Local Gravity Constraints Research Articles

Dynamical analysis of coupled curvature-matter scenario in viable f(R) dark energy models at de Sitter phase

We explore the interaction between dark matter and curvature-driven dark energy within viable f(R) gravity models, employing the phase-space analysis approach of linear stability theory. By incorporating an interacting term, denoted as Q=αHρ~m(κ23H2ρcurv+1) , into the continuity equations of both sectors, we examine dynamics of two f(R) gravity models that adhere to local gravity constraints and fulfill cosmological viability criteria. In de Sitter phase, our investigation reveals modifications of critical points compared to the conventional form, attributed to the introduced interaction. Through a comprehensive phase-space analysis, we illustrate the trajectories near critical points and outline the constraints on the phase space based on cosmological and cosmographic parameters. Furthermore, we can also observe stable behavior of this interacting system during the de Sitter phase of the Universe.

Symmetry restoration in the vicinity of neutron stars with a nonminimal coupling

We propose a new model of scalarized neutron stars (NSs) realized by a self-interacting scalar field ϕ nonminimally coupled to the Ricci scalar R of the form F(ϕ)R. The scalar field has a self-interacting potential and sits at its vacuum expectation value ϕv far away from the source. Inside the NS, the dominance of a positive nonminimal coupling over a negative mass squared of the potential leads to a symmetry restoration with the central field value ϕc close to 0. This allows the existence of scalarized NS solutions connecting ϕv with ϕc whose difference is significant, whereas the field is located in the vicinity of ϕ=ϕv for weak gravitational stars. The Arnowitt-Deser-Misner mass and radius of NSs as well as the gravitational force around the NS surface can receive sizable corrections from the scalar hair, while satisfying local gravity constraints in the Solar system. Unlike the original scenario of spontaneous scalarization induced by a negative nonminimal coupling, the catastrophic instability of cosmological solutions can be avoided. We also study the cosmological dynamics from the inflationary epoch to today and show that the scalar field ϕ finally approaches the asymptotic value ϕv without spoiling a successful cosmological evolution. After ϕ starts to oscillate about the potential minimum, the same field can also be the source for cold dark matter.

Cosmology in theories with spontaneous scalarization of neutron stars

In a model of spontaneous scalarization of neutron stars proposed by Damour and Esposito-Farese, a general relativistic branch becomes unstable to trigger tachyonic growth of a scalar field $\ensuremath{\phi}$ toward a scalarized branch. Applying this scenario to cosmology, there is fatal tachyonic instability of $\ensuremath{\phi}$ during inflation and matter dominance being incompatible with solar-system constraints on today's field value ${\ensuremath{\phi}}_{0}$. In the presence of a four-point coupling ${g}^{2}{\ensuremath{\phi}}^{2}{\ensuremath{\chi}}^{2}/2$ between $\ensuremath{\phi}$ and an inflaton field $\ensuremath{\chi}$, it was argued by Anson et al. that a positive mass squared heavier than the square of a Hubble expansion rate leads to the exponential suppression of $\ensuremath{\phi}$ during inflation and that ${\ensuremath{\phi}}_{0}$ can remain small even with the growth of $\ensuremath{\phi}$ after the radiation-dominated epoch. For several inflaton potentials approximated as $V(\ensuremath{\chi})={m}^{2}{\ensuremath{\chi}}^{2}/2$ about the potential minimum, we study the dynamics of $\ensuremath{\phi}$ during reheating as well as other cosmological epochs in detail. For certain ranges of the coupling $g$, the homogeneous field $\ensuremath{\phi}$ can be amplified by parametric resonance during a coherent oscillation of the inflaton. Incorporating the backreaction of created particles under a Hartree approximation, the maximum values of $\ensuremath{\phi}$ reached during preheating are significantly smaller than those obtained without the backreaction. We also find that the minimum values of $g$ consistent with solar system bounds on $\ensuremath{\phi}$ at the end of reheating are of order ${10}^{\ensuremath{-}5}$ and hence there is a wide range of acceptable values of $g$. Thus, the scenario proposed by Anson et al. naturally leads to the viable cosmological evolution of $\ensuremath{\phi}$ consistent with local gravity constraints, without modifying the property of scalarized neutron stars.

