Modern cosmology has a disturbing number of free parameters, and is based on only a small number of observations. An example of where this leads is the increasingly untenable idea that dark matter is responsible for most of the gravitational interaction in the universe. Dark matter is a conjecture, in order to bridge a yawning gap between what theorists predict, and astronomers observe. Most articles about cosmology in the popular and science press routinely express some or all of the following things:
- An increasing frustration in the field with negative results, as physicists flail from one hypothesis or experiment to the next, burning increasingly large telephone numbers of money on ever more preposterously complex instruments, satellites and colliders, in order to find something that can fit the bill as dark matter.
- Surprise at the newest results from experiments, or telescopic or other instrumental observations, that show things that the mainstream theory didn't predict, or that even directly contradict predictions. Good examples abound: null results from LHC and the Planck satellite, neutrino masses and flavours, temperatures of "gas clouds" or interstellar "winds", unexpected X-ray emissions from just about anything Chandra is pointed at, unexpectedly high strengths of magnetic fields, poles in the CMBR, "abnormal" lithium abundances, distant galaxy dust lanes and metallicity, and so on.
Instead of starting from scratch, or questioning assumptions, or searching for alternative models that might better fit the available observations (or at least fit to the same degree with fewer discrepancies), the field stubbornly sticks to the standard cold dark matter model, and either throws more parameters at it until it is floppy enough to wrap around whatever new contradictory observation has arisen, or invents a new fairy story to fill in the gaps, with a view to figuring out the nature of the fairies later (which in theory may end up as the same thing). Good examples of these fairies are dark energy, which was proposed to explain an observed feature of supernovæ light curves, and inflation, the idea that the universe expanded faster than the speed of light during the first moments of the big bang, in order to explain the contradiction between the extreme homogeneity of the CMBR and the observed non-homogeneity of what is referred to as "large scale structure" (roughly, the distribution, clustering, and cluster-clustering of galaxies).
Modified Gravity Theory (MOG)
John Moffat (of University of Toronto) proposes the Gravitational constant G is actually a new tensor varying with spacetime such that G/c is constant (Modified Gravity Theory). No dark matter or dark energy. 
Expansion as illusion
There are many interesting alternative explanations of the observed Hubble relation of H₀ ≈ 70 km s⁻¹ Mpc⁻¹. The question is whether they raise more problems than they solve.
Tired light hypothesis
The hypothesis that light is red-shifted as it loses energy to the cosmos travelling across vast distances, through some unknown mechanism that does not result in photon scatter. One potential mechanism is the Wolf Effect, where diffuse plasmas can produce a redshift in transmitted light.
Using the antisymmetric temporal part of the Ricci tensor to replace the symmetric g tensor in General Relativity, it is possible to derive H₀ = c/R as a general time dilation of approximately 70 km s⁻¹ Mpc⁻¹, where R is the Einstein radius of the Universe (approx. 13 Gly). This would mean that the observed Hubble redshift relation results from time dilation across cosmological distances, rather than the relativistic motion of galaxies in an expanding spacetime.
Horizon problem and Olber's Paradox
If light is indeed red-shifted over vast distances, then an infinite static Universe would not be ruled out by Olber's Paradox since sufficiently distant radiation would drop out of detectable range, producing an effective observability horizon.
Surface brightness anomaly
Standard Big Bang cosmology predicts surface brightness (magnitude per unit area) decreases as (z+1)⁻⁴ yet observations show the surface brightness of galaxies up to z=6 are constant, as expected in normal non-expanding space. Explaining this as galactic evolution results in further difficulties.
Cosmic Microwave Background (CMB)
A history of CMB predictions, unexpected results, adding more free parameters, rinse and repeat.
The cosmic rays are too energetic
There is a theoretical upper limit to the energy of cosmic ray particles of about 5 × 10⁵ TeV (the Greisen-Zatsepin-Kuzmin limit or "GZK" limit) due to the interaction with the Cosmic Microwave Background, yet we occasionally observe particles (dubbed "Oh My God Particles") with energies an order of magnitude higher. We don't currently have a cosmological mechanism for generating these energies, but a local plasma undergoing a Z-pinch, e.g. a planetary nebula or galactic nucleus, can easily generate them.
Computer and laboratory simulations show that at least the ISM (if not the stars themselves) could be rotating as a plasma filament pair constrained by MHD, producing the observed flat rotation profile. These simulations also produce a time progression through the observed galactic spiral and barred spiral morphologies, and may also explain the observed independence of the motions of the stars from that of the spiral arms, if only someone would run the simulations again. However this substitutes "we need dark matter to make it work" with "where does the colossal current driving the filaments come from?" but at least we don't have to go around making stuff up.
Halton Arp, famous for his 1966 Catalog of Peculiar Galaxies. Anomalous redshifts of quasars, and their association with the minor axis of foreground galaxies (e.g. Arp 92 / NGC 7603). Too frequent to be chance associations, too large an area to be lensing (and too frequent).
