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Axio-dilaton models are among the simplest scalar-tensor theories that contain the two-derivative interactions that naturally compete at low energies with the two-derivative inter-actions of General Relativity. Such models are well-motivated as the low energy fields arising from string theory compactification. We summarize these motivations and compute their cosmological evolution, in which the dilaton acts as dark energy and its evolution provides a framework for dynamically evolving particle masses. The derivative axion-dilaton couplings play an important role in the success of these cosmologies. We derive the equations for fluctuations needed to study their implications for the CMB anisotropy, matter spectra and structure growth. We use a modified Boltzmann code to study in detail four benchmark parameter choices, including the vanilla Yoga model, and identify couplings that give viable cosmologies, including some with surprisingly large matter-scalar interactions. The axion has negligible potential for most of the cosmologies we consider but we also examine a simplified model for which the axion potential plays a role, using axion-matter couplings motivated by phenomenological screening considerations. We find such choices can also lead to viable cosmologies., Comment: 38 pages, 8 figures

We revisit the flux of chameleons (light scalar particles which could play a role in the dark energy phenomenon) produced in the interior of the Sun. Our novel analysis incorporates various important details and new processes that have previously been overlooked, including the impact of the bulk magnetic field profile, as well as Primakoff production of chameleons in the electric fields of electrons and ions. In this paper we consider only the contributions of transverse photons. The production of chameleons from longitudinal electromagnetic excitations will be presented in a dedicated follow-up work. Demanding that the total flux of chameleons does not exceed 3% of the solar luminosity leads to the stringent upper limit on the chameleon-photon conformal coupling $\beta_\gamma \lesssim 10^{10}$, assuming that the height of the chameleon potential is set to the dark energy scale $\Lambda = 2.4$ meV, and independently of other couplings to matter. Although this bound is tighter than current upper limits on $\beta_{\gamma}$ from the CAST helioscope, these limits will have to be reassessed in terms of the updated solar chameleon flux we have computed. We argue that solar chameleons, potentially detectable in next-generation helioscopes such as IAXO, can be used to probe a region of chameleon parameter space that has yet to be covered., Comment: 11 + 7 pages, 6 figures. v2: minor changes to the text and to the title. Matches the published version. Code available at https://github.com/tomasoshea/chameleon

In this paper, we revisit the infrared (IR) divergences in de Sitter (dS) space using the wavefunction method, and explicitly explore how the resummation of higher-order loops leads to the stochastic formalism. In light of recent developments of the cosmological bootstrap, we track the behaviour of these nontrivial IR effects from perturbation theory to the non-perturbative regime. Specifically, we first examine the perturbative computation of wavefunction coefficients, and show that there is a clear distinction between classical components from tree-level diagrams and quantum ones from loop processes. Cosmological correlators at loop level receive contributions from tree-level wavefunction coefficients, which we dub classical loops. This distinction significantly simplifies the analysis of loop-level IR divergences, as we find the leading contributions always come from these classical loops. Then we compare with correlators from the perturbative stochastic computation, and find the results there are essentially the ones from classical loops, while quantum loops are only present as subleading corrections. This demonstrates that the leading IR effects are contained in the semi-classical wavefunction which is a resummation of all the tree-level diagrams. With this insight, we go beyond perturbation theory and present a new derivation of the stochastic formalism using the saddle-point approximation. We show that the Fokker-Planck equation follows as a consequence of two effects: the drift from the Schr\"odinger equation that describes the bulk time evolution, and the diffusion from the Polchinski's equation which corresponds to the exact renormalization group flow of the coarse-grained theory on the boundary. Our analysis highlights the precise and simple link between the stochastic formalism and the semi-classical wavefunction., Comment: 59 pages, 5 figures; v2: published version with minor revisions and references added

We revisit the connection between relativistic orbital precession, the Laplace-Runge-Lenz symmetry, and the $t$-channel discontinuity of scattering amplitudes. Applying this to scalar-tensor theories of gravity, we compute the conservative potential and orbital precession induced by both conformal/disformal-type couplings at second Post-Minkowskian order ($\mathcal{O} \left( G_N^2 \right)$), complementing the known third/first order Post-Newtonian results. There is a particular tuning of the conformal coupling for which the precession vanishes at leading PN order, and we show that this coincides with the emergence of a Laplace-Runge-Lenz symmetry and a corresponding soft behaviour of the amplitude. While a single scalar field inevitably breaks this symmetry at higher PN orders, certain supersymmetric extensions have recently been shown to have an exact Laplace-Runge-Lenz symmetry and therefore classical orbits do not precess at any PN order. This symmetry can be used to relate scattering amplitudes at different loop orders, and we show how this may be used to bootstrap the (classically relevant part of the) three-loop $2 \to 2$ scattering of charged black holes in $\mathcal{N}=8$ supergravity from existing two-loop calculations., Comment: 34 pages + 4 Appendices

The impact of light scalars coupled conformally and disformally to matter on the geodetic and frame-dragging (FD) precessions is calculated. For larger frequencies the disformal interaction becomes increasingly relevant. We use several satellite experiments and Pulsar time of arrival (ToA) measurements to derive bounds on the couplings, combining the Gravity Probe B, LARES, LAGEOS and GRACE results with pulsar timings. Forecasts for future constraints on the conformal and the disformal couplings based on the GINGER experiment, i.e. a future measurement of the Sagnac effect on Earth, the motion of S-stars around the galactic centre and future pulsar timing observations are presented., Comment: 14 pages; Accepted in Phys Rev D

