Recent content by Jaime Rudas

Wikipedia says: Does the quintessence really vary in space? Wouldn't that imply violating the cosmological principle? Or perhaps it refers to small-scale variations, while homogeneity would be preserved on large scales?

Ah, yes, now I understand: its area is equal to that of a sphere of the same radius 4πR².

In what sense the pseudo-sphere isn't "a global embedding – the complete unbounded hyperbolic plane in ##E^3##"? Is it, perhaps, because its "equator" is a "bound" (a singularity)?

What does "unit" mean in this context?

Is that "flat plane" two-dimensional or three-dimensional?

Wouldn't it be better to say that they do not meet condition (b) because they have a past spacetime boundary?

Yes, that's why I said "remember."

Remember that, under reasonable assumptions, the Borde-Guth-Vilenkin theorem demonstrates that inflationary cosmological models doesn't extend infinitely into the past.

Polaris? :wink:

It seems to me that, according to these two hypotheses, time was created in the Big Bang. Which makes me realize that saying that time did not exist before the Big Bang is, in fact, an oxymoron because if there was no time, there could not have been a before.

The article Where did the Big Bang happen? states: Is this really the case? Wouldn't it be more correct to say that the current consensus cosmological model is unable to describe anything that happened before, for example, the Planck time?

Where could I find some introductory text that would help me delve deeper into this?

Regarding this, I have the following question: Is it possible to embed a flat (Euclidean) two-dimensional surface in a curved, three-dimensional space?

From this, I understand that for a sphere of area ##A## around a very massive and dense star, its radius ##R## will be greater than ##\frac12 \sqrt{\frac A \pi}##. If this is correct, for the case of the sphere around the black hole, can its radius be calculated, or is it undefined?

On the other hand, the margin of error in calculating the age of the universe is on the order of hundreds of millions of years, so what happened in the first 380,000 years is irrelevant for calculating the observable universe radius.