It's also a misconception about the big bang, which is hard to imagine intuitively since it's not like an explosion in a given space, i.e., something expanding in space. It's the very creation of space-time itself out of a singularity. With the general theory of relativity, which is a classical relativistic field theory of a massless spin-1/2-field which can be reinterpreted as the space-time pseudometric of a pseudo-Riemannian manifold which makes up the four-dimensional space-time.
On a long-range scale, this space-time is homogeneous and isotropic, i.e., there is no exceptional point (particularly not something that you'd call a center) and not exceptional direction in space. More precisely formulated one should say, you can define a frame of reference, with respect to which each observer at rest sees a homogeneous and isotropic space. Due to this large symmetry, the corresponding space-times are mathematically classified in three types: closed (spherical), flat, open (hyperbolical). The space-times are named after their discoverers as Friedmann-Lemaitre-Robertson-Walker solutions of Einstein's field equation. The only function left to be calculated after choosing a fundamental frame of reference is a scale factor, which is a function of time. The particular solution of this function depends on the matter content, where matter is everything except gravitation, including according to the standard cosmological model usual (baryonic) matter, electromagnetic radiation, neutrinos (making only about 5% of the total matter content), dark matter made up of yet to be discovered unknown particles (about 20%) and the greatest mystery of all physics, dark energy (cosmological constant, about 75% of the matter content).
We have two main sources of information about the scale factor from the redshift of distant supernovae, which can be used as standard candles, and the high-precision measurement of the fulcutations of the cosmic microwave background radiation (CMBR) through satellites like COBE and WMAP. Recently the most precise instrument of this kind has been launched, the satellite PLANCK.
The CMBR is the relic radiation from the time where neutral atoms have formed from the charged atomic nuclei (mostly hydrogen and helium) and electrons floating around in the universe. This has been possible after about 400000 years after the big bang when the universe had cooled down below the socalled Mott-transition temperature, where the state of matter makes a phase transition from a plasma to a gas of neutral atoms. The plasma had been nearly in thermal equilibrium and as long as the particles of such a medium are charged, also the electromagnetic radiation is scattered around and thus in equilibrium with the medium. After the formation of a neutral gas, the radiation decouples. This means the spectrum of the radiation stays an equilibrium (Planck spectrum) at all times but becomes red shifted through the expansion of the scale factor, i.e., it becomes cooler. At the moment the temperature is about 2.7K and thus the maximum of the spectrum sits in the microwave region. The precise measurements of WMAP has revealed that the temperature fluctuates only with \delta T/T \simeq 10^{-5}. This makes the CMBR the most precise Planck spectrum ever measured! Nevertheless these tiny fluctuations can tell us about the state of the universe at recombination, i.e., 400000 years after the big bang. Together with the red-shift observables from supernovae (among other observations through the Hubble Space Telescope) these fluctuations tell us that our universe is flat to a high accuracy and that the expansion of the scale factor accelerates. This is only possible due to the large amount of dark energy in the universe since all normal matter acts decelerating since for normal matter gravity is always attractive.
We have no explanation for the amount of dark matter measured. It's one of the greatest enigmas of contemporary physics. Maybe the answer to this question is related with the so far unsolved theoretical problem to find a consistent quantum-theoretical description of gravitation (and most likely of space-time iteself).