Two-parametric f(R) dark energy model and some observational constraints

A modified [Formula: see text] viable model is proposed that behaves asymptotically as [Formula: see text]CDM and satisfies cosmological and local gravity constraints. Apart from a mass scale that is a priori defined, the model contains only one additional parameter, which is determined by the current value of the matter density parameter [Formula: see text]. Under the chameleon mechanism the model satisfies the thin shell restrictions for local gravity systems without imposing additional restrictions on model parameters. Signals of scalar–tensor regime in the growth of matter perturbations, are present. Using the mass scale to determine the matter density parameter today, the remaining free parameter covers the whole range of values needed to test the model against the more stringent constraints arising at galactic and galactic cluster scales. The finite time singularity of the model was analyzed. A comparison was made with known models with the same number of parameters.

Modified gravity with disappearing cosmological constant

New corrections to General Relativity are considered in the context of modified f(R) gravity, that satisfy cosmological and local gravity constraints. The proposed models behave asymptotically as R − 2Λ at large curvature and show the vanishing of the cosmological constant at the flat spacetime limit. The chameleon mechanism and thin shell restrictions for local systems were analyzed, and bounds on the models were found. The steepness of the deviation parameter m at late times leads to measurable signal of scalar-tensor regime in matter perturbations, that allows to detect departures form the ΛCDM model. The theoretical results for the evolution of the weighted growth rate fσ8(z), from the proposed models, were analyzed.

Spontaneous symmetry breaking in the late Universe and glimpses of the early Universe phase transitions à la baryogenesis

Spontaneous symmetry breaking is the foundation of electroweak unification and serves as an integral part of the model building beyond the standard model of particle physics and it also finds interesting applications in the late Universe. We review development related to obtaining the late cosmic acceleration from spontaneous symmetry breaking in the Universe at large scales. This phenomenon is best understood through Ginzburg–Landau theory of phase transitions which we briefly describe. Hereafter, we present elements of spontaneous symmetry breaking in relativistic field theory. We then discuss the “symmetron” scenario-based upon symmetry breaking in the late Universe which is realized by using a specific form of conformal coupling. However, the model is faced with “NO GO” for late-time acceleration due to local gravity constraints. We argue that the problem can be circumvented by using the massless [Formula: see text] theory coupled to massive neutrino matter. As for the early Universe, spontaneous symmetry breaking finds its interesting applications in the study of electroweak phase transition. To this effect, we first discuss in detail the Ginzburg–Landau theory of first-order phase transitions and then apply it to electroweak phase transition including technical discussions on bubble nucleation and sphaleron transitions. We provide a pedagogical exposition of dynamics of electroweak phase transition and emphasize the need to go beyond the standard model of particle physics for addressing the baryogenesis problem. Review ends with a brief discussion on Affleck–Dine mechanism and spontaneous baryogenesis. Appendixes include technical details on essential ingredients of baryogenesis, sphaleron solution, one-loop finite temperature effective potential and dynamics of bubble nucleation.

Cosmological dynamics of interacting dark energy and dark matter in viable models of f(R) gravity

In this work, we investigate the dynamics of the interacting dark energy and dark matter in viable models of $f(R)$ gravity by using a standard framework of dynamical system analysis. A simple form of the interacting dark energy $Q=3\alpha H\rho_{m}$ is used to study three viable models of $f(R)$ gravity which are consistent with local gravity constraints and satisfying conditions for the cosmological viability. As a result, we find that the fixed points are slightly modified from those obtained in the standard non-interacting analysis of $f(R)$ gravity proposed so far in the literature. In our models of adding this interaction, we find that the dynamical profiles of the universe in the viable $f(R)$ dark energy models are modified by the interaction term as well as their relevant model parameters. Moreover, our results yield the correct cosmological evolution with additional constraint parameter, $\alpha$, from the interacting dark energy.