Fractal large scale structure
The colour-magnitude diagram is the galactic equivalent of the HR diagram for stars. Luciano Pietronero demonstrates a fractal galaxy and void distribution in large datasets. This is important, because the "average density" of a fractal distribution tends to zero, in the same way that the length of a fractal coastline tends to infinity. A near-zero density for the Ω₀ parameter is in fact what we observe; near-zero at least in relation to the critical density value Ω₀ = 1, which is required for any exploding and expanding spacetime models to make any sense. Because of this, we simply presume that over 96 percent of the Universe is somehow hiding itself in some inconveniently undetectable way in dark matter, and now dark energy too, even though we have absolutely no direct observational evidence for it whatsoever.
Craziness? Okay try these on for size...
Electric stellar models
Electric Universe folks (crazy warning!) believe stars are composed mostly of molten iron and are powered like an inside-out electric arc furnace. There is no requirement for "magnetic reconnection" (which is a misunderstanding of fields anyway) to explain the massive temperature inversion from the 6000°K surface to the 2,000,000°K corona, and it can explain low neutrino flux without postulating neutrino flavour mutations because the observed fusion occurs in Z-pinches in the corona, explaining the temperature inversion. No strange convection columns or lengthy radiative transfer are required. Of course, this raises other problems instead: where is the vast electric current coming from? How is the star maintaining itself as a colossal anode for billions of years without going dark? There's only so much H⁺ it can produce. Why is the average density of the sun still only ~1400 kg/m³ (barely much more than water) and how is it resisting gravitational collapse into something much more dense - especially if it is supposed to be made of Fe + Ni instead of H + He? And so on.
No no - it's the neutron reactions
Enter Oliver Manuel, famous for his meteorite isotope work which contributed to our current theories of solar system evolution. Extrapolating from these theories, he now believes stellar cores are collapsed supernova remnant neutron bodies, emitting H⁺ from n-n interactions:
- "Thus solar luminosity, solar neutrinos and solar-wind hydrogen coming from the surface of an iron-rich object that formed on a collapsed SN remnant are fingerprints of energetic neutrons in the solar core. These generate luminosity, neutrinos, and an outflow of 3 x 10⁴³ H⁺ per year in the solar wind"
The implications of these ideas are staggering - iron stars have probably been around for a long time, and an external arc-powered star could "burn" for trillions of years.
Warning: may contain nuts
Sadly, some proponents of these more maverick models are also fans of Velikovsky, or believe aliens influenced ancient societies, or that lightning carved out the Grand Canyon, and other such cobblers, so it's very tempting to dismiss things without evaluating them properly. However, some at least have enough sense of humour to talk about "Fairie Dust" (Fabricated Ad-hoc Inventions Repeatedly Invoked in Efforts to Defend Untenable Scientific Theories).
- Disney, M. J. "Modern Cosmology: Science or Folktale?", Am. Sci. 95:5 p383, September 2007.
- Silk, J. "Will we ever know what dark matter is?", Cosmos on Nautilus, February 2017. A fairly typical article, by an Oxford cosmologist.
- A graph of the brightness of a supernova over time will show a characteristic decay curve. There is an observed change in the rate of this decay with distance, for a particular sub-group of supernovæ known as Type 1A, which are assumed to decay at a standardised rate proportional to their brightness.
- Moffat, J. W. "Reinventing Gravity". 288p hardcover, 24cm. Smithsonian, 2008.
- Wolf, E. "Non-cosmological redshifts of spectral lines", Nature 326 p363-365, March 1987.
- Jastrzebski, W. J. "Gravitation Demystified" (unpublished thesis in progress). RationalWiki, 2011.
- Lerner, E. J., Falomo, R., Scarpa, R. "UV surface brightness of galaxies from the local universe to z ~5", Int. J. Mod. Phys. D, 23:6, 1450058, May 2014. DOI 10.1142/S0218271814500588.
- Lerner, E. J. "Evidence for a Non-Expanding Universe: Surface Brightness Data From HUDF", AIP Conf. Proc. 822 p60-74, March 2006.
- Lerner, E. J. "Plasma Model of the Microwave Background", Laser and Particle Beams 6 p456-469, 1988.
- Lerner, E. J. "Radio Absorption by the Intergalactic Medium,", ApJ 361 p63-68, Septemper 1990.
- Bostick, W. H., "Experimental Study of Plasmoids", Electromagnetic Phenomena in Cosmical Physics, Proceedings from IAU Symposium no. 6, ed. Lehnert, B. p87. Cambridge University Press, 1958.
- Peratt, A. L.; Green, J. C., "On the evolution of interacting, magnetized, galactic plasmas". Astrophysics and Space Science 91:1 p19-33, March 1983.
- Pietronero, L.; Coleman, P. H. "The fractal structure of the universe", Physics Reports 213:6 p311-389, May 1992.
- Manuel, O. List of papers.
- Scott, D. E. "NASA pseudo-skeptic receives rebuttal from Electric Universe theorist", The Thunderbolts Project, 21 March 2009.
"The discovery of truth is prevented more effectively, not by the false appearance things present and which mislead into error, not directly by weakness of the reasoning powers, but by preconceived opinion." - Schopenhauer, Counsels and Maxims, Vol. II.