Running cosmological constant with observational tests

We investigate the running cosmological constant model with dark energy linearly proportional to the Hubble parameter, $\Lambda = \sigma H + \Lambda_0$, in which the $\Lambda$CDM limit is recovered by taking $\sigma=0$. We derive the linear perturbation equations of gravity under the Friedmann-Lema\"itre-Robertson-Walker cosmology, and show the power spectra of the CMB temperature and matter density distribution. By using the Markov chain Monte Carlo method, we fit the model to the current observational data and find that $\sigma H_0/ \Lambda_0 \lesssim 2.63 \times 10^{-2}$ and $6.74 \times 10^{-2}$ for $\Lambda(t)$ coupled to matter and radiation-matter, respectively, along with constraints on other cosmological parameters.Comment: 12 pages, 5 figures, version accepted by PL

Matter Power Spectra in Viable f(R)f(R) Gravity Models with Massive Neutrinos

We investigate the matter power spectra in the power law and exponential types of viable $f(R)$ theories along with massive neutrinos. The enhancement of the matter power spectrum is found to be a generic feature in these models. In particular, we show that in the former type, such as the Starobinsky model, the spectrum is magnified much larger than the latter one, such as the exponential model. A greater scale of the total neutrino mass, $\Sigma m_{\nu}$, is allowed in the viable $f(R)$ models than that in the $\Lambda$CDM one. We obtain the constraints on the neutrino masses by using the CosmoMC package with the modified MGCAMB. Explicitly, we get $\Sigma m_{\nu} < 0.451 \ (0.214)\ \mathrm{eV}$at 95the corresponding one for the$\Lambda$CDM model is$\Sigma m_{\nu} < 0.200\ \mathrm{eV}$. Furthermore, by treating the effective number of neutrino species$N_{\mathrm{eff}}$as a free parameter along with$\Sigma m_{\nu}$, we find that$N_{\mathrm{eff}} = 3.78^{+0.64}_{-0.84} (3.47^{+0.74}_{-0.60})$and$\Sigma m_{\nu} = 0.533^{+0.254}_{-0.411}$($< 0.386) \ \mathrm{eV}$ at 95% C.L. in the Starobinsky (exponential) model.Comment: 15 pages, 5 figures, updated version accepted by PL

Probing gravitational non-minimal coupling with dark energy surveys

We investigate observational constraints on a specific one-parameter extension to the minimal quintessence model, where the quintessence field acquires a quadratic coupling to the scalar curvature through a coupling constant $\xi$. The value of $\xi$ is highly suppressed in typical tracker models if the late-time cosmic acceleration is driven at some field values near the Planck scale. We test $\xi$ in a second class of models in which the field value today becomes a free model parameter. We use the combined data from type-Ia supernovae, cosmic microwave background, baryon acoustic oscillations and matter power spectrum, to weak lensing measurements and find a best-fit value $\xi > 0.289$ where $\xi = 0$ is excluded outside the 95 per cent confidence region. The effective gravitational constant $G_{\rm eff}$ subject to the hint of a non-zero $\xi$ is constrained to $-0.003 < 1- G_{\rm eff}/G < 0.033$ at the same confidence level on cosmological scales, and can be narrowed down to $1- G_{\rm eff}/G < 2.2 \times 10^{-5}$ when combining with Solar System tests.Comment: Context extended, figures and references added, title changed to match with accepted version for publicatio