Can the initial singularity be detected by cosmological tests?

In this paper, we raised the question of whether initial cosmological singularity can be proven by cosmological tests. The classical general relativity theory predicts the existence of singularity in the past if only some energy conditions are satisfied. On the other hand, the latest quantum gravity applications to cosmology suggest the possibility of avoiding the singularity and replacing it with a bounce. Bounce is the moment in the evolution of the Universe when the Universe’s size is minimum. Therefore the existence of observationally detected bounce in the Universe’s past could indicate the validity of the loop quantum gravity hypothesis and nonexistence of initial singularity which is present in the classical $\Lambda \mathrm{CDM}$. We investigated the bouncing model described by the generalized Friedmann-Robertson-Walker equation in the context of the observations of the currently accelerating universe. The distant type Ia supernovae data are used to constrain the bouncing evolutional scenario where the square of the Hubble function $H^2$ is given by the formula $H^2=H_0^2[{\Omega }_{m,0}(1+z{)}^m-{\Omega }_{n,0}(1+z{)}^n]$, where ${\Omega }_{m,0},{\Omega }_{n,0}>0$ are density parameters and $n>m>0$. In this paper are shown that, on the basis of the SNIa data, standard bouncing models can be ruled out at the $4\sigma$ confidence level. After adding the cosmological constant to the standard bouncing model (the extended bouncing model), we obtained as the best fit that the parameter ${\Omega }_{n,0}$ is equal to zero which means that the SNIa data do not support the bouncing term in the model. The bouncing term is statistically insignificant on the present epoch. We also demonstrated that BBN offers the possibility of obtaining stringent constraints of the extra term ${\Omega }_{n,0}$. The other observational test methods like CMB and the age of oldest objects in the Universe are also used. We use as well the Akaike informative criterion to select a model which best fits data and we concluded that the bouncing term should be ruled out by Occam’s razor, which makes the big-bang scenario more favorable than the bouncing scenario.

Figure 1

The phase portrait and the diagram of the potential function for BM model (all cases from Table ). The minimum of the potential function corresponds to a center on the phase plane. The acceleration region is located on the right from the $a_{\min }$.

Figure 2

The phase portrait and the diagram of the potential function for the $\Lambda \mathrm{BCDM}$ model. The minimum (maximum) of the potential function corresponds to a center (saddle) on the phase plane. The system is structurally unstable because of the presence of a nonhyperbolic critical point (a center).

Figure 3

Residuals (in mag) between the Einstein-de Sitter model and the Einstein-de Sitter itself (zero line), the $\Lambda \mathrm{CDM}$ flat model (upper curve), the best-fitted BM model (upper-middle curve), and the best-fitted BCDM model with $m=3$ (lower-middle curve) (with assumed $\mathcal{M}=15.955$).

Figure 4

For the extended bouncing model with $\mathcal{M}=15.955$, there are shown the confidence levels on the plane $({\Omega }_{n,0},n)$ minimized over parameter ${\Omega }_{m,0}$.

Figure 5

Extended bouncing model with $\mathcal{M}=15.955$. The density distribution for ${\Omega }_{n,0}$. Confidence level $68.3\%$ and $95.4\%$ are also marked on the figure.

Figure 6

Extended bouncing model with $\mathcal{M}=15.955$. The density distribution for $n$. Confidence level $68.3\%$ and $95.4\%$ are also marked on the figure.

Figure 7

The age of the Universe on particular $z$ for three classes of models: $\Lambda \mathrm{CDM}$ (middle curve), bouncing model BM (upper curve), and bouncing model with dust matter BCDM (lower curve). We marked the age of 4 extragalactic objects by stars (Table ).