On the determination of curvature and dynamical dark energy

Abstract

Constraining simultaneously the dark energy (DE) equation of state and thecurvature of the universe is difficult due to strong degeneracies. To circumvent thisproblem when analyzing data it is usual to assume flatness to constrain the DEor, conversely, to assume that the DE is a cosmological constant to constrainthe curvature. In this paper, we quantify the impact of such assumptions withan eye to future large surveys. We simulate future data for type Ia supernovae,the cosmic microwave background and baryon acoustic oscillations for a largerange of fiducial cosmologies allowing a small spatial curvature. We take intoaccount a possible time evolution of DE through a parameterized equation of state:w(a) = w0+(1−a)wa. We then fit the simulated data with a wrong assumption on the curvature or on the DEparameters.For a fiducial ΛCDM cosmology, if flatness is incorrectly assumed in the fit and if the true curvature is within the ranges0.01<Ωk<0.03 and −0.07<Ωk<−0.01, one will be led to conclude erroneously that an evolving DE is present, even with highstatistics.On the other hand, models with curvature and dynamical DE can be confused with a flatΛCDM model when the fit ignores a possible DE evolution. We find that, in the future, with highstatistics, such risks of confusion should be limited, but they are still possible, and biases inthe cosmological parameters might be important.We conclude by recalling that, in the future, it will be mandatory to perform somecomplete multi-probe analyses, leaving the DE parameters as well as the curvature as freeparameters.