Disformal Coupling Research Articles

Gravitational lensing from clusters of galaxies to test disformal couplings theories

In this study, we investigate the potential existence of a non-minimal coupling between dark matter and gravity using a compilation of galaxy clusters. We focus on the disformal scenario of a non-minimal model with an associated coupling length L. Within the Newtonian approximation, this model introduces a modification to the Poisson equation, characterized by a term proportional to L2∇2ρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2 \ abla ^2 \\rho $$\\end{document}, where ρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho $$\\end{document} represents the density of the DM field. We have tested the model by examining strong and weak gravitational lensing data available for a selection of 19 high-mass galaxy clusters observed by the CLASH survey. We have employed a Markov Chain Monte Carlo code to explore the parameter space, and two different statistical approaches to analyse our results: a standard marginalisation and a profile distribution method. Notably, the profile distribution analysis helps out to bypass some volume-effects in the posterior distribution, and reveals lower Navarro–Frenk–White concentrations and masses in the non-minimal coupling model compared to general relativity case. We also found a nearly perfect correlation between the coupling constant L and the standard Navarro–Frenk–White scale parameter rs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_s$$\\end{document}, hinting at a compelling link between these two lengths.

Positivity bounds on Higgs-portal freeze-in dark matter

We consider the relic density and positivity bounds for freeze-in scalar dark matter with general Higgs-portal interactions up to dimension-8 operators. When dimension-4 and dimension-6 Higgs-portal interactions are proportional to mass squares for Higgs or scalar dark matter in certain microscopic models such as massive graviton, radion or general metric couplings with conformal and disformal modes, we can take the dimension-8 derivative Higgs-portal interactions to be dominant for determining the relic density via the 2-to-2 thermal scattering of the Higgs fields after reheating. We discuss the implications of positivity bounds for microscopic models. First, massive graviton or radion mediates attractive forces between Higgs and scalar dark matter and the resultant dimension-8 operators respect the positivity bounds. Second, the disformal couplings in the general metric allow for the subluminal propagation of graviton but violate the positivity bounds. We show that there is a wide parameter space for explaining the correct relic density from the freeze-in mechanism and the positivity bounds can curb out the dimension-8 derivative Higgs-portal interactions nontrivially in the presence of the similar dimension-8 self-interactions for Higgs and dark matter.

Axial and polar stability of neutron stars in scalar-tensor theories with disformal coupling

Axial and polar stability of neutron stars in scalar-tensor theories with disformal coupling

Lensing with Generalized Symmetrons

Generalized symmetrons are models that have qualitatively similar features to the archetypal symmetron, but have barely been studied. In this article, we investigate for what parameter values the fifth forces induced by disformally coupling generalized symmetrons can provide an explanation for the difference between baryonic and lens masses of galaxies. While it is known that the standard symmetron struggles to provide an alternative source for the lensing otherwise attributed to particle dark matter, we show that some generalized symmetron models are more suitable for complying with existing constraints on disformal couplings. This motivates future studies of these only little-explored models.

Stringent pulsar timing bounds on light scalar couplings to matter

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.

Constraining disformal couplings with Redshift Space Distortion

We study a quintessence model for which the scalar field is disformally coupled to dark matter. The background mimics the ΛCDM cosmological evolution and the quintessence potential is not specified. A disformal effect due to the quintessential mass is seen in the growth rate of the cosmological structure on large scales. The disformal parameter renders no appreciable effect on the evolution of the total matter perturbation. An analysis of the conformal parameter and quintessential mass is investigated using the Redshift Space Distortion data to find the best-fit values that might explain the well-known σ 8 tension.

Anisotropic scalar field dark energy with a disformally coupled Yang–Mills field

In the context of scalar–tensor theories, the inclusion of new degrees of freedom coupled nonminimally to the gravitational sector might produce some appealing effects on the cosmic expansion history. We investigate this premise by including a canonical SU(2) Yang–Mills field to the total energy budget of the universe coupled to the standard quintessential field by a disformal transformation.From the dynamical system analysis, we study three cases of cosmological interest that span most of the physical phase space of the model: the uncoupled limit, the isotropic and the Abelian cases. New scaling solutions with a nonvanishing gauge field are found in all cases which can be interesting for early cosmological scenarios. Some of these scaling solutions even exhibit anisotropic features. Also, the background evolution of the universe is studied by means of numerical analysis. As an interesting result, the disformal coupling changes the equation of state of the gauge field from radiation to matter at some stages of the evolution of the universe, thereby the gauge field can contribute to some fraction of the total dark matter. We have also quantified the redshift-dependent contribution of the gauge field in the form of dark radiation during the radiation era to the effective number of relativistic species. This depends essentially on the initial conditions and, more importantly, on the disformal coupling function.

Dark energy interactions near the Galactic Center

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.

Spin-orbit effects for compact binaries in scalar-tensor gravity

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 0.5 PN or 1.5 PN order, while those that arise from a disformal coupling start at either 3.5 PN or 4.5 PN 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.

