Can the degeneracies in the gravity sector be broken?

Abstract

It has been long known that by appropriately modifying gravity one can always reproduce the expansion history of any dark energy model, e.g. the $\Lambda$CDM. This degeneracy cannot be broken with geometric probes like the Type Ia supernovae, the cosmic microwave background or the baryon acoustic oscillations since they are based on the measurement of distances and scales and therefore require the expansion history $H(z)$, so one may only hope to break this degeneracy by using dynamic probes like the growth rate data that track the matter density perturbations. We demonstrate that breaking this degeneracy is not currently possible by explicitly constructing $f(R)$, $f(G)$ and $f(T)$ theories that mimic exactly the $\Lambda$CDM model at the background level and confronting them against the latest observational cosmological data. We also determine the necessary improvement in the growth rate data in order to discriminate these theories from $\Lambda$CDM. We found that at least a threefold improvement is necessary, something which will be possible with a survey like Euclid.

14 pages, 5 figures, changes match published version

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• Cosmological constraints and comparison of viable $f(R)$ models
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• Using dark energy to suppress power at small scales
• Cosmological constraints on non-adiabatic dark energy perturbations
• Machine Learning and cosmographic reconstructions of quintessence and the Swampland conjectures
• Testing the $\Lambda$CDM paradigm with growth rate data and machine learning
• Degeneracy between CCDM and $\Lambda$CDM cosmologies
• Reconstruction of the null-test for the matter density perturbations
• The Effective Fluid approach for Modified Gravity and its applications
• Cosmological constraints with the Effective Fluid approach for Modified Gravity
• Structure formation in clustering DBI dark energy model with constant sound speed
• Lensing convergence and anisotropic dark energy in galaxy redshift surveys
• Constraints on a scalar-tensor model with Gauss-Bonnet coupling from SN Ia and BAO observations
• Structure formation in a non-canonical scalar field model of clustering dark energy