)..
The cause of the idea that dark energy is acceleration is due to the same illusion.
What happens is not an accelerating repulsive force, - but instead that space-time realities close to us (included us) gets comparable smaller (shrinks) due to the lost of universal gravity.
Gravity is stretching everything (included time). - When gravity gradually is lost the opposite happens.
So you have already all the mathematics you need. All you need to do is just
not to turn anything at its head, - and the universe is pretty simple.
Whether you better like the old expression; curvature of space, - or the stretching space-density framework, - is not important.
The point is rather first at all that you
understand WHAT matter / gravity does with space
and everything else.
Words and expression do have their own limits, but imagination shall not be bound to dead-end expressions.
!
.