Pulsar Timing constraints on scalar-tensor theories with conformal and disformal couplings to matter are discussed. Reducing the dynamics to the motion in the centre of mass frame and using the mean anomaly parametrisation, we find the first post-Newtonian corrections induced by the conformal and disformal interactions in the form of a generalized quasi-Keplerian solution. We also derive the radiation reaction force due to scalar radiation and the corresponding Post-Keplerian Parameters (PKP). We use different pulsar time of arrival (TOA) data sets to probe the scalar corrections to the PKP. In particular, we focus on systems with large orbital frequencies as the contributions to the PKP terms induced by the disformal coupling are sensitive to higher frequencies. We find that the most constraining { {pulsar timings}} are PSR B1913+16 and the double pulsar PSR J0737-3039A/B, being {{of the order of}} the Cassini bound on the conformal coupling obtained from the Shapiro effect in the solar system. { {The combined constraints using other pulsar timings give an upper bound on the conformal coupling $\beta^2 < 2.33 \cdot 10^{-5}$ and a lower bound on the disformal coupling scale of $\Lambda \geq 1.12 \ {\rm MeV}$ which is comparable to the Cassini bound and to the GW-170817 constraints respectively}}. Future measurements for pulsar timing with black hole companions are also discussed., Comment: 17 pages, 9 figures, Accepted in Phys. Rev. D

We compute bounds and forecasts on screened modified gravity theories, specialising to the chameleon model in Casimir force experiments. In particular, we investigate the classical interaction between a plate and sphere subject to a screened interaction of the chameleon type. We compare numerical simulations of the field profile and the classical pressure exerted on the sphere to analytical approximations for these non-linear field theories. In particular, we focus on the proximity force approximation (PFA) and show that, within the range of sphere sizes $R$ and plate-sphere distance $D$ simulated numerically, the PFA does not reproduce the numerical results. This differs from the case of linear field theories such as Newtonian gravity and a Yukawa model where the PFA coincides with the exact results. We show that for chameleon theories, the screening factor approximation (SFA) whereby the sphere is modelled as a screened sphere embedded in the external field due to the plates, fares better and can be used in the regime $D\gtrsim R$ to extract constraints and forecasts from existing and forthcoming data. In particular, we forecast that future Casimir experiments would corroborate the closing of the parameter space for the simplest of chameleon models at the dark energy scale., Comment: 27 pages, 6 figures

Future Gaia and Legacy Survey of Space and Time data releases, together with wide area spectroscopic surveys, will deliver large samples of resolved binary stars with phase space coordinates, albeit with low-cadence. Given an eccentricity law $f(\epsilon)$, we derive properties of (i) the velocity distribution $v/\sqrt{G M/r}$ normalised by the value for a circular orbit at the measured separation $r$; (ii) the astrometric acceleration distributions $a/\left(G M/r^2\right)$ again normalised to the circular orbit value. Our formulation yields analytic predictions for the full statistical distribution for some commonly used eccentricity laws, if the timescale of data-sampling is comparable to or exceeds the binary period. In particular, the velocity distribution for the linear eccentricity law is surprisingly simple. With Bayesian analysis, we suggest a method to infer the eccentricity distribution based on the measured velocity distribution., Comment: 6 figures; 6 pages

We compute bounds on screened scalar field theories from hydrogen-like systems. New light scalar fields generically have a direct coupling to matter. Such a coupling is strongly constrained by myriad experimental measurements. However, certain theories possess a {\it screening mechanism} that allows the effects of this coupling to weaken dynamically, and to evade many such bounds. We compute the perturbations to the energy levels of hydrogen-like systems due to screened scalar fields. We then use this result in two ways. First, we compute bounds from hydrogen spectroscopy, finding significantly weaker bounds than have been reported before as screening effects were overlooked. Second, we show that muonium is an intrinsically much more sensitive probe of screened scalar fields. For chameleon models, muonium experiments probe a large part of the parameter space that is as yet unexplored by low energy physics and has so far only been tested by high-energy particle physics experiments., Comment: 20 pages, 3 figures

In this paper we will list a few important goals that need to be addressed in the next decade, also taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant $H_0$, the $\sigma_8$--$S_8$ tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the $5.0\,\sigma$ tension between the {\it Planck} CMB estimate of the Hubble constant $H_0$ and the SH0ES collaboration measurements. After showing the $H_0$ evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the {\it Planck} CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density $\Omega_m$, and the amplitude or rate of the growth of structure ($\sigma_8,f\sigma_8$). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the $H_0$--$S_8$ tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals.[Abridged], Comment: Contribution to Snowmass 2021. 224 pages, 27 figures. Accepted for publication in JHEAp

High accuracy proper motions (PMs) of M31 and other Local Group satellites have now been provided by the {\it Gaia} satellite. We revisit the Timing Argument to compute the total mass $M$ of the Local Group from the orbit of the Milky Way and M31, allowing for the Cosmological Constant. We rectify for a systematic effect caused by the presence of the Large Magellanic Cloud (LMC). The interaction of the LMC with the Milky Way induces a motion towards the LMC. This contribution to the measured velocity of approach of the Milky Way and M31 must be removed. We allow for cosmic bias and scatter by extracting correction factors tailored to the accretion history of the Local Group. The distribution of correction factors is centered around $0.63$ with a scatter $\pm 0.2$, indicating that the Timing Argument significantly overestimates the true mass. Adjusting for all these effects, the estimated mass of the Local Group is $ M = 3.4^{+1.4}_{-1.1} \times 10^{12} M_{\odot}$ (68 % CL) when using the M31 tangential velocity $ 82^{+38}_{-35}$ km/s. Lower tangential velocity models with $59^{+42}_{-38}$ km/s (derived from the same PM data with a flat prior on the tangential velocity) lead to an estimated mass of $ M = 3.1^{+1.3}_{-1.0} \times 10^{12} M_{\odot}$ (68 % CL). By making an inventory of the total mass associated with the 4 most substantial LG members (the Milky Way, M31, M33 and the LMC), we estimate the known mass is in the range $3.7^{+0.5}_{-0.5} \times 10^{12} \, M_{\odot}$., Comment: Accepted in ApjL. Only minor textual changes in this version

