Covariant Galileon Research Articles

Nonlinear power spectrum and forecasts for a generalized cubic covariant Galileon

Nonlinear power spectrum and forecasts for a generalized cubic covariant Galileon

Probing modified gravity with integrated Sachs-Wolfe CMB and galaxy cross-correlations

We use the cross-correlation power spectrum of the integrated Sachs-Wolfe (ISW) effect in the cosmic microwave background (CMB) temperature anisotropy and galaxy fluctuations to probe the physics of late-time cosmic acceleration. For this purpose, we focus on three models of dark energy that belong to a sub-class of Horndeski theories with the speed of gravity equivalent to that of light: Galileon Ghost Condensate (GGC), Generalized Cubic Covariant Galileon (GCCG), and K-mouflage. In the GGC and GCCG models, the existence of cubic-order scalar self-interactions allows a possibility for realizing negative ISW-galaxy cross-correlations, while the K-mouflage model predicts a positive correlation similar to the Λ-cold-dark-matter (ΛCDM) model. In our analysis, we fix the parameters of each model to their best-fit values derived from a baseline likelihood analysis with observational data from CMB, baryon acoustic oscillations, and supernovae type Ia. Then we fit those best-fit models to the ISW-galaxy cross-correlation power spectrum extracted from a collection of photometric redshift surveys. We find that both GGC and GCCG best-fit models degrade the fit to the ISW-galaxy cross-correlation data compared to ΛCDM best-fit model. This is attributed to the fact that, for their best-fit values constrained from the baseline likelihood, the cubic-order scalar self-interaction gives rise to suppressed ISW tails relative to ΛCDM. The K-mouflage best-fit model is largely degenerate with the ΛCDM best-fit model and has a positively correlated ISW-galaxy power close to that of ΛCDM.

Self-tuning kinetic gravity braiding: cosmological dynamics, shift symmetry, and the tadpole

We study the self-tuning subclass of kinetic gravity braiding and obtain robust predictions on self-tuning and dynamics in the tadpole-free shift symmetric sector of the theory. In particular, we show inevitability of cosmic acceleration, prove the dynamical stability of this late-time asymptotic state, and derive ghost and gradient stability constraints on the self-tuning vacuum. We discuss the results concretely in the context of generalized cubic covariant Galileon theory and an exponential kinetic gravity braiding.

Growth of non-linear structures and spherical collapse in the Galileon Ghost Condensate model

We present a detailed study of the collapse of a spherical matter overdensity and the non-linear growth of large scale structures in the Galileon ghost condensate (GGC) model. This model is an extension of the cubic covariant Galileon (G3) which includes a field derivative of type $(\nabla_\mu\phi\nabla^\mu\phi)^2$ in the Lagrangian. We find that the cubic term activates the modifications in the main physical quantities whose time evolution is then strongly affected by the additional term. Indeed, the GGC model shows largely mitigated effects in the linearised critical density contrast, non-linear effective gravitational coupling and the virial overdensity with respect to G3 but still preserves peculiar features with respect to the standard $\Lambda$CDM cosmological model, e.g. both the linear critical density contrast and the virial overdensity are larger than those in $\Lambda$CDM. The results of the spherical collapse model are then used to predict the evolution of the halo mass function, non-linear matter and lensing power spectra. While at low masses the GGC model presents about 10% fewer objects with respect to $\Lambda$CDM, at higher masses for $z>0$ it predicts 10% ($z=0.5$)-20% ($z=1$) more objects per comoving volume. Using a phenomenological approach to include the screening effect in the matter power spectrum, we show that the difference induced by the modifications of gravity are strongly dependent on the screening scale and that differences can be up to 20% with respect to $\Lambda$CDM. These differences translate to the lensing power spectrum where qualitatively the largest differences with respect to the standard cosmological model are for $\ell<10^3$. Depending on the screening scale, they can be up to 25% on larger angular scales and then decrease for growing $\ell$. These results are obtained for the best fit parameters from linear cosmological data for each model.

