Detecting the cosmic acceleration with current data
  The deceleration parameter q as the diagnostic of the cosmological
accelerating expansion is investigated. By expanding the luminosity distance to
the fourth order of redshift and the so-called y-redshift in two redshift bins
and fitting the SNIa data (Union2), the marginalized likelihood distribution of
the current deceleration parameter shows that the cosmic acceleration is still
increasing, but there might be a tendency that the cosmic acceleration will
slow down in the near future. We also fit the Hubble evolution data together
with SNIa data by expanding the Hubble parameter to the third order, showing
that the present decelerating expansion is excluded within $2\sigma$ error.
Further exploration on this problem is also approached in a non-parametrization
method by directly reconstructing the deceleration parameter from the distance
modulus of SNIa, which depends neither on the validity of general relativity
nor on the content of the universe or any assumption regarding cosmological
parameters. More accurate observation datasets and more effective methods are
still in need to make a clear answer on whether the cosmic acceleration will
keep increasing or not.
