Supernova Constraints on Braneworld Dark Energy

TL;DR

This work investigates braneworld cosmologies as dark energy candidates, focusing on BRANE1 (B1), BRANE2 (B2), and Disappearing Dark Energy (DDE) scenarios. It derives the braneworld Hubble dynamics using a brane-bulk action with a characteristic length $l$ and presents the two main $H(z)$ branches for B1 and B2, along with DDE constraints that create transient acceleration and, in some cases, a future quiescent singularity. A 54-SN Ia maximum-likelihood analysis marginalizes over the nuisance parameter $\mathcal{M}$ to constrain $\Omega_m$, $\Omega_l$, and $\Omega_{\Lambda_b}$, finding B1 prefers $\Omega_{\Lambda_b}=0$ with $\Omega_m \gtrsim 0.3$, B2 favors $\Omega_m \lesssim 0.25$, and DDE fits best for $\Omega_m \lesssim 0.23$ with $\chi^2_{dof}$ close to LCDM. The results show braneworld models can match current SN data as well as LCDM in certain regions, and the paper discusses complementary tests such as angular-size distance, volume-redshift, and statefinder diagnostics to distinguish between models and assess their viability in light of broader cosmological data.

Abstract

Braneworld models of dark energy are examined in the light of observations of high redshift type Ia supernovae. Braneworld models admit several novel and even exotic possibilities which include: (i) The effective equation of state of dark energy can be more negative than in LCDM: $w \leq -1$; (ii) A class of braneworld models can encounter a `quiescent' future singularity at which the energy density and the Hubble parameter remain well behaved, but higher derivatives of the expansion factor ($\stackrel{..}{a}$, $\stackrel{...}{a}$ etc.) diverge when the future singularity is reached; (iii) The current acceleration of the universe is a {\em transient feature} in a class of models in which dark energy `disappears' after a certain time, giving rise to a matter dominated universe in the future. Since horizons are absent in such a space-time, a braneworld model with {\em transient acceleration} might help reconcile current supernova-based observations of an accelerating universe with the demands of string/M-theory. A maximum likelihood analysis reveals that braneworld models satisfy the stringent demands imposed by high redshift supernovae and a large region in parameter space agrees marginally better with current observations than LCDM. For instance, models with $w < -1 (> -1)$ provide better agreement with data than LCDM for $Ω_m \ggeq 0.3 (\lleq 0.25)$.

Figures (13)

• Figure 1: The behaviour of the deceleration parameter with redshift for DDE. Solid curves from top to bottom are DDE models with $\Omega_m=0.2$, and $\Omega_{\Lambda_b}=1.0, 1.5, 2.0$ respectively. The dashed line is SCDM with $\Omega_m=1$, the dot-dashed curve is LCDM with $\Omega_m=0.2$. The vertical dotted line marks the present epoch at $z=0$, and the horizontal dotted line marks a $q=0$ Milne universe. In the DDE models, the universe ceases to accelerate and becomes matter-dominated in the future, unlike the LCDM model which remains dark energy dominated at all future times.
• Figure 2: The BRANE2 universe can encounter a singularity lying in the future as demonstrated in this figure. The deceleration parameter becomes infinite as the singularity is approached while the Hubble parameter (and the density, pressure) remain finite. The vertical dot-dashed line corresponds to the present epoch $z=0$ while the dashed line represents the dimensionless Hubble parameter. The solid line shows the deceleration parameter $q(z)$. The model parameters are $\Omega_m = 0.15, ~\Omega_l = 0.4$. Although permitted by supernovae observations this particular model appears to be disfavored by clustering bounds on $\Omega_m$ (see Fig. \ref{['fig:contour2']}).
• Figure 3: The likelihood function is shown as a function of each of the parameters $\Omega_m, \ \Omega_l, \ \Omega_{\Lambda_b}$ and ${\cal M}$ after the remaining parameters have been marginalised. The top, middle and bottom panels show the likelihood curves for B1, B2, and DDE. The solid lines correspond to the value of the likelihood function for a given parameter after it has been marginalised over all other parameters, while the dashed lines show the likelihood function evaluated by fixing the other parameters at their maximum likelihood value. In all three cases the likelihood function is normalised with the maximum likelihood value set to unity.
• Figure 4: Confidence levels at $68.3\%$ (light grey inner contour) $95.4\%$ (medium grey contour) and $99.73\%$ (dark grey outer contour) are shown in the $\Omega_l$-$\Omega_m$ plane for BRANE1. Panel (a) represents confidence levels in the $\Omega_l$-$\Omega_m$ plane when marginalised over $\Omega_{\Lambda_b}$ and ${\cal M}$, while panel (b) shows the confidence levels marginalised over ${\cal M}$, with $\Omega_{\Lambda_b}=0$, the best-fit value. We see that taking the best-fit value of $\Omega_{\Lambda_b}=0$ instead of marginalising over it does not change the results appreciably. The dotted region represents the intersection of the $3\sigma$ confidence level with the observational constraint $0.2 \leq \Omega_m \leq 0.5$. The thick solid line in (b) represents the most likely value of $\Omega_l$ if the value of $\Omega_m$ is known exactly. We see that the BRANE1 model is in good agreement with SNe observations if the value of $\Omega_m$ is moderately high: $\Omega_m \hbox{$\buildrel > \over \sim$} ~ 0.3$. (It should be noted that the value of the five dimensional Planck mass corresponding to $\Omega_l \sim 1$ is $M \sim 100$ MeV.)
• Figure 5: The shaded region represents the intersection of the $3 \sigma$ confidence region in the $\Omega_m-\Omega_l$ plane for B1 with the observational constraint $0.2 \leq \Omega_m \leq 0.5$ ($\Omega_{\Lambda_b}=0$ is assumed). In panel (a) we show the values of different cosmological quantities determined at the present epoch. The dashed lines correspond to the current effective equation of state of braneworld dark energy for BRANE1 models: $w_0 = -1.70, \ -1.50, \ -1.30, \ -1.15, \ {\rm and} \ -1.05$ (top to bottom). The dotted lines correspond to the current age of the BRANE1 universe: $H_0 t_0 = 0.85, \ 0.90, \ 0.95, \ 1.02, \ {\rm and} \ 1.10$ (top to bottom). This corresponds to $t_0 ( {\rm Gyrs} ) = 11.8, \ 12.6, \ 13.3, \ 14.3 \ {\rm and} \ 15.4$ if $H_0=70 \ {\rm km/sec/Mpc}$. In panel (b) the dashed lines correspond to the epoch, $z_A$, at which the braneworld universe (B1) begins to accelerate: $z_A = 0.45, \ 0.60, \ 0.75, \ 0.90, \ {\rm and} \ 1.05$ (top to bottom).