General constraints on Horndeski wormhole throats

In this work, we consider the full Horndeski Lagrangian applied to wormhole geometries and present the full gravitational field equations. We analyse the general constraints imposed by the flaring-out conditions at the wormhole throat and consider a plethora of specific subclasses of the Horndeski Lagrangian, namely, quintessence/phantom fields, $k$-essence, scalar-tensor theories, covariant galileons, nonminimal kinetic coupling, kinetic gravity braiding, and the scalar-tensor representation of Gauss-Bonnet couplings, amongst others. The generic constraints analysed in this work serve as a consistency check of the main solutions obtained in the literature and draws out new avenues of research in considering applications of specific subclasses of the Horndeski theory to wormhole physics.

Phenomenology of the generalized cubic covariant Galileon model and cosmological bounds

We investigate the generalized cubic covariant Galileon model, a kinetically driven dark energy model within the Horndeski class of theories. The model extends the cubic covariant Galileon by including power laws of the field derivatives in the K-essence and cubic terms which still allow for tracker solutions. We study the shape of the viable parameter space by enforcing stability conditions which include the absence of ghost, gradient and tachyon instabilities and the avoidance of strong coupling at early time. We study here the relevant effects of the modifications induced by the model on some cosmological observables such as the cosmic microwave background (CMB), the lensing potential auto-correlation and the matter power spectrum. For this goal, we perform parameter estimation using data of CMB temperature and polarization, baryonic acoustic oscillations (BAO), redshift-space distortions (RSD), supernovae type Ia (SNIa) and Cepheids. Data analysis with CMB alone finds that the today's Hubble parameter $H_0$ is consistent with its determination from Cepheids at $1\sigma$, resolving the famous tension of the cosmological standard models. The joint analysis of CMB, BAO, RSD and SNIa sets a lower bound for the sum of neutrino masses which is $\Sigma m_\nu >0.11$ eV at 1$\sigma$, in addition to the usual upper limit. The model selection analysis based on the effective $\chi_\text{eff}^2$ and Deviance Information Criterion is not able to clearly identify the statistically favored model between $\Lambda$CDM and the generalized cubic covariant Galileon, from which we conclude that the latter model deserves further studies.

Cosmological data favor Galileon ghost condensate over ΛCDM

We place observational constraints on the Galileon ghost condensate model, a dark energy proposal in cubic-order Horndeski theories consistent with the gravitational-wave event GW170817. The model extends the covariant Galileon by taking an additional higher-order field derivative $X^2$ into account. This allows for the dark energy equation of state $w_{\rm DE}$ to access the region $-2<w_{\rm DE}<-1$ without ghosts. Indeed, this peculiar evolution of $w_{\rm DE}$ is favored over that of the cosmological constant $\Lambda$ from the joint data analysis of cosmic microwave background (CMB) radiation, baryonic acoustic oscillations (BAOs), supernovae type Ia (SNIa) and redshift-space distortions (RSDs). Furthermore, our model exhibits a better compatibility with the CMB data over the $\Lambda$-cold-dark-matter ($\Lambda$CDM) model by suppressing large-scale temperature anisotropies. The CMB temperature and polarization data lead to an estimation for today's Hubble parameter $H_0$ consistent with its direct measurements at 2$\sigma$. We perform a model selection analysis by using several methods and find a statistically significant preference of the Galileon ghost condensate model over $\Lambda$CDM.

Bounds from ISW-galaxy cross-correlations on generalized covariant Galileon models

Several modified cosmological models exist, which also try to address the tensions between data and predictions of the Λ-CDM model. Galileon models are particular scalar tensor theories that represent one such possibility. While it is commonly understood that there may be inconsistencies between predictions of some Galileon models and observations, in particular concerning ISW-galaxy cross-correlations, there is no proof yet that these models are completely ruled out. Indeed, by using a specific background in the generalized covariant Galileon theory known as the the tracker solution, here we show that, after imposing all standard theoretical stability constraints, it is still possible to identify a region in the parameter space of the model that allows for positive ISW-galaxy cross-correlations. By a physical interpretation in terms of a chi-square analysis, we confirm the expectation that in this viable region the predictions of generalized covariant Galileon theory on the tracker solution background have higher likelihood when they approach the physics of the Λ-CDM model.

