Nonlocal gravity. Conceptual aspects and cosmological predictions

TL;DR

Gravity's quantum effective action can be nonlocal in the infrared, motivating models where an IR mass scale emerges and modifies cosmology. The RR model, featuring a diffeomorphism-invariant $R\frac{1}{\Box^2}R$ term, acts as a dynamical conformal-mode mass and drives self-acceleration without a cosmological constant. It yields a phantom-like dark energy at the background level while preserving stable cosmological perturbations, and fits Planck+BAO+SNe data as well as ΛCDM, with a higher predicted $H_0$ and a nonzero sum of neutrino masses consistent with oscillation experiments. Gravitational waves in RR propagate at light speed, and standard sirens could help distinguish RR from ΛCDM in future observations. The work emphasizes a principled, minimal nonlocal modification that remains predictive and testable against current and upcoming cosmological datasets.

Abstract

Even if the fundamental action of gravity is local, the corresponding quantum effective action, that includes the effect of quantum fluctuations, is a nonlocal object. These nonlocalities are well understood in the ultraviolet regime but much less in the infrared, where they could in principle give rise to important cosmological effects. Here we systematize and extend previous work of our group, in which it is assumed that a mass scale $Λ$ is dynamically generated in the infrared, giving rise to nonlocal terms in the quantum effective action of gravity. We give a detailed discussion of conceptual aspects related to nonlocal gravity and of the cosmological consequences of these models. The requirement of providing a viable cosmological evolution severely restricts the form of the nonlocal terms, and selects a model (the so-called RR model) that corresponds to a dynamical mass generation for the conformal mode. For such a model: (1) there is a FRW background evolution, where the nonlocal term acts as an effective dark energy with a phantom equation of state, providing accelerated expansion without a cosmological constant. (2) Cosmological perturbations are well behaved. (3) Implementing the model in a Boltzmann code and comparing with observations we find that the RR model fits the CMB, BAO, SNe, structure formation data and local $H_0$ measurements at a level statistically equivalent to $Λ$CDM. (4) Bayesian parameter estimation shows that the value of $H_0$ obtained in the RR model is higher than in $Λ$CDM, reducing to $2.0σ$ the tension with the value from local measurements. (5) The RR model provides a prediction for the sum of neutrino masses that falls within the limits set by oscillation and terrestrial experiments. (6) Gravitational waves propagate at the speed of light, complying with the limit from GW170817/GRB 170817A.

Figures (12)

• Figure 1: Upper left panel: the function $\rho_{\rm DE}(x)/\rho_0$ for the RR model (setting $\Omega_{M}\simeq 0.294$ and $h_0\simeq 0.695$) against $x\equiv \ln a$. Upper right panel: the same quantity shown against the redshift $z$. Lower left panel: the DE equation of state $w_{\rm DE}(z)$. Lower right panel: the auxiliary fields $U(x)$ (blue, solid line) and $W(x)$ (red, dashed).
• Figure 2: Left panel: the relative difference $\Delta d/d=[d^{\rm RR}_{\rm com}-d^{\Lambda{\rm CDM}}_{\rm com}]/d^{\Lambda{\rm CDM}}_{\rm com}$ of comoving distances, using the same values of $h_0$ and $\Omega_{M}$ for both the RR and $\Lambda$CDM models. Right panel: $\Delta d/d$ using the best-fit values $\Omega_{M}\simeq 0.299$ and $h_0\simeq 0.695$ for RR, and $\Omega_{M}\simeq 0.309$ and $h_0\simeq 0.677$ for $\Lambda$CDM (see Table \ref{['tab:res1']}).
• Figure 3: As in Fig. \ref{['fig:backgRR']}, for the RR model with initial conditions $u_0=250$.
• Figure 4: The dimensionless quantity $k^{3/2}10^5\Psi_k$ against $\ln a$, for $\kappa=0.1$ (upper left panel), $\kappa=1$ (upper right panel) and $\kappa =5$ (lower panel). In each figure the blue solid line is the result in $\Lambda$CDM and the red dashed line is the result in the minimal RR model ($u_0=0$) with $c^U_k=0$. For this comparison, we have used the same fiducial values of the cosmological parameters in $\Lambda$CDM and in the RR model. On the scale of these plots, the results obtained with $c^U_k=\pm 10$ would be indistinguishable from the line with $c^U_k=0$.
• Figure 5: The relative differences $[\Psi_k^{\rm RR}-\Psi_k^{\Lambda{\rm CDM}}]/\Psi_k^{\Lambda{\rm CDM}}$ for $\kappa=0.1,1,5$, again setting $c^U_k=0$, against redshift, for the RR model.