Dark matter as scalaron in f(R) gravity models

We explore the scalar field obtained under the conformal transformation of the spacetime metric gμν from the Jordan frame to the Einstein frame in f(R) gravity. This scalar field is the result of the modification in the gravitational part of the Einstein's general relativistic theory of gravity. For f(R)=R1+δ/Rcδ, we find the effective potential of the scalar field and calculate the mass of the scalar field particle “scalaron”. It is shown that the mass of the scalaron depends upon the energy density of standard matter in the background (in solar system, mϕ∼ 10−16 eV) . The interaction between standard matter and scalaron is weak in the high curvature regime. This linkage between the mass of the scalaron and the background leads to the physical effects of dark matter and is expected to reflect the anisotropic propagation of scalaron in moving baryonic matter fields as in merging clusters (Bullet cluster, the Abell 520 system, MACS etc.). Such scenario also satisfies the local gravity constraints of f(R) gravity. We further calculate the equation of state of the scalar field in the action-angle variable formalism and show its distinct features as the dark matter and dark energy with respect to energy density of the scalar field at different values of the model parameter δ.

Dark matter as scalaron in f(R) gravity models

We explore the scalar field obtained under the conformal transformation of the spacetime metric $g_{\mu\nu}$ from the Jordan frame to the Einstein frame in $f(R)$ gravity. This scalar field is the result of the modification in the gravitational part of the Einstein's general relativistic theory of gravity. For $f(R)=\frac{R^{1+\delta}}{R_{c}^{\delta}}$, we find the effective potential of the scalar field and calculate the mass of the scalar field particle scalaron. It is shown that the mass of the scalaron depends upon the energy density of standard matter in the background. The interaction between standard matter and scalaron is weak in the high curvature regime. This linkage between the mass of the scalaron and the background leads to the physical effects of dark matter and is expected to reflect the anisotropic propagation of scalaron in moving baryonic matter fields as in merging clusters (Bullet cluster, the Abell 520 system, MACS etc.). Such scenario also satisfies the local gravity constraints of $f(R)$ gravity. We further calculate the equation of state of the scalar field in the action-angle variable formalism and show its distinct features as the dark matter and dark energy with respect to energy density of the scalar field at different values of the model parameter $\delta$.

Theoretical study of interaction between matter and curvature fluid in the theory of f(R)-gravity: Diffusion and friction

The relativistic diffusion process and friction have been studied, especially in the framework of [Formula: see text]-gravity theory. The study of relativistic diffusion and friction processes based on [Formula: see text]-gravity is an alternative solution to solve the incompatibility problem emerging in the attempt to couple between the Fokker–Planck equation [FPE] to the Einstein field equation [EFE] encountered by Calogero. The energy–momentum tensor of the cosmological scalar field as proposed by Calogero is replaced by the presence of additional terms in the field equation of [Formula: see text]-gravity. The additional energy–momentum tensor in the field equation of [Formula: see text]-gravity in this context is regarded to compensate for the presence of the diffusion and another process like friction. The additional energy–momentum tensor is also regarded as due to the so-called curvature fluid or background fluid. Here we assume the presence of interaction between matter and the background fluid in the form of physical processes like diffusion, friction, etc. We also assume that there is ‘interplay’ between diffusion process and friction. In other words, the diffusion process and friction are not independent. As examples, we consider some viable models of [Formula: see text] that satisfy both cosmological and local gravity constraints, i.e. [Formula: see text], and [Formula: see text]. Furthermore, we apply it to explain the diffusion and friction processes in the expanding universe by considering the Friedmann–Lemaitre–Robertson–Walker (FLRW) model.

Suppression of matter couplings with a vector field in generalized Proca theories

We derive the profile of a vector field coupled to matter on a static and spherically symmetric background in the context of generalized Proca theories. The cubic Galileon self-interaction leads to the suppression of a longitudinal vector component due to the operation of the Vainshtein mechanism. For quartic and sixth-order derivative interactions, the solutions consistent with those in the continuous limit of small derivative couplings correspond to the branch with the vanishing longitudinal mode. We compute the corrections to gravitational potentials outside a compact body induced by the vector field in the presence of cubic, quartic, and sixth-order derivative couplings, and show that the models can be consistent with local gravity constraints under mild bounds on the temporal vector component. The quintic Galileon interaction does not allow regular solutions of the longitudinal mode for a rapidly decreasing matter density outside the body.

