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The number density of neutrinos in the universe is totally dominated by primordial neutrinos created in the big bang when leptons and photons were in thermal equilibrium. … can be estimated in the context of the big bang model by assuming they cooled in the same way as photons (because they would have been ultra-relativistic and effectively massless particles in the early universe …

The difference between the two is very small at low redshifts, but becomes larger at higher redshifts, and depends on the expansion history of the universe and hence the cosmological parameters like $\ …

Expansion of the Universe, will light from some galaxies never reach us? … rare within our observable universe, even if common in the universe as a whole. …

Eventually (depending on $w$), the horizon shrinks to zero and the universe is torn apart in what is known as the "big rip". … For $w = -1.5$, this would happen in some 20 billion years time and the universe as we know it would end. …

The redshift of distant galaxies is mainly due to the expansion of space whilst the light has been travelling towards us. The "cumulative redshift" you refer to is the "cosmological redshift". Galaxi …

The universe at that time would have been matter dominated (the transition between radiation dominated and matter dominated occurred at $z\sim 3500$, so radiation pressure is negligible). … From this we obtain the baryonic density of the universe at $z=110$ as $1.1\times10^{-20}$ kg/m$^3$ and then using $$P = \rho k T/\mu m_u$$ we get $P = 2.2\times 10^{-14}$ N/m$^2$. …

The relative velocity between the Milky Way and Andromeda is of order 100 km/s. In 2.5 million years this amounts to relative motion of around 800 light years. Since the size of both galaxies is of o …

The gravitational wave "standard siren" technique described in the paper referred to actually gives a "luminosity distance" to the source, which in an expanding universe will be larger than the proper …

There is an implicit assumption here of homogeneity, that is that on large scales every bit of the universe behaves like every other bit at the same epoch. … The details of this are spelled out in According to Hubble's Law, how can the expansion of the Universe be accelerating? …

I don't have these textbooks to hand, so don't know (apart from the ionisation fraction that your question points out) what differences there are in the physics behind these calculations (e.g. see htt …

NB: The age of the universe is only near to $H_0^{-1}$ since this simple calculation ignores deceleration/acceleration. … Also note that the calculation does not need to know the size of the observable universe, nor is it relevant since we can't measure the redshift of something outside the observable universe... 1: This …

We can't locate the centre of the universe because there isn't one. Every part of the universe was part of the big bang and there are numerous duplicates on Physics SE that address this. e.g. … Does the universe have a center? Can the coordinate of the big bang point be calculated via observed universe or it is impossible? Did the Big Bang happen at a point? …

The typical extinction for a line of sight out of our Galaxy (but avoiding the Galactic plane) is of order a few tenths of a magnitude at visible wavelengths (it is a factor of 10 less in the infrared …

The radiation temperature of the universe is proportional to $(1+z)$, where $z$ is the redshift. The epoch of recombination is at $z=1100$ and the temperatue was 3000K. … Whereas now you can see objects "in the past", at this early epoch the universe was opaque to radiation, so it would be more like being in thick (and very hot!) fog. …

The universe has not been accelerating for long enough to make that much difference to the flatness problem. … However, as recently as $\sim 6$ billion years ago, the universe was decelerating, would have had $\Omega \sim 1$ and thus $\dot{a}$ would have been larger before that. …