Benevento, Giampaolo
Raveri, Marco
Lazanu, Andrei
Bartolo, Nicola
Liguori, Michele
Brax, Philippe
Valageas, Patrick

We investigate cosmological constraints on K-mouflage models of modified gravity. We consider two scenarios: one where the background evolution is free to deviate from Lambda CDM (K-mouflage) and another one which reproduces a Lambda CDM expansion (K-mimic), implementing both of them into the EFTCAMB code. We discuss the main observational signatures of these models and we compare their cosmological predictions to different datasets, including CMB, CMB lensing, SNIa and different galaxy catalogues. We argue about the possibility of relieving the H-0 and weak lensing tensions within these models, finding that K-mouflage scenarios effectively ease the tension on the Hubble Constant. Our final 95% C.L. bounds on the epsilon(2,0) parameter that measures the overall departure from Lambda CDM (corresponding to epsilon(2,0) =3D 0) are -0.04 <=3D epsilon(2,0) <=3D 0 for K-mouflage and 0 <=3D epsilon(2,0) <=3D 0.002 for K-mimic. These translate into an upper bound for the coupling strength beta < 0.22 for K-mouflage and beta < 0.026 for K-mimic. In the former case the main constraining power comes from changes in the background expansion history, while in the latter case the model is strongly constrained by measurements of the amplitude of matter perturbations. The sensitivity of these cosmological constraints closely matches that of solar system probes. We show that these constraints could be significantly tightened with future ideal probes like CORE.

We investigate the impact of modified-gravity models on the Lyman-alpha power spectrum. Building a simple analytical modeling, based on a truncated Zeldovich approximation, we estimate the intergalactic medium power spectrum and the Lyman-alpha flux decrement power spectrum along the line of sight. We recover the results of numerical simulations for f(R)-gravity models and present new results for K-mouflage scenarios. We find that the shape of the distortion due to the modified gravity depends on the model, through the scale-dependence or not of their growth rate. This is more clearly seen in the three-dimensional power spectrum than in the one-dimensional power spectrum, where the line-of-sight integration smoothes the deviation. Whilst the Lyman-alpha power spectrum does not provide competitive bounds for f(R) theories, it could provide useful constraints for the K-mouflage models. Thus, the efficiency of the Lyman-alpha power spectrum as a probe of modified-gravity scenarios depends on the type of screening mechanism and the related scale dependence it induces. The prospect of a full recovery of the three-dimensional Lyman-alpha power spectrum from data would also lead to stronger constraints and a better understanding of screening mechanisms.

Brax, Philippe
Cespedes, Sebastian
Davis, Anne-Christine

The impact of the existence of gravitons with non-vanishing masses on the B-modes of the Cosmic Microwave Background (CMB) is investigated. We also focus on putative modifications to the speed of the gravitational waves. We find that a change of the graviton speed shifts the acoustic peaks of the CMB and then could be easily constrained. For the case of massive gravity, we show analytically how the B-modes are sourced in a manner differing from the massless case leading to a plateau at low l in the CMB spectrum. We also study the case when there are more than one graviton, and when pressure instabilities are present. The latter would occur in doubly coupled bigravity in the radiation era. We focus on the case where a massless graviton becomes tachyonic in the radiation era whilst a massive one remains stable. As the unstable mode decouples from matter in the radiation era, we find that the effects of the instability is largely reduced on the spectrum of B-modes as long as the unstable graviton does not grow into the non-linear regime. In all cases when both massless and massive gravitons are present, we find that the B-mode CMB spectrum is characterised by a low l plateau together with a shifted position for the first few peaks compared to a purely massive graviton spectrum, a shift which depends on the mixing between the gravitons in their coupling to matter and could serve as a hint in favour of the existence of multiple gravitons.