Weakly dynamic dark energy via metric-scalar couplings with torsion

We study the dynamical aspects of dark energy in the context of a non-minimally coupled scalar field with curvature and torsion. Whereas the scalar field acts as the source of the trace mode of torsion, a suitable constraint on the torsion pseudo-trace provides a mass term for the scalar field in the effective action. In the equivalent scalar-tensor framework, we find explicit cosmological solutions representing dark energy in both Einstein and Jordan frames. We demand the dynamical evolution of the dark energy to be weak enough, so that the present-day values of the cosmological parameters could be estimated keeping them within the confidence limits set for the standard LCDM model from recent observations. For such estimates, we examine the variations of the effective matter density and the dark energy equation of state parameters over different redshift ranges. In spite of being weakly dynamic, the dark energy component differs significantly from the cosmological constant, both in characteristics and features, for e.g. it interacts with the cosmological (dust) fluid in the Einstein frame, and crosses the phantom barrier in the Jordan frame. We also obtain the upper bounds on the torsion mode parameters and the lower bound on the effective Brans-Dicke parameter. The latter turns out to be fairly large, and in agreement with the local gravity constraints, which therefore come in support of our analysis.

Screening fifth forces in generalized Proca theories

For a massive vector field with derivative self-interactions, the breaking of the gauge invariance allows the propagation of a longitudinal mode in addition to the two transverse modes. We consider generalized Proca theories with second-order equations of motion in a curved space-time and study how the longitudinal scalar mode of the vector field gravitates on a spherically symmetric background. We show explicitly that cubic-order self-interactions lead to the suppression of the longitudinal mode through the Vainshtein mechanism. Provided that the dimensionless coupling of the interaction is not negligible, this screening mechanism is sufficiently efficient to give rise to tiny corrections to gravitational potentials consistent with solar-system tests of gravity. We also study the quartic interactions with the presence of non-minimal derivative coupling with the Ricci scalar and find the existence of solutions where the longitudinal mode completely vanishes. Finally, we discuss the case in which the effect of the quartic interactions dominates over the cubic one and show that local gravity constraints can be satisfied under a mild bound on the parameters of the theory.

Constraining ƒ(R) Gravity by the Large-Scale Structure

Over the past few decades, general relativity and the concordance ΛCDM model have been successfully tested using several different astrophysical and cosmological probes based on large datasets (precision cosmology). Despite their successes, some shortcomings emerge due to the fact that general relativity should be revised at infrared and ultraviolet limits and to the fact that the fundamental nature of dark matter and dark energy is still a puzzle to be solved. In this perspective, ƒ(R) gravity has been extensively investigated, being the most straightforward way to modify general relativity and to overcame some of the above shortcomings. In this paper, we review various aspects of ƒ(R) gravity at extragalactic and cosmological levels. In particular, we consider a cluster of galaxies, cosmological perturbations and N-body simulations, focusing on those models that satisfy both cosmological and local gravity constraints. The perspective is that some classes of ƒ(R) models can be consistently constrained by the large-scale structure.

A New Exponential Gravity

We propose a new exponential f(R) gravity model with f(R) = (R − λc) e λ(c/R)n and n > 3, λ ≥ 1, c > 0 to explain late-time acceleration of the universe. At the high curvature region, the model behaves like the Λ CDM model. In the asymptotic future, it reaches a stable de-Sitter spacetime. It is a cosmologically viable model and can evade the local gravity constraints easily. This model shares many features with other f(R) dark energy models like Hu-Sawicki model and Exponential gravity model. In it the dark energy equation of state is of an oscillating form and can cross phantom divide line ωde = −1. In particular, in the parameter range 3 < n ≤ 4, λ ∼ 1, the model is most distinguishable from other models. For instance, when n = 4, λ = 1, the dark energy equation of state will cross −1 in the earlier future and has a stronger oscillating form than the other models, the dark energy density in asymptotical future is smaller than the one in the high curvature region. This new model can evade the local gravity tests easily when n > 3 and λ > 1.