Galileon and generalized Galileon with projective invariance in a metric-affine formalism

We study scalar-tensor theories respecting the projective invariance in the metric-affine formalism. The metric-affine formalism is a formulation of gravitational theories such that the metric and the connection are independent variables in the first place. In this formalism, the Einstein-Hilbert action has an additional invariance, called the projective invariance, under a shift of the connection. Respecting this invariance for the construction of the scalar-tensor theories, we find that the Galileon terms in curved spacetime are uniquely specified at least up to quartic order which does not coincide with either the covariant Galileon or the covariantized Galileon. We also find an action in the metric-affine formalism which is equivalent to class ${}^2$N-I/Ia of the quadratic degenerated higher order scalar-tensor (DHOST) theory. The structure of DHOST would become clear in the metric-affine formalism since the equivalent action is just linear in the generalized Galileon terms and non-minimal couplings to the Ricci scalar and the Einstein tensor with independent coefficients. The fine-tuned structure of DHOST is obtained by integrating out the connection. In these theories, non-minimal couplings between fermionic fields and the scalar field may be predicted. We discuss possible extensions which could involve theories beyond DHOST.

Do current cosmological observations rule out all covariant Galileons?

We revisit the cosmology of Covariant Galileon gravity in view of the most recent cosmological data sets, including weak lensing. As a higher derivative theory, Covariant Galileon models do not have a $\Lambda$CDM limit and predict a very different structure formation pattern compared with the standard $\Lambda$CDM scenario. Previous cosmological analyses suggest that this model is marginally disfavoured, yet can not be completely ruled out. In this work we use a more recent and extended combination of data, and we allow for more freedom in the cosmology, by including a massive neutrino sector with three different mass hierarchies. We use the Planck measurements of Cosmic Microwave Background temperature and polarization; Baryonic Acoustic Oscillations measurements by BOSS DR12; local measurements of $H_0$; the joint light-curve analysis supernovae sample; and, for the first time, weak gravitational lensing from the KiDS collaboration. We find, that in order to provide a reasonable fit, a non-zero neutrino mass is indeed necessary, but we do not report any sizable difference among the three neutrino hierarchies. Finally, the comparison of the Bayesian Evidence to the $\Lambda$CDM one shows that in all the cases considered, Covariant Galileon models are statistically ruled out by cosmological data.

Comparison of Einstein-Boltzmann solvers for testing general relativity

We compare Einstein-Boltzmann solvers that include modifications to General Relativity and find that, for a wide range of models and parameters, they agree to a high level of precision. We look at three general purpose codes that primarily model general scalar-tensor theories, three codes that model Jordan-Brans-Dicke (JBD) gravity, a code that models f(R) gravity, a code that models covariant Galileons, a code that models Ho\v{r}ava-Lifschitz gravity and two codes that model non-local models of gravity. Comparing predictions of the angular power spectrum of the cosmic microwave background and the power spectrum of dark matter for a suite of different models, we find agreement at the sub-percent level. This means that this suite of Einstein-Boltzmann solvers is now sufficiently accurate for precision constraints on cosmological and gravitational parameters.

Dark Energy After GW170817: Dead Ends and the Road Ahead.

Multimessenger gravitational-wave (GW) astronomy has commenced with the detection of the binary neutron star merger GW170817 and its associated electromagnetic counterparts. The almost coincident observation of both signals places an exquisite bound on the GW speed |c_{g}/c-1|≤5×10^{-16}. We use this result to probe the nature of dark energy (DE), showing that a large class of scalar-tensor theories and DE models are highly disfavored. As an example we consider the covariant Galileon, a cosmologically viable, well motivated gravity theory which predicts a variable GW speed at low redshift. Our results eliminate any late-universe application of these models, as well as their Horndeski and most of their beyond Horndeski generalizations. Three alternatives (and their combinations) emerge as the only possible scalar-tensor DE models: (1)restricting Horndeski's action to its simplest terms, (2)applying a conformal transformation which preserves the causal structure, and (3)compensating the different terms that modify the GW speed (to be robust, the compensation has to be independent on the background on which GWs propagate). Our conclusions extend to any other gravity theory predicting varying c_{g} such as Einstein-Aether, Hořava gravity, Generalized Proca, tensor-vector-scalar gravity (TEVES), and other MOND-like gravities.

