Cosmological solutions and observational constraints on five-dimensional braneworld cosmology with gravitating Nambu-Goto matching conditions

We investigate the cosmological implications of the recently constructed five-dimensional braneworld cosmology with gravitating Nambu-Goto matching conditions. Inserting both matter and radiation sectors, we extract analytical cosmological solutions. Additionally, we use observational data from Type Ia supernovae and baryon acoustic oscillations, along with requirements of big bang nucleosynthesis and cosmic microwave background radiation, in order to impose constraints on the parameters of the model. We find that the scenario at hand is in good agreement with observations, and thus a small departure from the standard Randall-Sundrum scenario is allowed. However, the concordance $\mathrm{\Lambda }\mathrm{CDM}$ cosmology is still favored comparing to both the standard braneworld model and the present scenario.

Figure 1

Two-dimensional likelihood contours in the (${\mathrm{\Omega }}_{m0},\tilde{V}$) plane for the $\epsilon =-1$ branch and fixed $\tilde{c}$ to its Randall-Sundrum value ($\tilde{c}=2\tilde{V}{\rho }_{r0}/{\rho }_{*}$) from the SnIa (red and pink) and $\mathrm{SnIa}+\mathrm{BAO}$ (blue and light blue) data combinations. The light regions (pink and light blue, respectively) correspond to the $2\sigma$ confidence level, while the darker regions (red and blue, respectively) correspond to the $1\sigma$ confidence level. Note that in this specific plot the $1\sigma$ bound of the SnIa (red) data combinations is inside the $2\sigma$ bound of the $\mathrm{SnIa}+\mathrm{BAO}$ (light blue) data combinations.

Figure 2

Two-dimensional likelihood contours in the (${\mathrm{\Omega }}_{m0},\tilde{V}$) and (${\mathrm{\Omega }}_{m0},{\log }_{10}\tilde{c}$) planes for the $\epsilon =-1$ branch from the SnIa (red and pink) and $\mathrm{SnIa}+\mathrm{BAO}$ (blue and light blue) data combinations. The light regions (pink and light blue, respectively) correspond to the $2\sigma$ confidence level, while the darker regions (red and blue, respectively) correspond to the $1\sigma$ confidence level.

Figure 3

Two-dimensional likelihood contours of the dimensionless quantity $M^6{G}_N/{\rho }_{c0}$ versus ${\mathrm{\Omega }}_{m0}$, where ${\rho }_{c0}$ is the current critical density, for the $\epsilon =-1$ branch from the $\mathrm{SnIa}+\mathrm{BAO}$ data combinations. The lighter region corresponds to the $2\sigma$ confidence level, while the darker region corresponds to the $1\sigma$ confidence level.

Figure 4

Two-dimensional likelihood contours of $H_0{t}_0$ versus ${\mathrm{\Omega }}_{m0}$ for the $\epsilon =-1$ branch from the $\mathrm{SnIa}+\mathrm{BAO}$ data combinations. The lighter region corresponds to the $2\sigma$ confidence level, while the darker region corresponds to the $1\sigma$ confidence level.

Figure 5

Two-dimensional likelihood contours in the (${\mathrm{\Omega }}_{m0},\tilde{V}$), (${\mathrm{\Omega }}_{m0},{\log }_{10}\tilde{c}$), (${\mathrm{\Omega }}_{m0},{\mathrm{\Omega }}_{*}$), and ($\tilde{V},{\log }_{10}\tilde{c}$) planes, for the $\epsilon =+1$ branch, from the $\mathrm{SnIa}+\mathrm{BAO}$ data combinations. The lighter regions correspond to the $2\sigma$ confidence level, while the darker regions correspond to the $1\sigma$ confidence level.