There are two main areas under consideration :
(1) The Hot Big Bang Theory of the origin of the Universe;
(2) The so called “Missing Mass” or “Dark Matter”.
(1) The Hot Big Bang Theory of the origin of the Universe
Although Hot Big Bang Theory is well entrenched among “establishment” cosmologists, there is a growing body of astrophysicists who are finding observations contrary to that theory. Specifically this website reinforces this criticism by showing that the Hot Big Bang Theory violates the Laws of Thermodynamics.
The arguments here are based on experiments and rigorous calculations using well established thermodynamic experimental data. We are not dealing with mere “handwaving” arguments which are so often used by cosmologists.
(2) The “Missing Mass” or “Dark Matter”.
The second subject is a revealing answer to the conundrum of the “missing mass” which has been puzzling cosmologists for 50 years!
A careful study of the state of the Sun shows that surprisingly it must have a positive electrical charge. It follows that all hot stars in the galaxy hold onto a positive charge. The observational evidence indicates that this has an effect on their rotational velocities round the galaxy. This theory is developed to the point where the socalled “missing mass” is explained, which is also called “dark matter”.
This is not an unlikely speculation. Extensive astronomical observations support the new theory. In particular the theory predicts the characteristics of the orbits of lone brown dwarfs which are different from the orbits of other stars. A theory which has a quality of prediction has much to commend it.
Part 1; The Hot Big Bang Theory postulates that the early Universe was at a very high temperature and that the expansion of the Universe automatically brought about cooling.
The property of temperature and the action of expansion of fluids are in the realm of Thermodynamics which is an experimental science.
So what does Thermodynamics have to say about the free expansion of gases ? The answer is that the free expansion of an ideal gas is a constant temperature process. The belief by cosmologists that an expanding Universe would automatically cool down is mistaken. Click here for Experimental Evidence
A rigorous thermodynamic study of the Hot Big Bang Theory reveals many other fallacies.
For example, the expositions by Weinberg and by Alpher and Herman and others show a straight line relationship between fall in temperature and the expanding "scale factor". But the supposed cooling of primeval ionized hydrogen would have gone through association to atoms and then further association to hydrogen molecules.
These changes bring about severe kinks in these curves when these parameters are drawn out graphically; the same goes for graphs of temperature versus internal energy. A thorough analysis of the Thermodynamics shows conclusively that the Hot Big Bang Theory violates both the First and the Second Laws of Thermodynamics. This is all described with diagrams and detailed calculations in my book.
The reader should note that cosmologists have never done these calculations; they have never applied the correct thermodynamic properties of hydrogen. These properties are laid out in a TemperatureEntropy Diagram for hydrogen, which has never been available before now. The important point to understand is that a TemperatureEntropy Diagram contains a wealth of information which has a number of uses.
Some of the results of my calculations are shown in the diagram below.
The abscissa is the cube root of the volume of one kgmole of hydrogen; in effect this is a measure of the expansion factor of the Universe, i.e. the supposed expansion of the Universe follows the curves from left to right.
The ordinate is the energy in Joules associated with one kgmole of hydrogen.
Both scales are log10. The kinks in the curves when the internal energy of hydrogen is 3.6 x 10^{9 }Joule per kgmole come about because of the change in the properties of hydrogen as ions associate to atoms. It is evident from these graphs that the Hot Big Bang Theory does not conform to the Law of Conservation of Energy  neither internal energy nor radiation energy. This is one of a number of reasons which prove that the Hot Big Bang Theory is thermodynamically unsound.
A Discussion on the validity of Thermodynamics Applied to Cosmology and a commentary on the Status of Temperature in Science.
My book, “The Big Bang Exploded! Cosmology Corrected, A Commentary With Thermodynamics” has been published for over 8 years. No one has yet contacted me to point out any errors; in fact all my correspondents agree that my Thermodynamics is correct. However, one astronomer suggested that perhaps conventional Thermodynamics did not apply to the Cosmology of an expanding Universe; he believes that the Hot Big Bang Theory is still valid even although it violates the Laws of Thermodynamics because standard Thermodynamics is not relevant to Cosmology.
There are a number of answers to this contention.
First, many cosmologists state explicitly in their books that Cosmology is consistent with conventional Thermodynamics (e.g. P.C.W. Davies, Misner, Thorne and Wheeler).
