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Unsolved problems in the Big Bang model
The are few unsolved issues in the standard Big Bang model. These are as follows:
1. Horizon problem: There are portions of the universe that are visible to us but invisible to each other. Horizon problem points out that different region of the universe have not yet contacted each other due to the great distances between them, but nevertheless they have the same temperatures and other physical properties. We know that CMBR is found to be homogeneous everywhere. How it became possible? The observed isotropy of the CMB is the problem in this regard. Because we believe that information cannot travel faster than light. The resolution of this apparent inconsistency is offered by inflationary theory in which a homogeneous and isotropic scalar energy field dominates the universe at some very early period. According to Heisenberg, during the inflationary phase, there was a ‘Quantum thermal fluctuations’ which would be magnified to cosmic scale. These fluctuations serves as the seeds of all current structure in the universe. Inflation predicts that the primordial fluctuations are nearly scale invariant and Gaussian, which has been accurately confirmed by the measurement of the CMBR.
The instant before inflation began, universe was only about 
2. Flatness problem: According to Einstein field equations of general relativity, the structure of space-time is affected by the presence of matter and energy on small scales, space appears flat – as does the surface of the Earth if one looks at a small area. On large scale, space is bent by the gravitational effect of matter. The amount of bending (or curvature) of the universe depends on the density or matter/energy present. According to cosmology (Friedman – Lemaitre – Robotson – Waker metric), the universe may have positive, negative or zero spatial curvature depending on its total energy density (k).
Curvature is negative if k<0 (hyperbolic)
Curvature is positive if k>0 (spherical)
Curvature is flat if k=0 (flat)
Total energy density is a fine tuned parameter between the density of matter and energy in the universe. The values of total energy density departs rapidly from the critical value over cosmic time.
Now, the question is, during Big Bang nucleo-synthesis, what was the values of this parameter? Positive or negative or zero? How it was so fine tuned? We know that the reality that our universe is approximately flat. Thus, the value must be extremely close to ‘One’ (in 1 / 64 th) i.e. 
There is no known reason for the density of the universe to be so close to the critical density, this appears to be an unacceptably strange coincidence in the view of most astronomers.
Many attempts have been made to explain the flatness problem. Modern theory includes the idea of inflation which predicts the observed flatness of the universe. A brief period of extremely rapid expansion maintained the situation of flatness. Because, before the expansion (i.e. inflation) all matter and energy were intimately connected. At that time, the density is very close to (fine tuned) the critical density of the universe.
3. Magnetic monopole problem: Monopole is a hypothetical particle in physics that is a magnet with only one pole and it will have a net magnetic charge. In the year 1931, Dirac proposed quantum theory of magnetic charge. In his theory, he showed that the existence of monopole was consistent with Maxwell equations only if electric charges are quantized, which is experimentally observed. Since then, several systematic monopole searches have been performed. Now, we know that the monopole detection problem is an open problem in experimental physics.
The grand unification theory (GUT) and superstring theory (both theories successfully combine strong and electro-weak force) predicts the existence of magnetic monopole. According to GUT, the topological defects in space is termed as magnetic monopole. These defects were produced efficiently in the hot early universe, resulting in a density much higher than observed. No monopole is observed till date. It is believed that the inflation removed all topological defects from the observable universe. Thus, inflation drives the geometry to flatness, inflation maintains isotropy and inflation removes all point defects.
4. Baryon asymmetry: As we discussed in the Big Bang theory that an unknown process called Baryogenesis created the asymmetry. For baryogenesis to occur, Sakharov conditions must be satisfied. These require that Baryon number is not conserved, that c and cp- symmetry are violated and that the universe depart from thermodynamic equilibrium. All these conditions occur in the standard model, but the effect is not strong enough to explain the present baryon asymmetry. Baryon asymmetry lead the dominance of matter over antimatter.
5. Dark matter: Numerous observations (anisotropies in the CMB, galaxy cluster velocity dispersions, large scale structure distributions, gravitational lensing studies and x-ray measurement of galaxy clusters) have indicated the existence of dark matter. The rotation curve of galaxies hint that the dark matter particle exists in the halo of the galaxies. So, the dark matter is the reality. However, dark matter particles have not been observed in laboratories. Many candidates for dark matter have been proposed and several projects are underway. The standard big bang model have not explained the existence of dark matter particles.
6. Dark matter: Measurement of red shift magnitude relation for supernova indicate that the expansion of the universe has been accelerating since the universe was about half its present age. To explain this acceleration, general relativity requires ‘negative pressure’, called Dark (or Vacuum) energy. Negative pressure is a property of vacuum energy, but the exact nature of dark matter remains one of the great mystries of the Big Bang. Possible candidates include ‘Cosmological constant’ and ‘quintessence’ (hypothetical form of dark energy postulated as an explanation of observations of accelerating universe and is a scalar field). Results from the WMAP (2008) indicate that the universe today is 73% dark energy, 23% dark matter and 4.6% regular matter and less than 1% neutrinos.
i'll prolly get slapped for this, but... space is flat?