Spontaneous symmetry breaking in cosmos: the hybrid symmetron as a dark energy switching device

We consider symmetron model in a generalized background with a hopeto make it compatible with dark energy. We observe a ``no go'' theorem atleast in case of a conformal coupling. Being convinced of symmetronincapability to be dark energy, we try to retain its role forspontaneous symmetry breaking and assign the role of dark energyeither to standard quintessence or F(R) theory which are switchedon by symmetron field in the symmetry broken phase. The scenarioreduces to standard Einstein gravity in the high density region.After the phase transition generated by symmetron field, either theF(R) gravity or the standard quintessence are induced in the lowdensity region. we demonstrate that local gravity constraints andother requirements are satisfied although the model could generatethe late-time acceleration of Universe.

Light mass galileons: Cosmological dynamics, mass screening and observational constraints

In this Letter, we examine the cosmological viability of a light mass galileon field consistent with local gravity constraints. The minimal, L3=□ϕ(∂μϕ)2, massless galileon field requires an additional term in order to give rise to a viable ghost free late time acceleration of Universe. The desired cosmological dynamics can either be achieved by incorporating an additional terms in the action such as (L4,L5) – the higher order galileon Lagrangians or by considering a light mass field à la galileon field potential. We analyze the second possibility and find that: (1) The model produces a viable cosmology in the regime where the non-linear galileon field is subdominant, (2) the Vainshtein mechanism operates at small scales where the non-linear effects become important and contribution of the field potential ceases to be significant. Also the small mass of the field under consideration is protected against strong quantum corrections thereby providing quantum stability to the system.

Vainshtein mechanism in second-order scalar-tensor theories

In second-order scalar-tensor theories we study how the Vainshtein mechanism works in a spherically symmetric background with a matter source. In the presence of the field coupling $F(\phi)=e^{-2Q\phi}$ with the Ricci scalar $R$ we generally derive the Vainshtein radius within which the General Relativistic behavior is recovered even for the coupling $Q$ of the order of unity. Our analysis covers the models such as the extended Galileon and Brans-Dicke theories with a dilatonic field self-interaction. We show that, if these models are responsible for the cosmic acceleration today, the corrections to gravitational potentials are generally small enough to be compatible with local gravity constraints.

COSMOLOGY OF CHAMELEONS WITH POWER-LAW COUPLINGS

In chameleon field theories, a scalar field can couple to matter with gravitational strength and still evade local gravity constraints due to a combination of self-interactions and the couplings to matter. Originally, these theories were proposed with a constant coupling to matter; however, the chameleon mechanism also extends to the case where the coupling becomes field dependent. We study the cosmology of chameleon models with power-law couplings and power-law potentials. It is found that these generalized chameleons, when viable, have a background expansion very close to ΛCDM, but can in some special cases enhance the growth of the linear perturbations at low redshifts. For the models we consider, it is found that this region of the parameter space is ruled out by local gravity constraints. Imposing a coupling to dark matter only, the local constraints are avoided, and it is possible to have observable signatures on the linear matter perturbations.

Chameleon dark energy models with characteristic signatures

In chameleon dark energy models, local gravity constraints tend to rule out parameters in which observable cosmological signatures can be found. We study viable chameleon potentials consistent with a number of recent observational and experimental bounds. A novel chameleon field potential, motivated by f(R) gravity, is constructed where observable cosmological signatures are present both at the background evolution and in the growth-rate of the perturbations. We study the evolution of matter density perturbations on low redshifts for this potential and show that the growth index today gamma_0 can have significant dispersion on scales relevant for large scale structures. The values of gamma_0 can be even smaller than 0.2 with large variations of gamma on very low redshifts for the model parameters constrained by local gravity tests. This gives a possibility to clearly distinguish these chameleon models from the Lambda-Cold-Dark-Matter model in future high-precision observations.