Observational constraints on Visser’s cosmological model

Theories of gravity for which gravitons can be treated as massive particles have presently been studied as realistic modifications of general relativity, and can be tested with cosmological observations. In this work, we study the ability of a recently proposed theory with massive gravitons, the so-called Visser theory, to explain the measurements of luminosity distance from the Union2 compilation, the most recent Type-Ia Supernovae (SNe Ia) data set, adopting the current ratio of the total density of nonrelativistic matter to the critical density (${\Omega }_m$) as a free parameter. We also combine the SNe Ia data with constraints from baryon acoustic oscillations (BAO) and cosmic microwave background (CMB) measurements. We find that, for the allowed interval of values for ${\Omega }_m$, a model based on Visser’s theory can produce an accelerated expansion period without any dark energy component, but the combined analysis (SNe $\mathrm{Ia}+\mathrm{BAO}+\mathrm{CMB}$) shows that the model is disfavored when compared with the $\Lambda \mathrm{CDM}$ model.

Figure 1

Hubble parameter as a function of the redshift for best-fit value obtained from SNe Ia. By using the different best-fit values, the curve does not change significantly.

Figure 2

Best-fit for the distance modulus versus redshift for the Visser model (solid gray line) and the $\Lambda \mathrm{CDM}$ model (dashed line). The SNe data were taken from the Union2 compilation [22].

Figure 3

Effective state parameter as a function of the redshift for the best-fit value obtained from SNe Ia.

Figure 4

Deceleration parameter as a function of the redshift for the best-fit value obtained from SNe Ia. Note that the acceleration phase is transient in the Visser model.