Cosmology, by definition, claims to be the science of our universe, i.e. of everything that exists (in more recent times it has even invented the 'idea' of parallel universes in order to accommodate things that do not exist).
The ambition to find the ultimate reason for the existence of everything may be acceptable as a (pseudo-) religious quest but hardly as an objective and rational scientific endeavour. It is obvious that the assumption of a 'creation' is logically inconsistent with the scientific principle of cause and effect. Any valid scientific approach is therefore necessarily tied to the infinite dimensions of space and time as the forms of existence (the argument of cosmologists that time and space came only into existence at the 'time' of the big bang is a logical contradiction in itself and therefore scientifically nonsense).
What has led cosmologists to abandon logic and establish a pseudo-scientific system that tries to explain the creation and ultimate fate of everything ? At least with regard to modern times, the reason has to be seen in the discovery of the 'global' redshift of galaxies (Hubble Law), which, as interpreted through the Doppler effect, led to the conclusion that all galaxies are receding from each other. Now, in a homogeneous and infinite universe this is not possible as it would mean that the average mass density would permanently decrease, which would violate the continuity equation for mass conservation (in other words, mass conservation demands that the mass density has to increase elsewhere if it decreases in a given region of space; obviously this rules out an overall decrease of the mass density (see the page The Expansion of the Universe Debunked
for more)). This on its own should already prove the physical impossibility of the expansion idea. However, in a kind of inversion of logical and physical principles, cosmologists decided then to tamper with the forms of existence and make space itself an object in some imaginary hyperspace. Yet even with this unphysical 'model', there remains the paradoxical consequence that not only the distances between galaxies but also the size of the latter should increase. Even atoms should become larger, altering therefore the fundamental frequencies for radiative transitions and resulting in an apparent blueshift for distant (young) galaxies (to evade this argument, cosmologists argue that physical systems held together by forces are exempt from the Hubble expansion, but this should then actually mean that the space in our solar system is unexpanded, and since light should adapt to the local scale of space, we should not see galaxies redshifted at all (which obviously contradicts observations)).
It is obvious that space (as well as time) can not be a subject of scientific investigation as we ourselves are objects within them.
The observed redshift of galaxies is therefore not a consequence of space expansion but only of (intergalactic) distance and one should look for a physical effect that delivers this redshift rather than try to involve 'known' physics by bending the rules of logic and common sense. A good candidate for the actual cause of the redshift is the intergalactic plasma electric field (see the page Plasma Theory of Hubble Redshift of Galaxies
on my site plasmaphysics.org.uk; regarding the argument by Big-Bang cosmologists that other than recessional redshifts would not yield the observed time dilation of supernova lightcurves, see the page Galactic Redshifts and Supernova Lightcurves
However, cosmologists can be accused of not only lacking a grasp of conceptual principles, but also of experimental expertise, as demonstrated by a crucial flaw in the WMAP
The concept of a 'curved space', which is essential for present cosmological models, is logically flawed because it assumes that the distance between two points in a given (curved) metric is the shortest possible distance, which however is only the case for the Euclidean metric (as the shortest distance between two points is by definition a straight line). Mathematicians frequently try for instance to illustrate the properties of 'curved space' through the example of a spherical (or otherwise curved) surface and the associated geometrical relationships. However, a surface is only a mathematical abstraction within the actual (3-dimensional) space and one can in fact connect any two points on the surface of a physical object through a straight line by drilling through it.
Strictly speaking, one can not assign any properties at all to space (or time) as these are the outer forms of existence and it makes as much sense to speak of a 'curved space' as of a 'blue space'. Any such properties must be restricted to objects existing within
space and time.
The concept of gravity being due to a space curvature, as promoted by General Relativity, is therefore also inconsistent and should be replaced by appropriate physical theories describing the trajectories of particles and/or light near these objects (see the Relativity
page for more).
One should also note here the inconsistency that cosmologists are making when assuming a resultant gravitational force in their models despite adhering to the cosmological principle of homogeneity and isotropy (which should logically imply a zero gravity force everywhere throughout the universe as equal and opposite forces cancel). This obviously completely invalidates their conclusion regarding the existence of Dark Matter
and Dark Energy.
But as indicated above, the primary mistake is of course to assume an expanding universe in the first place.