Abstract
Recent studies indicated that an anisotropic cosmic expansion may exist. In this paper, we use three data sets of type Ia supernovae (SNe Ia) to probe the isotropy of cosmic acceleration. For the Union2.1 data set, the direction and magnitude of the dipole are (l=309.3^{circ } {}^{+ 15.5^{circ }}_{-15.7^{circ }} , b = -8.9^{circ } {}^{ + 11.2^{circ }}_{-9.8^{circ }} ), and A=(1.46 pm 0.56) times 10^{-3} from dipole fitting method. The hemisphere comparison results are delta =0.20,l=352^{circ },b=-9^{circ }. For the Constitution data set, the results are (l=67.0^{circ }{}^{+ 66.5^{circ }}_{-66.2^{circ }}, b=-0.6^{circ }{}^{+ 25.2^{circ }}_{-26.3^{circ }}), and A=(4.4 pm 5.0) times 10^{-4} for dipole fitting and delta = 0.56,l=141^{circ },b=-11^{circ } for hemisphere comparison. For the JLA data set, no significant dipolar or quadrupolar deviation is found. We find previous works using (l, b, A) directly as fitting parameters may get improper results. We also explore the effects of anisotropic distributions of coordinates and redshifts on the results using Monte-Carlo simulations. We find that the anisotropic distribution of coordinates can cause dipole directions and make dipole magnitude larger. Anisotropic distribution of redshifts is found to have no significant effect on dipole fitting results.
Highlights
Type Ia supernovae (SNe Ia) are ideal standard candles [1]
We generate 2 × 106 effective samples for each data set for MCMC sampling
This is because that the best-fitting values represent the maximum point of probability density function (PDF), while the most probable values in presented figures are the maximum values of marginal PDF of l, b, A, respectively
Summary
Type Ia supernovae (SNe Ia) are ideal standard candles [1]. In 1998, the accelerating expansion of the Universe was discovered using the luminosity-redshift relation of SNe Ia [2,3]. The isotropy of the cosmic acceleration has been widely tested using SNe Ia. Generally, there are two different ways to study the possible anisotropy from SNe Ia. The first one is directly fitting the data to a specific anisotropic model (AM) [15,16,17]. The hemisphere comparison method divides samples into two hemispheres perpendicular to a polar axis, fits cosmological parameters using samples in each hemisphere independently and compares their differences. The dipole fitting (DF) method assumes a dipolar deviation on redshift-distance modulus relation, derives the dipole’s direction and magnitude using statistic approaches. We compare the DF fitting results of different SNe Ia samples and try to find the reason for the differences.
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