What "observations" show the Earth at the center of the observable universe?
All observations show this, beginning with one going outside, looking up, and noticing that the heavens revolve above us, in a regular and repeating pattern.
This is consistent with us being motionless at the center of a revolving cosmos (firmament).
It is also consistent with an Earth which revolves once per day on its own axis.
It is the second proposition which involves the Copernican Principle (i.e., Earth is in no special location, generalized as the "cosmological principle"- that there
are no special locations or directions in the cosmos).
If the Copernican Principle is true, then we should expect nothing at all unusual or special about our local system's ecliptic.
If geocentrism is true, we should expect the whole Universe to be related in its largest scale structure to this system's ecliptic- indeed, it would *have to be*, were geocentrism true.
The most recent, advanced, largest-scale observations of the cosmos ever undertaken by humanity, show that geocentrism's prediction in this respect has been affirmed, and that the Copernican Principle is
false.
It is now established that the plane of the ecliptic is cosmological:
1. The dipole, quadrupole, octupole, and higher poles of the CMB are aligned with the ecliptic, forming a cosmological so-called "Axis of Evil"- see Copi, Huterer et al 2010:
http://arxiv.org/pdf/1004.5602v2.pdf
Relevant excerpt:
"The study of alignments in the low-l CMB has found a number of peculiarities. We have shown that the alignment of the quadrupole and octopole planes is inconsistent with Gaussian, statistically isotropic skies at least at the 99% confidence level. Further a number of (possibly related) alignments occur at 95% confidence levels or greater. Put together these provide a strong indication that the full sky CMB WMAP maps are inconsistent with the standard cosmological model at large angles. Even more peculiar is the alignment of the quadrupole and octopole with solar system features (the ecliptic plane and the dipole)."
2. The "Axis of Evil" has been independently shown to be aligned with a preferred axis of galaxy spin-rotation directionality ("handedness") (Longo, 2007 et sequelae):
http://arxiv.org/abs/astro-ph/0703325
Relevant excerpt:
"In this article I study the distribution of spiral galaxies in the Sloan Digital Sky Survey (SDSS) to investigate whether the universe has an overall handedness. A preference for spiral galaxies in one sector of the sky to be left-handed or right-handed spirals would indicate a preferred handedness. The SDSS data show a strong signal for such an asymmetry with a probability of occurring by chance ~3.0 x 10-4. The asymmetry axis is at (RA,Dec) ~(202d,25d) with an uncertainty ~15d. The axis appears to be correlated with that of the quadrupole and octopole moments in the WMAP microwave sky survey, an unlikely alignment that has been dubbed "the axis of evil". Our Galaxy is aligned with its spin axis within 8.4d of this spiral axis."
3. Longo has since expanded his survey to include 15,158 clearly rotating spiral galaxies, the farthest 1.2 billion light years away (New Scientist, Oct 2011):
http://www.andyross.net/spin.htm
Relevant excerpts:
"The universe might be spinning. Michael Longo at the University of Michigan in Ann Arbor thinks so. At the heart of the story is conservation of parity: the universe does not tell left from right.......
"Longo looked at the southern sky, which is not covered by the SDSS. Stretching off as far as the telescope could see, along the same axis in the southern sky, he saw an excess of right-handed spirals. It was the opposite view of the same effect.
Longo says that if the asymmetry is real, the universe has a net angular momentum and was born in a spin."
3. Edwin Hubble reported a periodic, concentric distribution of galaxy redshifts with Earth at the center ("Observational Approach to Cosmology", 1937).
Relevant excerpt:
"Thus the density of the nebulae distribution increases outwards, symmetrically in all directions, leaving the observer in a unique position. Such a favoured position, of course, is intolerable; moreover, it represents a discrepancy with the theory, because the theory postulates homogeneity. Therefore, in order to restore homogeneity, and to escape the horror of a unique position, the departures from uniformity, which are introduced by the recession factors, must be compensated by the second term representing effects of spatial curvature."
4. The "spatial curvature" mentioned above is, exactly, the Copernican universe, the Friedman "expanding balloon" universe of the modern cosmological consensus. No such preferred directionality can exist in an FLRW universe, which is "expanding at every point".
5. Therefore the universe is not Copernican, or FLRW.
6. This concentric, periodic (non-random) distribution of galaxy redshifts with Earth at the center has been shown to be cosmological. This observationally falsifies the space-time curvature prediction (requirement) of homogeneity in the FLRW "consensus" cosmology- see Hirano Phys Rev D Nov 2010, abstract at:
http://prd.aps.org/abstract/PRD/v82/i10/e103513
Relevant excerpt from full paper:
“A widespread idea in cosmology is that the universe is homogeneous and isotropic above a certain scale. This hypothesis, usually called the cosmological principle (e.g., [1]), is thought to be a generalization of the Copernican principle that “the Earth is not in a central, specially favored position”. The assumption is that any observer at any place at the same epoch would see essentially the same picture of the large scale distribution of galaxies in the universe.
"However, according to a Fourier analysis by Hartnett & Hirano [2], the galaxy number count N from redshift z data (N–z relation) indicates that galaxies have preferred periodic redshift spacings.........A natural interpretation is that concentric spherical shells of higher galaxy number densities surround us, with their individual centers situated at our location.”
7. There is additional evidence of a polarization of quasar photons along the same "Axis of Evil":
http://orbi.ulg.ac.be/bitstream/2268/81301/1/london_mar07.pdf
Relevant excerpt:
"• Evidence for large-scale angular correlations of quasar polarization vectors (in regions of ~ 1 Gpc size at z ~ 1)
• The mean polarization angle changes with redshift
• The effect is statistically significant (> 99.9%) in a sample of 355
quasars
• Instrumental and interstellar polarization cannot produce a redshift dependent effect
• The effect seems stronger along an axis close to the CMB dipole and the “axis of evil”
This is some of the observational evidence that Earth is at or near the center of the observable universe.