Density should remain the same. Think of the volume as a cube, then you notice that only one of the 3 sides shrinks. An since it shrinks by the same factor that the apparent mass increases, the two cancel out and the density remains the same.

The problem is, in simple words, is like asking what is the product of 0 times infinity.

The likelihood that we happen to exist in a multiverse is infinitesimal. But since everything that can happen will happen an infinite number of times says that there is an infinitude of us peppered in the multiverse. So our probability of existing times the number of times we exist in the multiverse is (pick a number!).

In short, the argument professor Steinhardt makes is convincing but not fatal.

I accept that inflation is eternal but where along this eternal inflation are we? Has inflation been on-going infinitely long? (I doubt it.. nature seems to abhor infinities).

SO, by the anthropic principal, since we exit, a universe compatible with our existence had to have formed and we exist. I accept that there is an untold (I calculate gogolplex +3 of them, for sure ;-))number of universes that also contain something like us.

Yes. I believe that ‘time’ is a local property (of the quanta) because when LQG quanta interact there is a before-interaction-after. This means that there is a causal relationship (in the interaction). To be shown is how ‘time’ as we know it emerges from local time.

I personally believe that space is just a coordinate system. I believe that space is the stage where energy differences are played out. Different energy levels at ‘near by’ points give rise to emergent properties. So even dimensions must be an emergent property and most likely the number of dimensions at various points in space are different. The more intriguing question is what is energy and what is time.

Things we thought we knew as absolute turn out to be scale-specific (ex: water is a fluid at our physical scale but atoms at the molecular level). So as we change the scale we investigate it is reasonable to expect new ‘absolutes’ associated with that scale. The more interesting questions is how many scale regions are there in nature?