It is becoming increasingly clear that large but rare fluctuations of the primordial curvature field, controlled by the tail of its probability distribution, could have dramatic effects on the current structure of the universe -- {\it e.g.} via primordial black-holes. However, the use of standard perturbation theory to study the evolution of fluctuations during inflation fails in providing a reliable description of how non-linear interactions induce non-Gaussian tails. Here, we use the stochastic inflation formalism to study the non-perturbative effects from multi-field fluctuations on the statistical properties of the primordial curvature field. Starting from the effective action describing multi-field fluctuations, we compute the joint probability density function and show that enhanced non-Gaussian tails are a generic feature of slow-roll inflation with additional degrees of freedom., Comment: 32 pages + appendices, 4 figures

We show how light scalar fields can account for the discrepancy between the theoretical and observed values of the anomalous magnetic moment of the (anti)muon. When coupled to both matter and photons, light scalar fields induce a change of the anomalous magnetic moment of charged particles. This arises from two concurrent effects. Classically, light scalars induce a change of the cyclotron frequency, complementing the electromagnetic effects coming from the magnetic and electric fields used experimentally. Light scalars also contribute to the anomalous magnetic moment quantum mechanically at the one-loop level. For unscreened scalar fields coupling with a Yukawa interaction to matter, these contributions are negligible after applying the Cassini bound on deviations from Newtonian gravity. On the other hand, screened scalars such as chameleons or symmetrons can couple strongly to matter in the laboratory and decouple in the Solar System. This allows us to probe branches of their parameter spaces where the recently measured anomalous magnetic moment of the (anti)muon can be accounted for in the chameleon and symmetron cases. This might be a hint that modified gravity is at play in the laboratory., Comment: 38 pages, 6 figures. Accepted for publication in PRD

We investigate scalar-tensor theories, motivated by dark energy models, in the strong gravity regime around the black hole at the centre of our galaxy. In such theories general relativity is modified since the scalar field couples to matter. We consider the most general conformal and disformal couplings of the scalar field to matter to study the orbital behavior of the nearby stars around the galactic star center $Sgr A^{*}$. Markov Chain Monte Carlo (MCMC) simulation yields a bound on the parameters of the couplings of the scalar field to matter. Using Bayesian Analysis yields the first constraints on such theories in the strong gravity regime., Comment: 10 pages; To appear in Phys Rev D

Gravitational waves provide us with a new window into our Universe, and have already been used to place strong constrains on the existence of light scalar fields, which are a common feature in many alternative theories of gravity. However, spin effects are still relatively unexplored in this context. In this work, we construct an effective point-particle action for a generic spinning body that can couple both conformally and disformally to a real scalar field, and we show that requiring the existence of a self-consistent solution automatically implies that if a scalar couples to the mass of a body, then it must also couple to its spin. We then use well-established effective field theory techniques to conduct a comprehensive study of spin-orbit effects in binary systems to leading order in the post-Newtonian (PN) expansion. Focusing on quasicircular nonprecessing binaries for simplicity, we systematically compute all key quantities, including the conservative potential, the orbital binding energy, the radiated power, and the gravitational-wave phase. We show that depending on how strongly each member of the binary couples to the scalar, the spin-orbit effects that are due to a conformal coupling first enter into the phase at either 0.5PN or 1.5PN order, while those that arise from a disformal coupling start at either 3.5PN or 4.5PN order. This suppression by additional PN orders notwithstanding, we find that the disformal spin-orbit terms can actually dominate over their conformal counterparts due to an enhancement by a large prefactor. Accordingly, our results suggest that upcoming gravitational-wave detectors could be sensitive to disformal spin-orbit effects in double neutron star binaries if at least one of the two bodies is sufficiently scalarised., Comment: 57 pages + appendices, 8 figures, 5 tables. v2: Version accepted for publication. Some minor clarifications added compared to v1

Low-energy effective field theories containing a light scalar field are used extensively in cosmology, but often there is a tension between embedding such theories in a healthy UV completion and achieving a phenomenologically viable screening mechanism in the IR. Here, we identify the range of interaction couplings which allow for a smooth resummation of classical non-linearities (necessary for kinetic/Vainshtein-type screening), and compare this with the range allowed by unitarity, causality and locality in the underlying UV theory. The latter region is identified using positivity bounds on the $2\to2$ scattering amplitude, and in particular by considering scattering about a non-trivial background for the scalar we are able to place constraints on interactions at all orders in the field (beyond quartic order). We identify two classes of theories can both exhibit screening and satisfy existing positivity bounds, namely scalar-tensor theories of $P(X)$ or quartic Horndeski type in which the leading interaction contains an odd power of $X$. Finally, for the quartic DBI Galileon (equivalent to a disformally coupled scalar in the Einstein frame), the analogous resummation can be performed near two-body systems and imposing positivity constraints introduces a non-perturbative ambiguity in the screened scalar profile. These results will guide future searches for UV complete models which exhibit screening of fifth forces in the IR., Comment: 34+12 pages, 6 figures

