only 2.5 sigma

After all, aside from the Planck data, the lambda-CDM model, which is the standard model of the universe, seems to work really well. Using just six parameters, it seems to fit our observations of the universe, albeit a flat universe, nearly perfectly.

Neutrino Properties and the Cosmological Tensions in the ΛCDMMode

e-fold of cosmic expansion

We review three distance measurement techniques beyond the local universe: (1) gravitational lens time delays, (2) baryon acoustic oscillation (BAO), and (3) HI intensity mapping. We describe the principles and theory behind each method, the ingredients needed for measuring such distances, the current observational results, and future prospects. Time delays from strongly lensed quasars currently provide constraints on H0H_0 with < 4% uncertainty, and with 1% within reach from ongoing surveys and efforts. Recent exciting discoveries of strongly lensed supernovae hold great promise for time-delay cosmography. BAO features have been detected in redshift surveys up to z <~ 0.8 with galaxies and z ~ 2 with Ly-αα forest, providing precise distance measurements and H0H_0 with < 2% uncertainty in flat ΛΛCDM. Future BAO surveys will probe the distance scale with percent-level precision. HI intensity mapping has great potential to map BAO distances at z ~ 0.8 and beyond with precisions of a few percent. The next years ahead will be exciting as various cosmological probes reach 1% uncertainty in determining H0H_0, to assess the current tension in H0H_0 measurements that could indicate new physics.

The ‘radiation negligible’ approximation is pretty good from about 100 million years after the start of expansion, when the radiation energy density dropped to less than 1% of the matter energy density.

The traditional unit of the Hubble constant as used by Edwin Hubble is kilometers per second per Megaparsec. From an educational p.o.v. it was an unfortunate choice, because it seems to imply a recession speed, while it is really a fractional rate of increase of distance. It is a distance divided by a distance, all divided by time. So its natural unit is 1/time, for which we can choose any convenient timescale

Exponential expansion means that all cosmic distances will increase by a factor e (=2.718) every 17.3 billion years (or 17.3 Gy for short). This can be called the natural ‘e-fold time’ of our universe, since an increase by a factor e is called an e-folding.

the ‘particle horizon’

the cosmological communications horizon (also called the cosmic event horizon), which is how distant an observer can be and still receive a signal that we transmit today

Hubble radius. It is the distance at which the recession rate of an object equals the speed of light. In our natural units, it is simply the inverse of the Hubble constant H at the time.

cosmological recession rates are quite like the growth rate of money in an investment, which we normally express as a percentage return over a period of time. But, we can also express it as so many dollars earned per time period, which is essentially the present ‘speed of growth’ of the investment. Cosmic recession rates are similar to this sort of speed.The proper distance of a galaxy is equivalent to the investment amount, the Hubble constant is equivalent to the interest rate and the increase in proper distance is equivalent to the dollars earned. Divide the increase in proper distance (say km) by a time period (say seconds) and you have a recession rate in km/s. The larger the proper distance, the larger the recession rate, without any upper limit.

Suppose there are a zillion identical, straight blue bars supporting a zillion red cubes. Also suppose that due to some mechanism, each blue bar is continuously lengthening at a rate of one ‘red cube side length’ per year, while all the cubes remain unaffected, size-wise.

worm, who in the midst of his splendour is crumb-ing into dust

Here, we prove thatarbitrarilyinhomo-geneous and anisotropic cosmologies with “flat” (includingtoroidal) and “open” (including compacthyperbolic) spatial topology that are initially expandingmust continue to expand forever at least insome region at a rate bounded from below by a positive number,despite the presence of arbitrarilylarge density fluctuations and/or the formation of black holes

We describethe minimal modification required for self-acceleration and show that its maximum likelihood yieldsa 2.4σpoorer fit to cosmological observations compared to a cosmological constant, which, althoughmarginally still possible, questions the concept of cosmicacceleration from a genuine scalar-tensormodification of gravity.

Spherically Symmetric N-body Simulations with General Relativistic Dynamics