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Register a new userPlanck 2015 constraints on the non-flat $Lambda$CDM inflation model
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We study Planck 2015 cosmic microwave background (CMB) anisotropy data using the energy density inhomogeneity power spectrum generated by quantum fluctuations during an early epoch of inflation in the non-flat $Lambda$CDM model. Unlike earlier analyses of non-flat models, which assumed an inconsistent power-law power spectrum of energy density inhomogeneities, we find that the Planck 2015 data alone, and also in conjunction with baryon acoustic oscillation measurements, are reasonably well fit by a closed $Lambda$CDM model in which spatial curvature contributes a few percent of the current cosmological energy density budget. In this model, the measured Hubble constant and non-relativistic matter density parameter are in good agreement with values determined using most other data. Depending on parameter values, the closed $Lambda$CDM model has reduced power, relative to the tilted, spatially-flat $Lambda$CDM case, and can partially alleviate the low multipole CMB temperature anisotropy deficit and can help partially reconcile the CMB anisotropy and weak lensing $sigma_8$ constraints, at the expense of somewhat worsening the fit to higher multipole CMB temperature anisotropy data. Our results are interesting but tentative; a more thorough analysis is needed to properly gauge their significance.
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We perform Markov chain Monte Carlo analyses to put constraints on the non-flat $phi$CDM inflation model using Planck 2015 cosmic microwave background (CMB) anisotropy data and baryon acoustic oscillation distance measurements. The $phi$CDM model is a consistent dynamical dark energy model in which the currently accelerating cosmological expansion is powered by a scalar field $phi$ slowly rolling down an inverse power-law potential energy density. We also use a physically consistent power spectrum for energy density inhomogeneities in this non-flat model. We find that, like the closed-$Lambda$CDM and closed-XCDM models, the closed-$phi$CDM model provides a better fit to the lower multipole region of the CMB temperature anisotropy data compared to that provided by the tilted flat-$Lambda$CDM model. Also, like the other closed models, this model reduces the tension between the Planck and the weak lensing $sigma_8$ constraints. However, the higher multipole region of the CMB temperature anisotropy data are better fit by the tilted flat-$Lambda$CDM model than by the closed models.
We study Planck 2015 cosmic microwave background (CMB) anisotropy data using the energy density inhomogeneity power spectrum generated by quantum fluctuations during an early epoch of inflation in the non-flat XCDM model. Here dark energy is parameterized using a fluid with a negative equation of state parameter but with the speed of fluid acoustic inhomogeneities set to the speed of light. We use this simple parameterization of dynamical dark energy, that is relatively straightforward to use in a computation, in a first attempt to gain some insight into how dark energy dynamics and non-zero spatial curvature jointly affect the CMB anisotropy data constraints. Unlike earlier analyses of non-flat models, we use a physically consistent power spectrum for energy density inhomogeneities. We find that the Planck 2015 data in conjunction with baryon acoustic oscillation measurements are reasonably well fit by a closed XCDM model in which spatial curvature contributes a percent of the current cosmological energy density budget. In this model, the measured Hubble constant and non-relativistic matter density parameter are in good agreement with values determined using most other data. Depending on parameter values, the closed XCDM model has reduced power, relative to the tilted, spatially-flat $Lambda$CDM case, and appears to partially alleviate the low multipole CMB temperature anisotropy deficit and can help partially reconcile the CMB anisotropy and weak lensing $sigma_8$ constraints, at the expense of somewhat worsening the fit to higher multipole CMB temperature anisotropy data. However, the closed XCDM inflation model does not seem to improve the agreement much, if at all, compared to the closed $Lambda$CDM inflation case, even though it has one more free parameter. Our results are interesting but tentative; a more thorough analysis is needed to properly gauge their significance.
We determine constraints on spatially-flat tilted dynamical dark energy XCDM and $phi$CDM inflation models by analyzing Planck 2015 cosmic microwave background (CMB) anisotropy data and baryon acoustic oscillation (BAO) distance measurements. XCDM is a simple and widely used but physically inconsistent parameterization of dynamical dark energy, while the $phi$CDM model is a physically consistent one in which a scalar field $phi$ with an inverse power-law potential energy density powers the currently accelerating cosmological expansion. Both these models have one additional parameter compared to standard $Lambda$CDM and both better fit the TT + lowP + lensing + BAO data than does the standard tilted flat-$Lambda$CDM model, with $Delta chi^2 = -1.26 (-1.60)$ for the XCDM ($phi$CDM) model relative to the $Lambda$CDM model. While this is a 1.1$sigma$ (1.3$sigma$) improvement over standard $Lambda$CDM and so not significant, dynamical dark energy models cannot be ruled out. In addition, both dynamical dark energy models reduce the tension between the Planck 2015 CMB anisotropy and the weak lensing $sigma_8$ constraints.
We constrain spatially-flat tilted and nonflat untilted scalar field ($phi$) dynamical dark energy inflation ($phi$CDM) models by using Planck 2015 cosmic microwave background (CMB) anisotropy measurements and recent baryonic acoustic oscillation distance observations, Type Ia supernovae apparent magnitude data, Hubble parameter measurements, and growth rate data. We assume an inverse power-law scalar field potential energy density $V(phi)=V_0 phi^{-alpha}$. We find that the combination of the CMB data with the four non-CMB data sets significantly improves parameter constraints and strengthens the evidence for nonflatness in the nonflat untilted $phi$CDM case from $1.8sigma$ for the CMB measurements only to more than $3.1sigma$ for the combined data. In the nonflat untilted $phi$CDM model current observations favor a spatially closed universe with spatial curvature contributing about two-thirds of a percent of the present cosmological energy budget. The flat tilted $phi$CDM model is a 0.4$sigma$ better fit to the data than is the standard flat tilted $Lambda$CDM model: current data allow for the possibility that dark energy is dynamical. The nonflat tilted $phi$CDM model is in better accord with the Dark Energy Survey bounds on the rms amplitude of mass fluctuations now ($sigma_8$) as a function of the nonrelativistic matter density parameter now ($Omega_m$) but it does not provide as good a fit to the larger-multipole Planck 2015 CMB anisotropy data as does the standard flat tilted $Lambda$CDM model. A few cosmological parameter value measurements differ significantly when determined using the tilted flat and the untilted nonflat $phi$CDM models, including the cold dark matter density parameter and the reionization optical depth.
We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be $n_mathrm{s} = 0.968 pm 0.006$ and tightly constrain its scale dependence to $d n_s/d ln k =-0.003 pm 0.007$ when combined with the Planck lensing likelihood. When the high-$ell$ polarization data is included, the results are consistent and uncertainties are reduced. The upper bound on the tensor-to-scalar ratio is $r_{0.002} < 0.11$ (95% CL), consistent with the B-mode polarization constraint $r< 0.12$ (95% CL) obtained from a joint BICEP2/Keck Array and Planck analysis. These results imply that $V(phi) propto phi^2$ and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as $R^2$ inflation. Three independent methods reconstructing the primordial power spectrum are investigated. The Planck data are consistent with adiabatic primordial perturbations. We investigate inflationary models producing an anisotropic modulation of the primordial curvature power spectrum as well as generalized models of inflation not governed by a scalar field with a canonical kinetic term. The 2015 results are consistent with the 2013 analysis based on the nominal mission data.
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