General Relativity and the $\Lambda$CDM framework are currently the standard lore and constitute the concordance paradigm. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology the last two decades, offer the motivation and lead a large amount of research to be devoted in constructing various extensions and modifications. All extended theories and scenarios are first examined under the light of theoretical consistency, and then are applied to various geometrical backgrounds, such as the cosmological and the spherical symmetric ones. Their predictions at both the background and perturbation levels, and concerning cosmology at early, intermediate and late times, are then confronted with the huge amount of observational data that astrophysics and cosmology are able to offer recently. Theories, scenarios and models that successfully and efficiently pass the above steps are classified as viable and are candidates for the description of Nature. This work is a Review of the recent developments in the fields of gravity and cosmology, presenting the state of the art, high-lighting the open problems, and outlining the directions of future research. Its realization was performed in the framework of the COST European Action ``Cosmology and Astrophysics Network for Theoretical Advances and Training Actions''., Comment: 543 pages

We explore the prospects for direct detection of dark energy by current and upcoming terrestrial dark matter direct detection experiments. If dark energy is driven by a new light degree of freedom coupled to matter and photons then dark energy quanta are predicted to be produced in the Sun. These quanta free-stream towards Earth where they can interact with Standard Model particles in the detection chambers of direct detection experiments, presenting the possibility that these experiments could be used to test dark energy. Screening mechanisms, which suppress fifth forces associated with new light particles, and are a necessary feature of many dark energy models, prevent production processes from occurring in the core of the Sun, and similarly, in the cores of red giant, horizontal branch, and white dwarf stars. Instead, the coupling of dark energy to photons leads to production in the strong magnetic field of the solar tachocline via a mechanism analogous to the Primakoff process. This then allows for detectable signals on Earth while evading the strong constraints that would typically result from stellar probes of new light particles. As an example, we examine whether the electron recoil excess recently reported by the XENON1T collaboration can be explained by chameleon-screened dark energy, and find that such a model is preferred over the background-only hypothesis at the $2.0\sigma$ level, in a large range of parameter space not excluded by stellar (or other) probes. This raises the tantalizing possibility that XENON1T may have achieved the first direct detection of dark energy. Finally, we study the prospects for confirming this scenario using planned future detectors such as XENONnT, PandaX-4T, and LUX-ZEPLIN., Comment: 24 pages, 5 figures. v3: included discussions on screening and propagation of dark energy quanta, added Table summarizing how screening is evaded in other stellar objects. Version accepted for publication in PRD. Cartoon version of our main results available in the source files. Code publicly available at https://github.com/lucavisinelli/XENONCHAM

We launch a first investigation into how a light scalar field coupled both conformally and disformally to matter influences the evolution of spinning point-like bodies. Working directly at the level of the equations of motion, we derive novel spin-orbit and spin-spin effects accurate to leading order in a nonrelativistic and weak-field expansion. Crucially, unlike the spin-independent effects induced by the disformal coupling, which have been shown to vanish in circular binaries due to rotational symmetry, the spin-dependent effects we study here persist even in the limit of zero eccentricity, and so provide a new and qualitatively distinct way of probing these kinds of interactions. To illustrate their potential, we confront our predictions with spin-precession measurements from the Gravity Probe B experiment and find that the resulting constraint improves upon existing bounds from perihelion precession by over 5 orders of magnitude. Our results therefore establish spin effects as a promising window into the disformally coupled dark sector., Comment: 22 pages + an appendix, 3 figures. v2: Version accepted for publication. Typos in Table 1, Eq. (3.21), and Eq. (3.26) have been corrected

Developing our understanding of how correlations evolve during inflation is crucial if we are to extract information about the early Universe from our late-time observables. To that end, we revisit the time evolution of scalar field correlators on de Sitter spacetime in the Schrodinger picture. By direct manipulation of the Schrodinger equation, we write down simple "equations of motion" for the coefficients which determine the wavefunction. Rather than specify a particular interaction Hamiltonian, we assume only very basic properties (unitarity, de Sitter invariance and locality) to derive general consequences for the wavefunction's evolution. In particular, we identify a number of "constants of motion": properties of the initial state which are conserved by any unitary dynamics. We further constrain the time evolution by deriving constraints from the de Sitter isometries and show that these reduce to the familiar conformal Ward identities at late times. Finally, we show how the evolution of a state from the conformal boundary into the bulk can be described via a number of "transfer functions" which are analytic outside the horizon for any local interaction. These objects exhibit divergences for particular values of the scalar mass, and we show how such divergences can be removed by a renormalisation of the boundary wavefunction - this is equivalent to performing a "Boundary Operator Expansion" which expresses the bulk operators in terms of regulated boundary operators. Altogether, this improved understanding of the wavefunction in the bulk of de Sitter complements recent advances from a purely boundary perspective, and reveals new structure in cosmological correlators., Comment: 63 pages + 2 appendices, 4 figures

The symmetron is a typical example of screened modified gravity, wherein the symmetron force is dynamically suppressed in dense environments. This allows it to hide in traditional tests of gravity. However, the past decade has seen great experimental progress towards measuring screened forces in the laboratory or in space. Screening relies on nonlinearities in the equation of motion, which significantly complicates the theoretical analysis of such forces. Here, we present a calculation of the symmetron force between a dense plate and sphere surrounded by vacuum. This is done via semi-analytical approaches in two limiting cases, based on the size of the sphere: large spheres are analyzed via the proximity force approximation, whilst small spheres are treated as screened test particles. In the intermediate regime we solve the problem numerically. Our results allow us to make contact with Casimir force experiments, which often employ a plate and sphere configuration for practical reasons, and may therefore be used to constrain symmetrons. We use our results to forecast constraints on the symmetron's parameters for a hypothetical Casimir experiment that is based on the current state of the art. The forecasts compare favorably to other leading laboratory tests of gravity, particularly atom interferometry and bouncing neutrons. We thus conclude that near-future Casimir experiments will be capable of placing tight new bounds on symmetrons. Our results for the symmetron force are derived in a scale-invariant way, such that although we here focus on Casimir experiments, they may be applied to any other plate-sphere system, ranging from microscopic to astrophysical scales., Comment: 16 pages, 8 figures