The GW170817/GRB 170817A/AT 2017gfo Association: Some Implications for Physics and Astrophysics

Abstract On 2017 August 17, a gravitational-wave event (GW170817) and an associated short gamma-ray burst (GRB 170817A) from a binary neutron star merger had been detected. The follow-up optical/infrared observations also identified the macronova/kilonova emission (AT 2017gfo). In this work, we discuss some implications of the remarkable GW170817/GRB 170817A/AT 2017gfo association. We show that the ∼1.7 s time delay between the gravitational-wave (GW) and GRB signals imposes very tight constraints on the superluminal movement of gravitational waves (i.e., the relative departure of GW velocity from the speed of light is ) or the possible violation of the weak equivalence principle (i.e., the difference of the gamma-ray and GW trajectories in the gravitational field of the galaxy and the local universe should be within a factor of ). The so-called Dark Matter Emulators and a class of contender models for cosmic acceleration (“Covariant Galileon”) are ruled out as well. The successful identification of lanthanide elements in the macronova/kilonova spectrum also excludes the possibility that the progenitors of GRB 170817A are a binary strange star system. The high neutron star merger rate (inferred from both the local sGRB data and the gravitational-wave data) together with the significant ejected mass strongly suggest that such mergers are the prime sites of heavy r-process nucleosynthesis.

Fab Four self-interaction in quantum regime

Quantum behavior of the John Lagrangian from the Fab Four class of covariant Galileons is studied. We consider one-loop corrections to the John interaction due to cubic scalar field interaction. Counter terms are calculated, one appears because of massless scalar field theory infrared issues, another one lies in the George class, and the rest of them can be reduced to the initial Lagrangian up to surface terms. The role of quantum corrections in the context of cosmological applications is discussed.

Cosmological implications of a shift symmetric Galileon field

A ghost-free metric formulation of the recently proposed covariant Galileon model \cite{RPgal} which retains the internal shift symmetry has been constructed. This presents a new result because the covariant Galileon models introduced so far in the literature lacks the full Galileon symmetry. We demonstrate that the same general procedure is applicable to all the Galileon interaction terms and the resulting ghost-free Galileon action respecting internal shift symmetry cannot predict the late time acceleration of the universe. However, weakly breaking the shift symmetry in the covariant Galileon Lagrangian, allows us to include an appropriate potential term which can explain late time acceleration, in accordance with recent findings in the literature.

Hi_class: Horndeski in the Cosmic Linear Anisotropy Solving System

We present the public version of hi_class (www.hiclass-code.net), an extension of the Boltzmann code CLASS to a broad ensemble of modifications to general relativity. In particular, hi_class can calculate predictions for models based on Horndeski's theory, which is the most general scalar-tensor theory described by second-order equations of motion and encompasses any perfect-fluid dark energy, quintessence, Brans-Dicke, f(R) and covariant Galileon models. hi_class has been thoroughly tested and can be readily used to understand the impact of alternative theories of gravity on linear structure formation as well as for cosmological parameter extraction.

No need for dark matter in galaxy clusters within Galileon theory

Modified gravity theories with a screening mechanism have acquired much interest recently in the quest for a viable alternative to General Relativity on cosmological scales, given their intrinsic property of being able to pass Solar System scale tests and, at the same time, to possibly drive universe acceleration on much larger scales. Here, we explore the possibility that the same screening mechanism, or its breaking at a certain astrophysical scale, might be responsible of those gravitational effects which, in the context of general relativity, are generally attributed to Dark Matter. We consider a recently proposed extension of covariant Galileon models in the so-called ``beyond Horndeski'' scenario, where a breaking of the Vainshtein mechanism is possible and, thus, some peculiar observational signatures should be detectable and make it distinguishable from general relativity. We apply this model to a sample of clusters of galaxies observed under the CLASH survey, using both new data from gravitational lensing events and archival data from X-ray intra-cluster hot gas observations. In particular, we use the latter to model the gas density, and then use it as the only ingredient in the matter clusters' budget to calculate the expected lensing convergence map. Results show that, in the context of this extended Galileon, the assumption of having only gas and no Dark Matter at all in the clusters is able to match observations. We also obtain narrow and very interesting bounds on the parameters which characterize this model. In particular, we find that, at least for one of them, the general relativity limit is excluded at 2σ confidence level, thus making this model clearly statistically different and competitive with respect to general relativity.

