https://doi.org/10.1140/epjp/s13360-022-03343-w
Regular Article
An empirical investigation into cosmological tensions
1
Instituto de Fisica, Universidade Federal Fluminense, 24210-346, Niteroi, RJ, Brazil
2
Scuola Superiore Meridionale, Largo San Marcellino 10, 80138, Napoli, Italy
3
Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Via Cintia, 80126, Napoli, Italy
Received:
2
September
2022
Accepted:
29
September
2022
Published online:
13
October
2022
The possibility that the 
tension is a sign of a physics beyond the 
CDM model is one of the most exciting possibilities in modern cosmology. The challenge of solving this problem is complicated by several factors, including the worsening of the tension on 
parameter when that on is raised. Furthermore, the perspective from which the problem is viewed should not be underestimated, since the tension on can also be interpreted as a tension on the size of the acoustic horizon, 
, which deserves proper discussion. The common approach in the literature consists in proposing a new model that can resolve the tension and treat the new parameters of the theory as free in the analysis. However, allowing additional parameters to vary often results in larger uncertainties on the inferred cosmological parameters, causing an apparent relaxing in the tension due to the broaden in the posterior, instead of a genuine shift in the central value of 
. To avoid this, we consider here an empirical approach that assumes specific non-standard values of the CDM extensions and we analyse how the important parameters in the context of the tension vary accordingly. For our purposes, we study simple extensions of the standard cosmological model, such as a phantom DE component (with Equation of State 
) and extra relativistic species in the early universe (so that 
). We obtain relations between variation in the value of w and 
and changes in , 
and . In this way an empirical relation between and is provided, that is a first step in understanding which classes of theoretical models, and with which characteristics, could be able to break the correlation between the two tensions.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