We consider the implications of the swampland conjectures on scalar-tensor theories defined in the Einstein frame in which the scalar interaction is screened. We show that chameleon models are not in the swampland provided the coupling to matter is larger than unity and the mass of the scalar field is much larger than the Hubble rate. We apply these conditions to the inverse power law chameleon and the symmetron. We then focus on the dilaton of string theory in the strong coupling limit, as defined in the string frame. We show that solar system tests of gravity imply that viable dilaton models are not in the swampland. In the future of the Universe, if the low energy description with a single scalar is still valid and the coupling to matter remains finite, we find that the scalar field energy density must vanish for models with the chameleon and symmetron mechanisms. Hence in these models dark energy is only a transient phenomenon. This is not the case for the strongly coupled dilaton, which keeps evolving slowly, leading to a quasi de Sitter space-time., Comment: 24 pages

When augmenting our cosmological models or gravitational theories with an additional light scalar field, any coupling between matter and this scalar can affect the orbital motion of binary systems. Ordinarily, the new force mediated by the scalar can be naturally the same order of magnitude as the usual gravitational force and therefore is tightly constrained. We show that a disformal coupling between the scalar and matter can lead to a novel screening mechanism in which these fifth forces are suppressed by several orders of magnitude at sufficiently small separations and large relative velocities (such as solar system scales). This is a result of resumming a class of ladder diagrams, which suppresses the propagation of scalar signals between the two bodies. Moreover, we are able to relate potential ambiguities in this resummation to non-perturbative effects (which are invisible to perturbation theory). As a result, solar system tests and future gravitational wave observations can now be used to place meaningful constraints on scalar-tensor theories with disformal couplings. We exemplify this using observational bounds on the precession of planetary orbits., Comment: 42 pages, 6 figures, 1 appendix

In chameleon $f(R)$-gravity, the fifth force will lead to `upturns' in galaxy rotation curves near the screening radius. The location of the upturn depends on the cosmic background value of the scalar field $f_{R0}$, as well as the mass, size and environment of the galaxy. We search for this signature of modified gravity in the SPARC sample of measured rotation curves, using an MCMC technique to derive constraints on $f_{R0}$. Assuming NFW dark matter haloes and with $f_{R0}$ freely varying for each galaxy, most galaxies prefer $f(R)$ gravity to $\Lambda$CDM, but there is a large spread of inferred $f_{R0}$ values, inconsistent with a single global value. Requiring instead a consistent $f_{R0}$ value for the whole sample, models with $\log_{10}|f_{R0}| > -6.1$ are excluded. On the other hand, models in the range $-7.5<\log_{10}|f_{R0}|<-6.5$ seem to be favoured with respect to $\Lambda$CDM, with a significant peak at -7. However, this signal is largely a result of galaxies for which the $f(R)$ signal is degenerate with the core/cusp problem, and when the NFW profile is replaced with a cored halo profile, $\Lambda$CDM gives better fits than any given $f(R)$ model. Thus, we find no convincing evidence of $f(R)$ gravity down to the level of $|f_{R0}| \sim 6 \times 10^{-8}$, with the caveat that if cored halo density profiles cannot ultimately be explained within $\Lambda$CDM, a screened modified gravity theory could possibly provide an alternative solution for the core/cusp problem. However, the $f(R)$ models studied here fall short of achieving this., Comment: Updated to match version accepted by MNRAS. 19 pages, 11 figures (inc. appendix). All code and plotting scripts are publicly available

While no-hair theorems forbid isolated black holes from possessing permanent moments beyond their mass, electric charge, and angular momentum, research over the past two decades has demonstrated that a black hole interacting with a time-dependent background scalar field will gain an induced scalar charge. In this paper, we study this phenomenon from an effective field theory (EFT) perspective. We employ a novel approach to constructing the effective point-particle action for the black hole by integrating out a set of composite operators localized on its worldline. This procedure, carried out using the in-in formalism, enables a systematic accounting of both conservative and dissipative effects associated with the black hole's horizon at the level of the action. We show that the induced scalar charge is inextricably linked to accretion of the background environment, as both effects stem from the same parent term in the effective action. The charge, in turn, implies that a black hole can radiate scalar waves and will also experience a "fifth force." Our EFT correctly reproduces known results in the literature for massless scalars, but now also generalizes to massive real scalar fields, allowing us to consider a wider range of scenarios of astrophysical interest. As an example, we use our EFT to study the early inspiral of a black hole binary embedded in a fuzzy dark matter halo., Comment: 18 pages + appendices, 5 figures. v2: Minor clarifications added and several typos fixed

We show how a nearly massless scalar field conformally and disformally coupled to matter can affect the dynamics of two bodies in their inspiralling phase before merging. We discuss both the conservative dynamics, e.g. how the energy of the bound system is corrected by the conformal and disformal interactions, and the dissipative part where scalars and gravitons are emitted. The first disformal correction to the Einstein-Infeld-Hoffmann Lagrangian is obtained using both the Fokker method relying on the equations of motion and an Effective Field Theory approach using Feynman diagrams. This leads to a correction to the energy functional at the 2PN level for eccentric orbits, which vanishes for circular orbits up to the 7PN order. The dissipative power from the disformal interaction gives a correction to the monopole and quadrupole terms in the presence of a conformal coupling. Although this correction vanishes for circular orbits at leading order, this is not the case for elliptical orbits allowing us to derive a bound on the disformal coupling from the time drift of the period for the Hulse-Taylor binary pulsar, which is slightly stronger than the one from fifth force tests. We conclude that the prospect of observing disformal effects for inspiralling systems lies in the accurate monitoring of eccentric trajectories as expected for the LISA experiment., Comment: 24 pages, 3 figures

