Observational constraints on Starobinsky $f(R)$ cosmology from cosmic expansion and structure growth data

Abstract

The unknown physical nature of the Dark Energy motivates in cosmology the study of modifications of the gravity theory at large distances. One of these types of modifications are the theories known as f (R) gravity. In this paper we use observational data to both constraint and test the Starobinsky f (R) model [57], using updated measurements from the dynamics of the expansion of the universe, H(z), and the growth rate of cosmic structures, [f σ8](z), where the distinction between the concordance ΛCDM model and modified gravity models, f (R), become clearer. We use MCMC likelihood analyses to explore the parameters space of the f (R) model using H(z) and [f σ8](z) data, both individually and jointly, and further check which of the models better fit the joint data. To further test the Starobinsky model, we use a method proposed by Linder [38], where the data from the observables is jointly binned in redshift space. This allows to further explore the model's parameter that better fits the data in comparison to the ΛCDM model. Our analyses show that the result from the MCMC run using [f σ8](z) data alone fits the analyzed model better than using the joint data. At the end, we reaffirm that this joint analysis is able to break the degenerescence between modified gravity models through the f σ8 observable, as the original author proposed; our results show that the f (R) Starobinsky model although not favored by the available data, cannot be discarded and is a possible alternative to the ΛCDM model.

Unveiling the Universe with emerging cosmological probes

“…In particular, it has been found that CC are extremely useful in combination with other cosmological probes (SNe, BAO, CMB) to increase the accuracy on cosmological parameters (such as X k , X m and H 0 , see, e.g., Haridasu et al 2018;Gómez-Valent and Amendola 2018;Lin et al 2021), to determine the time evolution of the dark energy EoS (Moresco et al 2016a;Zhao et al 2017;Di Valentino et al 2020;, and also to provide tighter constraints on the number of existing relativistic species and on the sum of neutrino masses by breaking the existing degeneracies between parameters (Moresco et al 2012b(Moresco et al , 2016a. As suggested by Linder (2017), the measured H(z) data have also been used in combination with the growth rate of cosmic structures to construct a new diagram to disentangle cosmological models (Moresco and Marulli 2017;Basilakos and Nesseris 2017;Bessa et al 2021). Finally, the CC data, in combination with BAO and SNe, have proven to be extremely useful also to test the distanceduality relation and measure the transparency (or equivalently, the opacity) of the Universe (Holanda et al 2013;Santos-da-Costa et al 2015;Chen et al 2016b;Vavryčuk and Kroupa 2020;Bora and Desai 2021;Renzi et al 2021).…”

Inferring $$S_8(z)$$ and $$\gamma (z)$$ with cosmic growth rate measurements using machine learning

“…The literature reports diverse compilations of measurements of the growth rate of cosmic structures, [ f σ 8 ](z) (see, e.g. [32][33][34]), which we update here. Our compilation of f (z) data, shown in Table 1, follows these criteria:…”

Correcting the gravitational dipole direction for a partial sky survey

“…In the standard model of cosmology, known as ΛCDM model, the phase of accelerated expansion is caused by a fluid (dark energy) of negative pressure and constant equation of state ω = −1. However, several theories [4][5][6] developed over time are able to reproduce the effects of dark energy, but, still, only with more accurate cosmological observations we will have a definitive answer.…”