Disformal couplings in a ΛCDM background cosmology

The coupled quintessence model with disformal couplings is treated here to mimic the ΛCDM background. Using this approach, the quintessence potential does not have to be specified. The model considers a generic fluid coupled to the quintessence, which is specified to be either dark matter or a relativistic fluid. The background consists of a cosmological constant and another uncoupled generic fluid, to cater for three studied scenarios. The cosmological dynamics is investigated for the coupled quintessence model, whose disformal couplings depend on the equation of state of both generic fluids. The scenario, whereby both generic fluids are dark matter, was further analysed for an expansion history of the mimicking model. The analysis confirms that the mass scale of the quintessence influences the disformal characteristics of the dynamical system, which is portrayed by the evolution of an effective conformal coupling.

Spin precession as a new window into disformal scalar fields

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 withspin-precession measurements from the Gravity Probe B experiment andfind that the resulting constraint improves upon existing bounds fromperihelion precession by over 5 orders of magnitude. Our results therefore establish spin effects as a promising window into the disformally coupled dark sector.

Dark D-brane cosmology: From background evolution to cosmological perturbations

We study the cosmological predictions of the dark D-brane model, in which dark matter resides on a D-brane moving in a higher-dimensional space. By construction, dark matter interacts only gravitationally with the standard model sector in this framework. The dark energy scalar field is associated with the position of the D-brane, and its dynamics is encoded in a Dirac-Born-Infeld action. On the other hand, dark matter is identified with matter on the D-brane, that naturally couples to dark energy \textit{via} a disformal coupling. We analyse the numerical evolution of the cosmological background, highlighting the fact that there are two regimes of interest: one, in which the coupling is positive throughout; and another, in which the coupling is negative at the present. In the latter, there is the enticing possibility of having scenarios in which the coupling is positive for a significant part of the evolution, before decreasing towards negative values. In both cases, the coupling is very small at early times, and only starts to grow during the late matter dominated era. We also derive the equations for the linear cosmological perturbations, an expression for the effective time-dependent gravitational coupling between dark matter particles and present the numerical results for the CMB anisotropy and matter power spectra. This allows for a direct comparison of the predictions for the growth of large scale structure with other disformal quintessence models.

Potential-driven inflation with disformal coupling to gravity

In this paper, we investigate the potential-driven inflation models with a disformal coupling to Einstein Gravity, to find out the effects of such a coupling on these models. We consider a simple coupling form which introduces only one parameter, and three inflation models, namely the chaotic inflation, the Higgs inflation, and the monodromy inflation. We find that the disformal coupling can have some modifications to the observational variables of these models such as the power spectrum, the spectral index as well as the tensor/scalar ratio, although not too large due to the constraints on the disformal coupling parameter. With these modifications, one has the opportunity of improving models that lie on the edge of the favorable regions of Planck observational data, such as monodromy inflation. Moreover, the non-trivial sound speed of tensor perturbations (gravitational waves) may come out, due to the coupling of gravity and kinetic terms of the field.

Novel screening with two bodies: summing the ladder in disformal scalar-tensor theories

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.

Dark matter relic density from conformally or disformally coupled light scalars

Thermal freeze-out is a prominent example of dark matter (DM) production mechanism in the early Universe that can yield the correct relic density of stable weakly interacting massive particles (WIMPs). At the other end of the mass scale, many popular extensions of the Standard Model predict the existence of ultralight scalar fields. These can be coupled to matter, preferentially in a universal and shift-symmetry-preserving way. We study the impact of such conformal and disformal couplings on the relic density of WIMPs, without introducing modifications to the thermal history of the Universe. This can either result in an additional thermal contribution to the DM relic density or suppress otherwise too large abundances compared to the observed levels. In this work, we assume that the WIMPs only interact with the standard model via the light scalar portal. We use simple models of fermionic or scalar DM, although a similar discussion holds for more sophisticated scenarios, and predict that their masses should be between $\ensuremath{\sim}100\text{ }\text{ }\mathrm{GeV}$ and several TeV to comply both with the DM abundance and current bounds on the couplings of the light scalars to matter at the LHC. Future searches will tighten these bounds.

Spontaneous vectorization in the presence of vector-field coupling to matter

We examine the possibility of spontaneous vectorization in the vector-tensor theories with the vector conformal and disformal couplings to matter. We study the static and spherically symmetric solutions of the relativistic stars with the nontrivial profile of the vector field satisfying the boundary conditions ${A}_{\ensuremath{\mu}}\ensuremath{\rightarrow}0$ at the spatial infinity, where ${A}_{\ensuremath{\mu}}$ represents the vector field. First, we study the linear perturbations about the general relativistic (GR) stellar solutions with the vanishing vector field ${A}_{\ensuremath{\mu}}=0$. We show that the pure vector disformal coupling causes the ghost or gradient instability of the GR stars, indicating the breakdown of the hyperbolicity on the GR stellar backgrounds. On the other hand, the pure conformal coupling causes the tachyonic instability of the GR solutions and would lead to the spontaneous growth of the vector field toward the nontrivial solutions as in the manner of spontaneous scalarization in the scalar-tensor theories. We then construct the static and spherically symmetric solutions of the relativistic stars with 0 and 1 nodes of the vector field in the presence of the pure disformal coupling. We find that the properties of the solutions with the nontrivial vector field are similar to those of the generalized Proca theories. As in the mass-radius diagram the branches of the 0 and 1 node solutions are disconnected to that of the GR solutions in the lower density regimes, they may be formed from the selected choice of the initial conditions. We also construct the 0 node solutions in the case of the pure conformal coupling, and show that the branch of these solutions is connected to that of the GR solutions in both the low and high density regions and hence would arise spontaneously via the continuous evolution from the GR solutions. Finally, we briefly discuss the combined effects of the conformal and disformal couplings on the nontrivial solutions.

