Hi, i'm wondering what the main theories for the state/structure of the universe are and what they consist of? Not the creation but the current state/structure of it.
The so-called Lambda-CDM (or LCDM or [itex]\Lambda[/itex]CDM) is the standard concordance model that best describes the evolution and current state of the universe. It is the standard hot big bang model that describes a universe expanding and cooling from an early hot and dense period, through the cold dark matter (CDM)-assisted formation of large scale structure, to the current epoch of dark energy-dominated expansion (the Lambda in LCDM). LCDM assumes a scale invariant spectrum of Gaussian, adiabatic density perturbations as the initial seeds of structure formation, which so far provides the best fit to data.
I think that perfect scale invariance of the spectrum is not what is observed and that the degree of deviation from scale invariance is very important. Am I correct in the assertion that if it were perfect scale invariance, then the density deviations over length scales typical of the whole observed last scattering surface would be much less than observed?
It is true that the Harrison-Zel'dovich (scale invariant) spectrum is claimed by WMAP7 to be ruled out at 3 sigma, favoring instead a power law spectrum with a spectral index, n, centered at around n=0.97. However, when model selection is taken into consideration, this conclusion no longer holds up to scrutiny. Model selection concerns itself with the question: suppose we have a base model, where n = 1 is set and not free to vary (the Harrison-Zel'dovich (HZ) model), and suppose we have a competing model where n is allowed to vary freely within some range. The second model has one more additional free parameter than the first, and will consequently provide a better fit to the data simply on account of this additional freedom. Model selection works to ensure that the addition of this free parameter is warranted by the data in the first place. So, it's not simply a matter of counting sigmas; one must also determine whether the data favors a more complex model. When this analysis is carried out, it is found that the evidence against the HZ spectrum is not substantial. See http://arxiv.org/abs/arXiv:0912.1614. The HZ spectrum can also be made to fit by considering more general reionization scenarios: http://arxiv.org/abs/arXiv:1003.4763