Using the Tilted flat-ΛCDM and the Untilted Non-flat ΛCDM Inflation Models to Measure Cosmological Parameters from a Compilation of Observational Data

Abstract

We use the physically-consistent tilted spatially-flat and untilted non-flat ΛCDM inflation models to constrain cosmological parameter values with the Planck 2015 cosmic microwave background (CMB) anisotropy data and recent Type Ia supernovae measurements, baryonic acoustic oscillations (BAO) data, growth rate observations, and Hubble parameter measurements. The most dramatic consequence of including the four non-CMB data sets is the significant strengthening of the evidence for non-flatness in the non-flat ΛCDM model, from 1.8σ for the CMB data alone to 5.1σ for the full data combination. The BAO data is the most powerful of the non-CMB data sets in more tightly constraining model parameter values and in favoring a spatially-closed Universe in which spatial curvature contributes about a percent to the current cosmological energy budget. The untilted non-flat ΛCDM model better fits the large-angle CMB temperature anisotropy angular spectrum and is more consistent with the Dark Energy Survey constraints on the current value of the rms amplitude of mass fluctuations (σ 8 ) as a function of the current value of the nonrelativistic matter density parameter (Ω m ) but does not provide as good a fit to the smaller-angle CMB temperature anisotropy data as does the tilted flat-ΛCDM model. Some measured cosmological parameter values differ significantly between the two models, including the reionization optical depth and the baryonic matter density parameter, both of whose 2σ ranges (in the two models) are disjoint or almost so. Subject headings: cosmological parameters -cosmic background radiation -large-scale structure of universe -inflation -observations -methods:statistical

Signs of dynamical dark energy in current observations

“…We have already seen a weakening of DDE evidence in the case of the CPL as compared to the XCDM, owing to the presence of one more parameter in the former case as compared to the latter. The effects of curvature in this kind of analyses have been studied for the main models under consideration in [27][28][29][30][31], and previously in [26,84]. For instance, in [27] (see also references therein) the authors show that in the non-flat ΛCDM model the spatial curvature also allows a decrease of the central value of σ 8 (0) when only the TT+lowP+lensing Planck 2015 CMB data is employed in the fitting analysis.…”

“…[18][19][20][21] and references therein. Other recent works, in contrast, find a variety of levels of evidence in different contexts or simply no sizeable deviation from the ΛCDM, see [22][23][24][25][26][27][28][29][30][31][32][33][34] and references therein, for example.…”

General theory of cosmological perturbations in open and closed universes from the Horndeski action

“…However, the fact that Ω K is bounded to be small does not mean that Ω K is actually equal to zero. Some works even suggest that flat models are less favored by data [6][7][8][9][10][11]. Therefore, it is interesting to consider the possibility that there is a tiny spatial curvature K = 0 and…”

Effect of the spatial curvature of the Universe on the form of the gravitational potential

“…Non-CMB data mildly favor a closed spatial hypersurface [4]. If one uses inflation power spectra in non-flat models, there is also some evidence for a mildly closed Universe in these data [5][6][7]. Most of such constraints are based on some cosmological models (e.g., ΛCDM), i.e.…”