Cosmological attractors to general relativity and spontaneous scalarization with disformal coupling

The canonical scalar-tensor theory model which exhibits spontaneous scalarization in the strong-gravity regime of neutron stars has long been known to predict a cosmological evolution for the scalar field which generically results in severe violations of present-day Solar System constraints on deviations from general relativity. We study if this tension can be alleviated by generalizing this model to include a disformal coupling between the scalar field $\varphi$ and matter, where the Jordan frame metric ${\tilde g}_{\mu\nu}$ is related to the Einstein frame one $g_{\mu\nu}$ by ${\tilde g}_{\mu\nu}=A(\varphi)^2 (g_{\mu\nu}+\Lambda\, \partial_\mu \varphi \, \partial_\nu\varphi)$. We find that this broader theory admits a late-time attractor mechanism towards general relativity. However, the existence of this attractor requires a value of disformal scale of the order $\Lambda\gtrsim H_0^{-2}$, where $H_0$ is the Hubble parameter of today, which is much larger than the scale relevant for spontaneous scalarization of neutron stars $\Lambda \sim R_s^{2}$ with $R_s (\sim 10^{-22} H_0^{-1})$ being the typical radius of these stars. The large values of $\Lambda$ necessary for the attractor mechanism (i) suppress spontaneous scalarization altogether inside neutron stars and (ii) induce ghost instabilities on scalar field fluctuations, thus preventing a resolution of the tension. We argue that the problem arises because our disformal coupling involves a dimensionful parameter.

Generalized disformal coupling leads to spontaneous tensorization

We show that gravity theories involving disformally transformed metrics in their matter coupling lead to spontaneous growth of various fields in a similar fashion to the spontaneous scalarization scenario in scalar-tensor theories. Scalar-dependent disformal transformations have been investigated in this context, and our focus is understanding the transformations that depend on more general fields. We show that vector-dependent disformal couplings can be obtained in various different ways, each leading to spontaneous vectorization as indicated by the instabilities in linearized equations of motion. However, we also show that spontaneous growth is not evident beyond vectors. For example, we could not identify a spontaneous growth mechanism for a spinor field through disformal transformations, even though there is a known example for conformal transformations. This invites further work on the fundamental differences between the two types of metric transformations. We argue that our results are relevant for observations in strong gravity such as gravitational wave detections due to their promise of large deviations from general relativity in this regime.

Limitations on Standard Sirens tests of gravity from screening

Modified gravity theories with an effective Newton constant that varies over cosmological timescales generally predict a different gravitational wave luminosity distance than General Relativity. While this holds for a uniform variation, we show that if locally screened at the source and at the observer as required to pass stringent astrophysical tests of gravity, the General Relativistic distance is restored. In the absence of such a screening, the same effect must modify electromagnetic luminosity distances inferred from supernovae Type Ia, to the extent that the effects can cancel in the comparison. Hence, either the modifications considered employ screening, which leaves no signature in Standard Sirens of a cosmological modification of gravity, or screening does not operate, in which case there can be a signal that is however well below the forseeable sensitivity of the probe when astrophysical bounds are employed. We recover these results both in the Jordan and Einstein frames, paying acute attention to pecularities of each frame such as the notion of redshift or geodesic motions. We emphasise that despite these limitations, Standard Sirens provide valuable independent tests of gravity that differ fundamentally from other probes, a circumstance that is generally important for the wider scope of gravitational modifications and related scenarios. Finally, we use our results to show that the gravitational wave propagation is not affected by dark sector interactions, which restores a dark degeneracy between conformal and disformal couplings that enables observationally viable cosmic self-acceleration to emenate from those.

Cosmic acceleration sourced by modification of gravity without extra degrees of freedom

In this paper, we investigate a scenario in which late-time cosmic acceleration might arise due to coupling between dark matter and baryonic matter without resorting to dark energy or large-scale modification of gravity associated with extra degrees of freedom. The scenario can give rise to late-time acceleration in Jordan frame and no acceleration in Einstein frame — generic modification of gravity caused by disformal coupling. Using a simple parametrization of the coupling function, in maximally disformal case, we constrain the model parameters by using the age constraints due to globular cluster data. We also obtain observational constraints on the parameters using [Formula: see text] datasets. In this case, we distinguish between phantom and non-phantom acceleration and show that the model can give rise to phantom behavior in a narrow region of parameter space.