We consider how a nearly massless scalar field conformally and disformally coupled to matter can affect the dynamics of gravitationally interacting bodies. We focus on the case of two interacting objects and we obtain the effective metric driving the dynamics of the two body system when reduced to one body in the centre of mass frame. We then concentrate on the case of a light particle in the scalar and gravitational fields generated by a heavy object and find the effects of the conformal and disformal couplings on the body's trajectory such as the advance of perihelion and the Shapiro time delay. The disformal coupling leads to a negligible contribution to the Shapiro effect and therefore no constraint from the Cassini experiment. On the other hand, it contributes to the perihelion advance leading to a weak bound on the strength of the disformal coupling itself. Finally, we remark that the disformal coupling gives rise to a contribution to the perihelion advance which varies quadratically with the mass of the heavy body, leading to possible strong effects for stars in the vicinity of astrophysical black holes. For neutron stars in a binary system, the disformal effects vary as the quartic power of the size of the orbit which might lead to interesting consequences in the inspiralling phase prior to a merger., Comment: 26 pages, to appear in PRD

In holographic inflation, the $4D$ cosmological dynamics is postulated to be dual to the renormalization group flow of a $3D$ Euclidean conformal field theory with marginally relevant operators. The scalar potential of the $4D$ theory ---in which inflation is realized--- is highly constrained, with use of the Hamilton--Jacobi equations. In multi-field holographic realizations of inflation, fields additional to the inflaton cannot display underdamped oscillations (that is, their wavefunctions contain no oscillatory phases independent of the momenta). We show that this result is exact, independent of the number of fields, the field space geometry and the shape of the inflationary trajectory followed in multi-field space. In the specific case where the multi-field trajectory is a straight line or confined to a plane, it can be understood as the existence of an upper bound on the dynamical masses $m$ of extra fields of the form $m \leq 3 H / 2$ up to slow roll corrections. This bound corresponds to the analytic continuation of the well known Breitenlohner--Freedman bound found in AdS spacetimes in the case when the masses are approximately constant. The absence of underdamped oscillations implies that a detection of "cosmological collider" oscillatory patterns in the non-Gaussian bispectrum would not only rule out single field inflation, but also holographic inflation or any inflationary model based on the Hamilton--Jacobi equations. Hence, future observations have the potential to exclude, at once, an entire class of inflationary theories, regardless of the details involved in their model building., Comment: References added. Discussion expanded to include arbitrary number of fields. Matches published version in PRL

Current constraints on gravity are relatively weak on galactic and intergalactic scales. Screened modified gravity models can exhibit complex behaviour there without violating stringent tests of gravity within our Solar System. They might hence provide viable extensions of the theory of gravity. Here, we use galaxy kinematics to constrain screened modified gravity models. We focus on chameleon $f(R)$ gravity and predict its impact on galaxy rotation curves and radial acceleration relations. This is achieved by post-processing state-of-the-art galaxy formation simulations from the \textsc{auriga project}, using the \textsc{mg-gadget} code. For a given galaxy, the surface dividing screened and un-screened regions adopts an oblate shape, reflecting the disc morphology of the galaxy's mass distribution. At the `screening radius'---the radius at which screening is triggered in the disc plane---characteristic `upturns' are present in both rotation curves and radial acceleration relations. The locations of these features depend on various factors, such as the galaxy mass, the concentration of the density profile and the value of the background field amplitude $f_{R0}$. Self-screening of stars and environmental screening also play a role. For Milky Way-size galaxies, we find that a model with $|f_{R0}|=10^{-7}$ results in rotation curves that are indistinguishable from $\Lambda$CDM, while for $|f_{R0}| \geq 2 \times 10^{-6}$ the simulated galaxies are entirely unscreened, violating Solar System constraints. For intermediate values, distinct upturns are present. With a careful statistical analysis of existing samples of observed rotation curves, including lower mass objects, constraints on $f(R)$ gravity with a sensitivity down to $|f_{R0}|\sim10^{-7}$ should be possible., Comment: 16 pages, 11 figures. Accepted for publication in MNRAS

We study the implications of the recent detection of gravitational waves emitted by a pair of merging neutron stars and their electromagnetic counterpart, events GW170817 and GRB170817A, on the viability of the doubly coupled bimetric models of cosmic evolution, where the two metrics couple directly to matter through a composite, effective metric. We demonstrate that the bounds on the speed of gravitational waves place strong constraints on the doubly coupled models, forcing either the two metrics to be proportional at the background level or the models to become singly coupled. Proportional backgrounds are particularly interesting as they provide stable cosmological solutions with phenomenologies equivalent to that of $\Lambda$CDM at the background level as well as for linear perturbations, while nonlinearities are expected to show deviations from the standard model., Comment: 21 pages in two-column format, 7 figures. V2: matches published version