Secondly, many cosmologists use thermodynamic equations to justify the Hot Big Bang Theory; they use these equations wrongly, but the fact that they use them at all indicates that they believe Thermodynamics to be valid.
The third reason is more profound and it gets to the real heart of the subject. We start by asking the question “What is temperature?” Temperature is a thermodynamic property which is measured with a thermometer, just as length is measured by measuring rods and time is measured by a clock.
But strictly speaking, temperature is measured by a Carnot heat cycle, and indeed, in Low Temperature Physics that is what we do, we put a sample of a paramagnetic salt through a Carnot cycle. I mention this in passing to emphasize that this reasoning is based on good practical Science.
It can be proved by means of the Carnot Theorem, that temperatures measured by a Carnot cycle are identical with temperatures measured with the ideal gas thermometer,  and if that were not so, a substantial proportion of Physics and Chemistry would be invalid!
But the Carnot cycle and the Carnot Theorem depend on the First and Second Laws of Thermodynamics for their validity. Therefore cosmologists cannot make statements about temperature like “A few seconds after the Hot Big Bang the temperature of the Universe was 10 billion degrees Kelvin” unless they accede to the Laws of Thermodynamics.
I put it to my critics that this argument is unassailable, and as I wrote above, it is based on good sound Science. Therefore cosmologists cannot wriggle out of their fallacious notions by pleading that Thermodynamics is not relevant to their theories.
The Cosmic Microwave Background Radiation does NOT prove that the Hot Big Bang Theory is correct.
It has frequently been asserted that the discovery of the cosmic background radiation by Penzias and Wilson is proof of the validity of the Hot Big Bang Theory of the origin of the Universe. In reality this is not the case because the expansion of the Universe at the time of the supposed “Fireball” would not produce the perfect blackbody radiation which is actually observed.
To establish the case,  one way or the other,  requires a detailed study of the thermodynamic properties of the plasma when it supposedly passed through a state of
“decoupling” and the matter went from being opaque to being transparent. To quote Mather (1986)
“The electrons of the primeval plasma attach themselves permanently to atomic nuclei and form complete atoms. After this event the electrons could no longer collide frequently with photons – the Universe became abruptly transparent to radiation”.
The reasoning presented here analyses the thermodynamic state of matter (according to the theory) when the degree of ionization was a small fraction. For the purposes of simplicity, it is assumed that all the matter is hydrogen.
Thermodynamics.
We consider three temperatures, 3468, 3300 and 2850 K, which span the period of
“decoupling” of the supposed early Universe.
These 3 states all have the same entropy, 929 kJ kgmole^{1} K^{1}; this conforms to the statements by S. Weinberg, P.C.W. Davies, M. Longair and other cosmologists that the expansion of the Universe is isentropic.
The thermodynamic states are also displayed graphically in the diagram; this is a section of a much larger TemperatureEntropy Diagram for hydrogen which is to be found in my book (Bligh, 2000) which gives details of how these thermodynamic data are calculated and which explains why TemperatureEntropy Diagrams are powerful tools for carrying out thermodynamic analyses.
The diagram shows three isobars which are relevant to the epoch of the “decoupling”. An important feature is that these curves contain inflexions because the association of ions into atoms results in hydrogen not obeying the ideal gas laws. One curve for constant volume is included in order to show that volume (or density) also goes through an inflexion at conditions of association of ions.
All data are consistent for one kgmole of hydrogen,
H_{2}⇔2H ⇔ 2H+ + 2e
Cosmologists give a range of estimates for the density of the present Universe (Peebles 1968) but a middle value is
2 x 10^{27} g/cm^{3} = 2 x 10^{27 } kg/m^{3} ;
this is equivalent to a volume of 10^{27} m^{3} per kgmole. We use a model in which we consider the Universe to be a matrix of expanding cubes, in which case a notional kgmole of hydrogen is now in a cube, side 10^{9}m.
The side of a cube containing one kgmole is a measure of the “scaling factor” of the Universe.
Therefore case [1] has expanded by 10^{9}/(5.84 x 10^{5} ) = 1712.
We apply Wien’s Law, this expansion shifts the peak of the wavelength of the “blackbody spectrum” by a factor of 1712 and this gives an apparent temperature of the present blackbody spectrum as 3468/1712 = 2.02 K.
In case [2] expansion is 10^{9}/(8.24 x 10^{5} ) = 1214.
Again applying Wien’s Law, we arrive at a present blackbody spectrum of 3300/1214 =2.72K.
