Cosmology Notes/draft

What is wrong with cosmology?

The current scientific consensus on the nature and evolution of the Universe is that all the matter and energy in the Universe spontaneously exploded outward as a Big Bang from a single point in space, and has continued to expand ever since. This model was formulated at a time when scientists were not even sure there were galaxies outside our own Milky Way. However, the truly colossal advancements in observational astronomy over the last 50 years, from ground-based telescopes, satellites, and space-probes to the revolutionary advances in data processing and computing power, has lead to a seldom-admitted crisis of theory versus observation in cosmology.

The current model is based on these assumptions and observations:

1. the "Cosmological Principle" - the postulate that the Universe is both isotropic (the same in all directions) and homogeneous (matter distribution is "smooth" on a sufficiently large scale),
2. that the Cosmic Microwave Background Radiation (CMBR) is the afterglow from the Big Bang,
3. that the Hubble relation, the highly isotropic relation between a galaxy's redshift and its brightness (and therefore roughly, its distance) and its redshift, shows that the Universe is expanding, and
4. that the abundance of primordial elements (the amount of H, He, and Li in the Universe) can be calculated from the model to match observations.

The trouble is, there is now amassing evidence that each of these assumptions is either false, or only true-ish. Recent data can only be accommodated by adjusting an increasing number of free parameters in the model, making it increasingly unwieldy and less and less "elegant" as time goes on. As a consequence of this fudge-factoring, over the last 50 years or so an increasing number of artifacts have been postulated in order to paper over the numbers required to make the model work. These things, in rough order, are:

1. black holes,
2. dark matter,
3. "Cosmic Inflation", and
4. dark energy.

Many of these recent observations and experimental results, when NOT crammed into a failing prevailing model, and considered in isolation from any existing model, point to a potentially very different concept of the Universe: that it may very well turn out to be infinite, eternal, static (non-expanding), fractal, and quite possibly self-renewing. This essay will be an attempt to pull many of these disparate streams of observations, data, and discussion from many places and present a coherent argument for why I believe this to be so.

General Relativity

The current model is based on a particular mathematical solution (called the Friedman-Lemaître-Robertson-Walker metric, or FLRW for short) of Einstein's field equations in his theory of General Relativity. General Relativity describes the Universe in terms of masses interacting with and distorting spacetime, a four dimensional mathematical space (a Riemannian manifold) which has the three dimensions of normal "Euclidean" space, plus one of time. One of the results of considering the Universe in this way is that gravity becomes no more than the linear trajectories of the moving masses in this four dimensional space, rather than a separate, arbitrary force that needs to be separately considered.

This model has a parameter Ω representing average density - assuming the matter distribution of the Universe is homogeneous - that determines the overall curvature of spacetime. If the parameter is exactly one, then spacetime is "flat", equivalent to normal Euclidean space. If not, then spacetime is curved, leading to expansion or contraction, either bounded or unbounded depending on whether Ω is smaller or greater than one. This model was formulated in the 1920s, so when Edwin Hubble discovered his redshift relation a few years later, it was heralded as proof of an expanding spacetime, and an affirmation of the FLRW model.

TODO

Given the observed expansion rate, the observed matter distribution is far from sufficient to produce a required Ω value close to one; matter alone only adds up to about 0.04 which doesn't fit. Scientists then postulated dark matter to make up the difference, even though they still to this day do not know what it is. In the 1990s, observations of supernovæ purportedly showed that the rate of expansion has been slowly increasing over time, which requires a dark energy field to make things fit. So now we have Ω consisting of 4% matter, 23% dark matter, and 73% dark energy. All attempts so far to directly measure or quantify either dark matter or dark energy have failed. Cosmic inflation was thrown in to

All that is pointless anyway since we now know (from recent SDSS, Hubble, and later galaxy survey data) that matter is distributed fractally with dimension D=2 even at the largest observable scale, so the assumption that matter is distributed homogeneously is false, which means Ω is meaningless, which invalidates modelling the Universe with a FLRW metric.

Curiously, by definition this fractal distribution of matter has an average density that tends to zero over ever increasing scales, rendering Ω even more pointless as a meaningful measurement.