Chameleon and symmetron theories serve as archetypal models for how light scalar fields can couple to matter with gravitational strength or greater, yet evade the stringent constraints from classical tests of gravity on Earth and in the Solar System. In this work, we investigate how a precision measurement of the electron magnetic moment places meaningful constraints on both chameleons and symmetrons. Two effects are identified: First, virtual chameleons and symmetrons run in loops to generate quantum corrections to the intrinsic value of the magnetic moment; a common process widely considered in the literature for many scenarios beyond the Standard Model. A second effect, however, is unique to scalar fields that exhibit screening. A scalar bubblelike profile forms inside the experimental vacuum chamber and exerts a fifth force on the electron, leading to a systematic shift in the experimental measurement. In quantifying this latter effect, we present a novel approach that combines analytic arguments and a small number of numerical simulations to solve for the bubblelike profile quickly for a large range of model parameters. Taken together, both effects yield interesting constraints in complementary regions of parameter space. While the constraints we obtain for the chameleon are largely uncompetitive with those in the existing literature, this still represents the tightest constraint achievable yet from an experiment not originally designed to search for fifth forces. We break more ground with the symmetron, for which our results exclude a large and previously unexplored region of parameter space. Central to this achievement are the quantum correction terms, which are able to constrain symmetrons with masses in the range $\mu \in [10^{-3.88},10^8]\,\text{eV}$, whereas other experiments have hitherto only been sensitive to 1 or 2 orders of magnitude at a time., Comment: 18 pages + appendices, 12 figures. Abstract abridged for arXiv submission. v2: Minor typos corrected to match PRD version

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., Comment: Instability section updated. Some references added

We consider gravitational waves from the point of view of both their production and their propagation in doubly coupled bigravity in the metric formalism. In bigravity, the two gravitons are coupled by a non-diagonal mass matrix and show birefrigence. In particular, we find that one of the two gravitons propagates with a speed which differs from one. This deviation is tightly constrained by both the gravitational Cerenkov effect and the energy loss of binary pulsars. When emitted from astrophysical sources, the Jordan frame gravitational wave, which is a linear combination of the two propagating gravitons, has a wave form displaying beats. The best prospect of detecting this phenomenon would come from nano-Hertz interferometric experiments., Comment: 19 pages, 1 figure

In a large class of scalar-tensor theories that are potential candidates for dark energy, a nonminimal coupling between the scalar and the photon is possible. The presence of such an interaction grants us the exciting prospect of directly observing dark sector phenomenology in the electromagnetic spectrum. This paper investigates the behavior of one-electron atoms in this class of modified gravity models, exploring their viability as probes of deviations from general relativity in both laboratory and astrophysical settings. Building heavily on earlier studies, our main contribution is threefold: A thorough analysis finds additional fine-structure corrections previously unaccounted for, which now predict a contribution to the Lamb shift that is larger by nearly 4 orders of magnitude. In addition, they also predict a scalar-mediated photon-photon interaction, which now constrains the scalar's coupling to the photon independently of the matter coupling. This was not previously possible with atomic precision tests. Our updated constraints are $\log_{10}\beta_m \lesssim 13.4$ and $\log_{10}\beta_\gamma \lesssim 19.0$ for the matter and photon coupling, respectively, although these remain uncompetitive with bounds from other experiments. Second, we include the effects of the nuclear magnetic moment, allowing for the study of hyperfine structure and the 21 cm line, which hitherto have been unexplored in this context. Finally, we also examine how a background scalar leads to equivalence principle violations., Comment: Minor updates to match PRD version

We consider the scalar field profile around relativistic compact objects such as neutron stars for a range of modified gravity models with screening mechanisms of the chameleon and Damour-Polyakov types. We focus primarily on inverse power law chameleons and the environmentally dependent dilaton as examples of both mechanisms. We discuss the modified Tolman-Oppenheimer-Volkoff equation and then implement a relaxation algorithm to solve for the scalar profiles numerically. We find that chameleons and dilatons behave in a similar manner and that there is a large degeneracy between the modified gravity parameters and the neutron star equation of state. This is exemplified by the modifications to the mass-radius relationship for a variety of model parameters., Comment: 24 pages, 7 figures

Atomic interferometry can be used to probe dark energy models coupled to matter. We consider the constraints coming from recent experimental results on models generalising the inverse power law chameleons such as $f(R)$ gravity in the large curvature regime, the environmentally dependent dilaton and symmetrons. Using the tomographic description of these models, we find that only symmetrons with masses smaller than the dark energy scale can be efficiently tested. In this regime, the resulting constraints complement the bounds from the E\"otwash experiment and exclude small values of the symmetron self-coupling., Comment: 26 pages, 3 figures

We present a novel way to investigate scalar field profiles around black holes with an accretion disc for a range of models where the Compton wavelength of the scalar is large compared to other length scales. By analysing the problem in "Weyl" coordinates, we are able to calculate the scalar profiles for accretion discs in the static Schwarzschild, as well as rotating Kerr, black holes. We comment on observational effects., Comment: 19 pages, 5 figures

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. 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 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. 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 non-trivial mass matrix whose origin follows from the potential term of bigravity. This mixing leads to gravitational birefringence., Comment: 47 pages, 8 figures

In this work we study the role of disformal transformation on cosmological backgrounds and its relation to the speed of sound for tensor modes. A speed different from one for tensor modes can arise in several contexts, such as Galileons theories or massive gravity, nevertheless the speed is very constrained to be one by observations of gravitational wave emission. It has been shown that in inflation a disformal trans- formation allows to set the speed for tensor modes to one without making changes to the curvature power spectrum. Here we show that this invariance does not hold when considering the CMB anisotropy power spectrum. It turns out that the after doing the transformation there is an imprint on the acoustic peaks and the diffusion damping. This has interesting consequences; here we explore quartic galileon theories which allow a modified speed for tensor modes. For these theories the transformation can be used to constraint the parameter space in different regimes.