In case [3] expansion is 10^{9}/(1.156 x 10^{6}) = 865, which gives a present blackbody radiation equivalent to 2850/865 = 3.29 K.
In the TABLE below, the thermodynamic data for hydrogen apply to three states during the period of “decoupling” of the supposed early Universe. These three states all have the same entropy, 929 kJ kgmole^{1 }K^{1 };this conforms to the statements by cosmologists that the expansion of the Universe is isentropic; the expansion through these three states is also displayed on the TemperatureEntropy Diagram.
Note that case [2] was specially selected to give the observed value of the cosmic microwave background. Therefore according to “received wisdom” the “fireball” which generated the microwave background radiation must have had thermodynamic properties very close to state [2].
Discussion.
Now in the theory it is reasonable to assume that the operation of “decoupling” took place over a period of time (Lepp and Stancil give a time in the order of 100,000 years) that is to say, as the primeval Universe went from being opaque to being transparent there was a range of conditions of being partially transparent.
States [1] and [3] were chosen arbitrarily as being typical borderline cases, which would also generate some of the microwave background, but these would have the appearance of a blackbody curve for 2.02 K and 3.29 K respectively. Therefore we should expect the microwave background to be NOT a perfect blackbody curve for 2.7 K, but a SMEARED or COMPOSITE curve.
The measured results from the COBE satellite (Mather et al. and Fixsel et al. 1994) give a microwave background for a perfect 2.7 K curve; this perfect blackbody curve is not what we should expect from the thermodynamic analysis. Therefore these COBE results  far from confirming the Hot Big Bang Theory,  provide strong evidence AGAINST the Hot Big Bang Theory.
There is the counterargument that at the time that the radiation was generated the temperature was inversely proportional to the scale factor of the Universe. Therefore there is not a smearing of the blackbody spectrum because with the subsequent expansion of the Universe the scaling exactly compensates for the radiation characteristic of the previously decoupled photons. However this argument is not valid because during the proposed epoch of decoupling the matter in the Universe does not obey the ideal gas laws as is shown by the inflexions of the curves in the TemperatureEntropy Diagram already described, i.e. the premise that the equilibrium temperature of radiation is inversely proportional to the scale factor is not true.
In a nutshell; it is necessary to do rigorous thermodynamic calculations as presented in the table in order to obtain the correct results. It is impossible to do these calculations without a TemperatureEntropy Diagram or its equivalent.
These calculations show that at this hypothetical epoch when nearly all electrons became associated, the radiation would not lead to the present background radiation which has a perfect blackbody spectrum.
References;
Bligh, B.R., The Big Bang Exploded ! Cosmology Corrected, A Commentary With Thermodynamics (published July 2000), this includes extensive thermodynamic calculations for hydrogen and a TemperatureEntropy Diagram.
IBSN 0953877604
Davies, P.C.W., The Physics of Time Asymmetry p. 89, (published by Surrey University Press, 1974).
Fixsen, D.J. et al. “Cosmic Microwave Background Dipole Spectrum Measured by the COBE Firas Instrument”, The Astrophysical Journal, Vol. 420, page 445, Jan. 1994).
Lepp, S. and Stancil, P.C. "Molecules in the Early Universe and Primordial Structure Formation" from The Molecular Astrophysics of Stars and Galaxies 1998, edited by Hartquist, T.W. and Williams, D.A.
Longair, M., letter to me, Bernard R. Bligh.
Mather, J.C. “A Look at the Primeval Explosion”, New Scientist, 16 January 1986.
Mather, J.C. et al. “Measurement of the Cosmic Microwave Background Spectrum by the COBE Firas Instrument”, The Astrophysical Journal, Vol. 420, page 439, Jan. 1994).
Mitchell, W.C. The Cult of the Big Bang, Was There A Bang?, (Cosmic Sense Books) 1994, p. 102. ISBN 0964318806.
Peebles, P.J.E. “Recombination of the Primeval Plasma”, The Astrophysical Journal, Vol. 153, p. 1, July 1968.
Peebles, P.J.E. et al. “The Case for the Relativistic Hot Big Bang Cosmology” Nature, Vol. 352, 29 August 1991, p. 769.
Weinberg, S., Gravitation and Cosmology p. 536 (J. Wiley and Son, New York, 1972).
Weinberg, S., Cosmology (Oxford University Press, 2008).