Gravity at the horizon: on relativistic effects, CMB-LSS correlations and ultra-large scales in Horndeski's theory

We address the impact of consistent modifications of gravity on the largest observable scales, focusing on relativistic effects in galaxy number counts and the cross-correlation between the matter large scale structure (LSS) distribution and the cosmic microwave background (CMB). Our analysis applies to a very broad class of general scalar-tensor theories encoded in the Horndeski Lagrangian and is fully consistent on linear scales, retaining the full dynamics of the scalar field and not assuming quasi-static evolution. As particular examples we consider self-accelerating Covariant Galileons, Brans-Dicke theory and parameterizations based on the effective field theory of dark energy, using the hi class code to address the impact of these models on relativistic corrections to LSS observables. We find that especially effects which involve integrals along the line of sight (lensing convergence, time delay and the integrated Sachs-Wolfe effect—ISW) can be considerably modified, and even lead to O(1000%) deviations from General Relativity in the case of the ISW effect for Galileon models, for which standard probes such as the growth function only vary by O(10%). These effects become dominant when correlating galaxy number counts at different redshifts and can lead to ∼ 50% deviations in the total signal that might be observable by future LSS surveys. Because of their integrated nature, these deep-redshift cross-correlations are sensitive to modifications of gravity even when probing eras much before dark energy domination. We further isolate the ISW effect using the cross-correlation between LSS and CMB temperature anisotropies and use current data to further constrain Horndeski models. Forthcoming large-volume galaxy surveys using multiple-tracers will search for all these effects, opening a new window to probe gravity and cosmic acceleration at the largest scales available in our universe.

Cosmology with a successful Vainshtein screening in theories beyond Horndeski

We propose a dark energy model where a scalar field $\phi$ has nonlinear self-interactions in the presence of a dilatonic coupling with the Ricci scalar. This belongs to a sub-class of theories beyond Horndeski, which accommodates covariant Galileons and Brans-Dicke theories as specific cases. We derive conditions under which the scalar sound speed squared $c_{\rm s}^2$ is positive from the radiation era to today. Since $c_{\rm s}^2$ remains to be smaller than the order of 1, the deviation from Horndeski theories does not cause heavy oscillations of gauge-invariant gravitational potentials. In this case, the evolution of matter perturbations at low redshifts is similar to that in the coupled dark energy scenario with an enhanced gravitational interaction. On the spherically symmetric background with a matter source, the existence of field self-interactions suppresses the propagation of fifth force inside a Vainshtein radius. We estimate an allowed parameter space in which the model can be compatible with solar system constraints while satisfying conditions for the cosmological viability of background and perturbations.

Existence and disappearance of conical singularities in Gleyzes-Langlois-Piazza-Vernizzi theories

In a class of Gleyzes-Langlois-Piazza-Vernizzi theories, we derive both vacuum and interior Schwarzschild solutions under the condition that the derivatives of a scalar field $\ensuremath{\phi}$ with respect to the radius $r$ vanish. If the parameter ${\ensuremath{\alpha}}_{\mathrm{H}}$ characterizing the deviation from Horndeski theories approaches a nonzero constant at the center of a spherically symmetric body, we find that the conical singularity arises at $r=0$ with the Ricci scalar given by $R=\ensuremath{-}2{\ensuremath{\alpha}}_{\mathrm{H}}/{r}^{2}$. This originates from violation of the geometrical structure of four-dimensional curvature quantities. The conical singularity can disappear for the models in which the parameter ${\ensuremath{\alpha}}_{\mathrm{H}}$ vanishes in the limit that $r\ensuremath{\rightarrow}0$. We propose explicit models without the conical singularity by properly designing the classical Lagrangian in such a way that the main contribution to ${\ensuremath{\alpha}}_{\mathrm{H}}$ comes from the field derivative ${\ensuremath{\phi}}^{\ensuremath{'}}(r)$ around $r=0$. We show that the extension of covariant Galileons with a diatonic coupling allows for the recovery of general relativistic behavior inside a so-called Vainshtein radius. In this case, both the propagation of a fifth force and the deviation from Horndeski theories are suppressed outside a compact body in such a way that the model is compatible with local gravity experiments inside the solar system.