Modified gravity theories often contain a scalar field of gravitational strength which interacts with matter. We examine constraints on the range and the coupling strength of a scalar gravitational degree of freedom using a subset of current data that can be safely analyzed within the linear perturbation theory. Using a model-independent implementation of scalar-tensor theories in MGCAMB in terms of two functions of the scale factor describing the mass and the coupling of the scalar degree of freedom, we derive constraints on the $f(R)$, generalized chameleon, Symmetron and Dilaton models. Since most of the large scale structure data available today is from relatively low redshifts, only a limited range of observed scales is in the linear regime, leading to relatively weak constraints. We then perform a forecast for a future large scale structure survey, such as Large Synoptic Survey Telescope (LSST), which will map a significant volume at higher redshifts, and show that it will produce much stronger constraints on scalar interactions in specific models. We also perform a principal component analysis and find that future surveys should be able to provide tight constraints on several eigenmodes of the scalar mass evolution., Comment: 15 pages, 13 figures, 4 tables. Uses MGCAMB and CosmoFish codes

We analyse the speed of gravitational waves in coupled Galileon models with an equation of state $\omega_\phi=-1$ now and a ghost-free Minkowski limit. We find that the gravitational waves propagate much faster than the speed of light unless these models are small perturbations of cubic Galileons and the Galileon energy density is sub-dominant to a dominant cosmological constant. In this case, the binary pulsar bounds on the speed of gravitational waves can be satisfied and the equation of state can be close to -1 when the coupling to matter and the coefficient of the cubic term of the Galileon Lagrangian are related. This severely restricts the allowed cosmological behaviour of Galileon models and we are forced to conclude that Galileons with a stable Minkowski limit cannot account for the observed acceleration of the expansion of the universe on their own. Moreover any sub-dominant Galileon component of our universe must be dominated by the cubic term. For such models with gravitons propagating faster than the speed of light, the gravitons become potentially unstable and could decay into photon pairs. They could also emit photons by Cerenkov radiation. We show that the decay rate of such speedy gravitons into photons and the Cerenkov radiation are in fact negligible. Moreover the time delay between the gravitational signal and light emitted by explosive astrophysical events could serve as a confirmation that a modification of gravity acts on the largest scales of the Universe., Comment: 17 pages, 3 figures

Modified gravity models with screening in local environments appear in three different guises: chameleon, K-mouflage and Vainshtein mechanisms. We propose to look for differences between these classes of models by considering cosmological observations at low redshift. In particular, we analyse the redshift dependence of the fine structure constant and the proton to electron mass ratio in each of these scenarios. When the absorption lines belong to unscreened regions of space such as dwarf galaxies, a time variation would be present for chameleons. For both K-mouflage and Vainshtein mechanisms, the cosmological time variation of the scalar field is not suppressed in both unscreened and screened environments, therefore enhancing the variation of constants and their detection prospect. We also consider the time variation of the redshift of distant objects using their spectrocopic velocities. We find that models of the K-mouflage and Vainshtein types have very different spectroscopic velocities as a function of redshift and that their differences with the $\Lambda$-CDM template should be within reach of the future ELT- HIRES observations., Comment: 18 pages, 10 figures

We compute corrections to the inflationary potential due to conformally coupled non-relativistic matter. We find that under certain conditions of the matter coupling, inflation may be interrupted abruptly. We display this in the superconformal Starobinsky model, where matter is conformally coupled to the Einstein frame metric. These corrections may easily stop inflation provided that there is an initial density of non-relativistic matter. Since these additional heavy degrees of freedom generically occur in higher dimension theories, for example as Kaluza-Klein modes, this effect can arise in multiple scenarios., Comment: Matches published version

We investigate laboratory tests of dark energy theories which modify gravity in a way generalising the inverse power law chameleon models. We make use of the tomographic description of such theories which captures $f(R)$ models in the large curvature limit, the dilaton and the symmetron. We consider their effects in various experiments where the presence of a new scalar interaction may be uncovered. More precisely, we focus on the Casimir, Eot-wash and neutron experiments. We show that dilatons, symmetrons and generalised chameleon models are efficiently testable in the laboratory. For generalised chameleons, we revise their status in the light of forthcoming Casimir experiments like CANNEX in Amsterdam and show that they are within reach of detection., Comment: 30 pages, 5 figures

We investigate the cosmological properties of Galileon models with positive kinetic terms. We include both conformal and disformal couplings to matter and focus on constraints on the theory that arise because of these couplings. The disformal coupling to baryonic matter is extremely constrained by astrophysical and particle physics effects. The disformal coupling to photons induces a cosmological variation of the speed of light and therefore distortions of the Cosmic Microwave Background spectrum which are known to be very small. The conformal coupling to baryons leads to a variation of particle masses since Big Bang Nucleosynthesis which is also tightly constrained. We consider the background cosmology of Galileon models coupled to Cold Dark Matter (CDM), photons and baryons and impose that the speed of light and particle masses respect the observational bounds on cosmological time scales. We find that requiring that the equation of state for the Galileon models must be close to -1 now restricts severely their parameter space and can only be achieved with a combination of the conformal and disformal couplings. This leads to large variations of particle masses and the speed of light which are not compatible with observations. As a result, we find that cosmological Galileon models are viable dark energy theories coupled to dark matter but their couplings, both disformal and conformal, to baryons and photons must be heavily suppressed making them only sensitive to CDM., Comment: 23 pages, 9 figures

Scalar field theories that possess a Vainshtein mechanism are able to dynamically suppress the associated fifth forces in the presence of massive sources through derivative non-linearities. The resulting equations of motion for the scalar are highly non-linear and therefore very few analytic solutions are known. Here we present a brief investigation of the structure of Vainshtein screening in symmetrical configurations, focusing in particular on the spherical, cylindrical and planar solutions that are relevant for observations of the cosmic web. We consider Vainshtein screening in both the Galileon model, where the non-linear terms involve second derivatives of the scalar, and a k-essence theory, where the non-linear terms involve only first derivatives of the scalar. We find that screening, and consequently the suppression of the scalar force, is most efficient around spherical sources, weaker around cylindrical sources and can be absent altogether around planar sources., Comment: 11 pages, 1 figure; v2 publication version, minimal changes for clarity