We consider the consequences of the leading quartic corrections to the Einstein-Hilbert action of gravity at low energy. Using the equivalence between the scalar R-2 contribution and a scalar-tensor field theory, we analyze the possible ways of detecting the associated scalaron and suggest that short distance tests of gravity, and in particular future tests of Newton's law aboard satellites, would provide the best environment to detect such a modification of gravity. We also analyze the regimes for which the R2 theory would result as a low energy manifestation of putative high energy UV completions involving extra dimensions. In the four-dimensional N =3D 1 supergravity limit of such extra-dimensional models, the R-2 models would emerge from the stabilization of a nearly no-scale super field such as the ones associated to the Kahler modulus corresponding to the breathing mode of a six-dimensional compactification.

Brax, Philippe
Davis, Anne-Christine
Noller, Johannes

We analyse the late time cosmology and the gravitational properties of doubly coupled bigravity in the constrained vielbein formalism (equivalent to the metric formalism) when the mass of the massive graviton is of the order of the present Hubble rate. We focus on one of the two branches of background cosmology where the ratio between the scale factors of the two metrics is algebraically determined. We find that the late time physics depends on the mass of the graviton, which dictates the future asymptotic cosmological constant. The Universe evolves from a matter dominated epoch to a dark energy dominated era where the equation of state of dark energy can always be made close to -1 now by appropriately tuning the graviton mass. We also analyse the perturbative spectrum of the theory in the quasi-static approximation, well below the strong coupling scale where no instability is present, and we show that there are five scalar degrees of freedom, two vectors and two gravitons. In Minkowski space, where the four Newtonian potentials vanish, the theory manifestly reduces to one massive and one massless graviton. In a cosmological FRW background for both metrics, four of the five scalars are Newtonian potentials which lead to a modification of gravity on large scales. The fifth one gives rise to a ghost which decouples from pressure-less matter in the quasi-static approximation. In this scalar sector, gravity is modified with effects on both the growth of structure and the lensing potential. In particular, we find that the Sigma parameter governing the Poisson equation of the weak lensing potential can differ from one in the recent past of the Universe. Overall, the nature of the modification of gravity at low energy, which reveals itself in the growth of structure and the lensing potential, is intrinsically dependent on the couplings to matter and the potential term of the vielbeins. We also find that the time variation of Newton's constant in the Jordan frame can easily satisfy the bound from solar system tests of gravity. Finally we show that the two gravitons present in the spectrum have a nontrivial mass matrix whose origin follows from the potential term of bigravity. This mixing leads to gravitational birefringence.

Berge, Joel
Brax, Philippe
Pernot-Borras, Martin
Uzan, Jean-Philippe

This paper revisits deviations from Newtonian gravity described by a Yukawa interaction that can arise from the existence of a finite range fifth force. We show that the standard multipolar expansion of the Earth gravitational potential can be generalised. In particular, the multipolar coefficients depend on the distance to the centre of the Earth and are therefore not universal to the Earth system anymore. This offers new ways of constraining such Yukawa interactions and demonstrates explicitly the limits of the Newton-based interpretation of geodesy experiments. In turn, limitations from geodesy data restrict the possibility of testing gravity in space. The gravitational acceleration is described in terms of spin-weighted spherical harmonics allowing us to obtain the perturbing force entering the Lagrange-Gauss secular equations. This is then used to discuss the correlation between geodesy and modified gravity experiments and the possibility to break their degeneracy. Finally we show that, given the existing constraints, a Yukawa fifth force is expected to be sub-dominant in satellite dynamics and space geodesy experiments, as long as they are performed at altitudes greater than a few hundred kilometres. Gravity surveys will have to gain at least two orders of magnitude in instrumental precision before satellite geodesy could be used to improve the current constraints on modified gravity.

Brax, Philippe
Burrage, Clare
Davis, Anne-Christine

We review laboratory constraints on theories of modified gravity and show that they are complementary to cosmological and astrophysical tests. We particularly focus on the environmentally dependent. dilaton, as a worked example to show how such constraints are derived. Finally we discuss precision photons experiments, and why these may also give us information about possible modifications of gravity.