Cosmic transparency and acceleration

In this paper, by considering an absorption probability independent of photon wavelength, we show that current type Ia supernovae (SNe Ia) and gamma-ray burst (GRB) observations plus high-redshift measurements of the cosmic microwave background (CMB) radiation temperature support cosmic acceleration regardless of the transparent-universe assumption. Two flat scenarios are considered in our analyses: the $\mathrm{\Lambda }\mathrm{CDM}$ model and a kinematic model. We consider $\tau (z)=2\ln (1+z{)}^{ϵ}$, where $\tau (z)$ denotes the opacity between an observer at $z=0$ and a source at $z$. This choice is equivalent to deforming the cosmic distance duality relation as $D_L{D}_A^{-1}=(1+z{)}^{2+ϵ}$ and, if the absorption probability is independent of photon wavelength, the CMB temperature evolution law is $T_{\mathrm{CMB}}(z)=T_0(1+z{)}^{1+2ϵ/3}$. By marginalizing on the $ϵ$ parameter, our analyses rule out a decelerating universe at 99.99% C.L. for all scenarios considered. Interestingly, by considering only SNe Ia and GRBs observations, we obtain that a decelerated universe—indicated by ${\mathrm{\Omega }}_{\mathrm{\Lambda }}\le 0.33$ and $q_0>0$—is ruled out around $1.5\sigma$ C.L. and $2\sigma$ C.L., respectively, regardless of the transparent-universe assumption.

Figure 1

In panel (a) we plot the 740 luminosity distances of SNe Ia [61]. In panel (b) we plot the 42 $T_{\mathrm{cmb}}$ measurements. In panel (c) we plot the 162 luminosity distances of GRBs [62].

Figure 2

In panel (a) the black solid and red dash-dotted lines correspond to the analyses using SNe Ia and GRBs, respectively, within the flat $\mathrm{\Lambda }\mathrm{CDM}$ framework. In panel (b) the black solid, red dash-dotted, and blue dashed lines correspond to the analyses using SNe Ia, GRBs, and $T_{\mathrm{CMB}}(z)$, respectively, within the flat $\mathrm{\Lambda }\mathrm{CDM}$ framework. The filled contours are from the joint analysis. All contours are for 68.3%, 95.4%, and 99.73% C.L. [except for the filled region in panel (b); for this panel the contours are for 68.3%, 95.4%, and 99.99% C.L.].

Figure 3

In panel (a) the black solid and red dash-dotted lines correspond to the analyses using SNe Ia and GRBs, respectively, within the kinematic model. The filled contours are from the joint analysis. In panel (b) the black solid, red dash-dotted, and blue dashed lines correspond to the analyses using SNe Ia, GRBs, and $T_{\mathrm{CMB}}(z)$, respectively, within the kinematic framework. The filled contours are from the joint analysis. All contours are for 68.3%, 95.4%, and 99.73% C.L. (except for the filled region in panel (b); for this panel the contours are for 68.3%, 95.4%, and 99.99% C.L.).

Figure 4

In panel (a) we plot the likelihoods for ${\mathrm{\Omega }}_{\mathrm{\Lambda }}$ by marginalizing on $ϵ$ by using only SNe Ia plus GRB observations (blue line) and SNe I, GRB, and $T_{\mathrm{CMB}}(z)$ (black line). In panel (b) we plot the likelihoods for $q_0$ by marginalizing on $ϵ$ by using only SNe Ia plus GRB observations (blue line) and SNe I, GRB, and $T_{\mathrm{CMB}}(z)$ (black line). The horizontal lines correspond to $1\sigma$ (68.3%) and $2\sigma$ C.L. (95.4%).