Abstract
ABSTRACT We constrain the expansion history of the Universe and the cosmological matter density fraction in a model-independent way by exclusively making use of the relationship between background and perturbations under a minimal set of assumptions. We do so by employing a Gaussian process to model the expansion history of the Universe from present time to the recombination era. The expansion history and the cosmological matter density are then constrained using recent measurements from cosmic chronometers, Type-Ia supernovae, baryon acoustic oscillations, and redshift-space distortion data. Our results show that the evolution in the reconstructed expansion history is compatible with the Planck 2018 prediction at all redshifts. The current data considered in this study can constrain a Gaussian process on H(z) to an average $9.4 {{\ \rm per\ cent}}$ precision across redshift. We find Ωm = 0.224 ± 0.066, lower but statistically compatible with the Planck 2018 cosmology. Finally, the combination of future DESI measurements with the CMB measurement considered in this work holds the promise of $8 {{\ \rm per\ cent}}$ average constraints on a model-independent expansion history as well as a five-fold tighter Ωm constraint using the methodology developed in this work.
Highlights
When observing and characterising the Universe on large scales, there are two broadly different, yet intertwined, types of observations (Peebles 1980)
B we present the results of the alternative analyses described at the end of Sect. 2 and show that, despite the different treatments of the Gaussian process (GP), they produce statistically compatible constraints for the cosmological functions as well as for the cosmological parameters, and similar uncertainties on both
5 CONCLUSIONS In this work we have developed a method to obtain constraints on H (z) and Ωm purely based on the relationship between the expansion history and the linear growth rate
Summary
When observing and characterising the Universe on large scales, there are two broadly different, yet intertwined, types of observations (Peebles 1980). In the first type of observation, one endeavours to constrain the expansion rate of the Universe at different times. This can be done by measuring the expansion rate itself or through a variety of cosmological distance measures: angular diameter distances, luminosity distances, standard sirens, etc. If a(t) is the scale factor of the Universe at cosmic time t, the expansion rate at that time can be defined as H [a(t)] = a/a (where the overdot is derivative with regards to cosmic time). Assuming zero spatial curvature, it is possible to derive expressions for the luminosity (D L) and angular diameter distances (D A) by multiplying and dividing Eqn 1 by (1 + z), respectively:
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