Non-local gravity and comparison with observational datasets. II. Updated results and Bayesian model comparison with ΛCDM

Abstract

We present a comprehensive and updated comparison with cosmological observations of two non-local modifications of gravity previously introduced by our group, the so called RR and RT models. We implement the background evolution and the cosmological perturbations of the models in a modified Boltzmann code, using CLASS. We then test the non-local models against the Planck 2015 TT, TE, EE and Cosmic Microwave Background (CMB) lensing data, isotropic and anisotropic Baryonic Acoustic Oscillations (BAO) data, JLA supernovae, H 0 measurements and growth rate data, and we perform Bayesian parameter estimation. We then compare the RR, RT and ΛCDM models, using the Savage-Dickey method. We find that the RT model and ΛCDM perform equally well, while the performance of the RR model with respect to ΛCDM depends on whether or not we include a prior on H 0 based on local measurements. arXiv:1602.03558v2 [astro-ph.CO] 22 May 2016 2 This is analogous to the fact that, in a Deser-Woodard type model, a term of the form R µν f (2 −1 Rµν ) shows instabilities [60].3 See also app. B below, where we will discuss a related issue on the comparison with Lunar Laser Ranging, raised in [64].4 It should also be appreciated that a non-local model such as the RT or the RR model only introduces one new parameter m, which replaces the cosmological constant in ΛCDM. By comparison, bigravity replaces the cosmological constant by a set of 5 parameters βn, n = 0, . . . , 4 and also introduces a new Planck mass associated to the second metric, and viable solutions are searched tuning this parameter space. Similarly, in the Deser-Woodard model one tunes a whole function f (X).

Conformal symmetry and nonlinear extensions of nonlocal gravity

“…This produces a realistic background FRW evolution, without the need of introducing a cosmological constant. Its cosmological perturbations are well-behaved, both in the scalar [45] and in the tensor sector [44,46]. The study of the effect of its cosmological perturbations shows that the predictions of the model are consistent with CMB, supernovae, Baryon Acoustic Oscillations (BAO) and structure formation data [45,47,48].…”

“…This allowed us to perform Bayesian parameter estimation and a detailed quantitative comparison with ΛCDM, that shows that the model fits the data at a level which is statistically indistinguishable from ΛCDM. 3 Having passed all these tests the model deserves a name, and we have dubbed it the "RT" See also Appendix A of [44] for the clarification of an issue on the comparison with Lunar Laser Ranging data. 3 It should also be appreciated that this model only introduces one new parameter m, which replaces the cosmological constant in ΛCDM.…”

“…In practice, at least within the space of theories that we have explored, we find that only models constructed uniquely with the Ricci scalar work. At a finer level of resolution, using again the Boltzmann code modified for nonlocal theories, in [44] we have repeated the comparison with observations using the 2015 Planck data (which were not yet publicly available when [49] appeared) as well as with an extended set of BAO and structure formation data. A Bayesian model comparison between ΛCDM, the RT and RR models has then been performed.…”

“…A more detailed quantitative analysis will require the computation of the cosmological perturbations and their implementations in a Boltzmann code, as performed in [44,45,49] for the RR and RT nonlocal model. We hope to report on this in the future.…”

“…Indeed, these specific nonlocal models also have a given structure of cosmological perturbations, which differs ΛCDM, and which also affect the parameter estimation in these models. Thus, to perform a quantitative Bayesian comparison between the performance of a nonlocal model with that of ΛCDM, there is no alternative to the full analysis, as done for the RT and RR models in [44,49]. However, to have a first estimate of whether a model is viable, we can just compare the value of wðaÞ obtained from the nonlocal model with the limits on w 0 or on (w 0 , w a ) obtained comparing wCDM or the (w 0 , w a ) model to the data, which has been done in the 2015 Planck dark energy paper [64].…”