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We study the Solar System constraints on covariant $f(Q)$ gravity. The covariant $f(Q)$ theory is described by the metric and affine connection, where both the torsion and curvature vanish. Considering a model including a higher nonmetricity-scalar correction, $f(Q)= Q +\alpha Q^{n} - 2\Lambda$, we derive static and spherically symmetric solutions, which represent the Schwarzschild-de Sitter solution with higher-order corrections, for two different ansatz of the affine connection. On the obtained spacetime solutions, we investigate the perihelion precession, light deflection, Shapiro delay, Cassini constraint, and gravitational redshift in the $f(Q)$ gravity. We place bounds on the parameter $\alpha$ with $n=2, 3$ in our model of $f(Q)$ gravity, using various observational data in the Solar System., Comment: 27 pages, 1 figures, 2 tables

In this work, we analyze the characteristics of electromagnetic (EM) radiation associated with scalar and axion field oscillations in different background field setups. Because the scalar field and axion field have different parity and couple with the EM field in different forms, the EM signals generated by the scalar and axion can be used to distinguish them. More interestingly, resonance effects amplify the difference between the two fields and consequent EM signal strength, which helps us distinguish and detect them in future observations., Comment: 27 pages,6 figures

We investigate compact stars in the noninteger power (NIP) model of $f(R)$ gravity theory, which includes the higher-curvature correction to the Einstein-Hilbert action. The mass-radius relation of the compact stars in the NIP model predicts large deviations from those in the general relativity in the low-mass region, potentially allowing us to test the NIP model by future astrophysical observations. We also study the nonvanishing scalar hair surrounding the compact star and demonstrate that the chameleon mechanism works efficiently. They result in distinct scalar profiles inside and outside the star, which implies screening the fifth force mediated by the scalar field., Comment: 35 pages, 27 figures

We investigate future singularities originating from the anisotropy in the Universe. We formulate a new class of singularities in the homogeneous and anisotropic universe, comparing them with the known singularities in the homogeneous and isotropic universe. We also discuss the physical consequences of the new singularities. Moreover, we develop a novel reconstruction method for the anisotropic universe by introducing four scalar fields to reconstruct cosmological models in which future singularities appear. We present an explicit example where the anisotropy may grow in the future up to singularity., Comment: 19 pages, version to appear in PRD

This work investigates Early Dark Energy (EDE) scenarios as a potential precombination solution to the Hubble tension problem in the $F(R)$ gravity theory. We first develop a dimensionless quantity to visualize the density ratio between the EDE field and matter. Following existing scenarios, we then discuss conditions under which the Hubble tension could be alleviated by introducing a temporary injection of $10\%$ fractional energy around the time of matter-radiation equality between $z=10^{3}-10^{4}$. We further confront these models with local gravity tests and find inconsistencies with observations. Taking a broader view, we convert constraints from local gravity tests into constraints for general EDE in $F(R)$ gravity. We eventually arrive at a no-go theorem for $F(R)$ gravity, which restricts nontrivial modifications to General Relativity in the early universe., Comment: v1: 26 pages, 11 figures

$f(Q)$ gravity is an extension of the symmetric teleparallel equivalent to general relativity (STEGR). This work shows that based on the scalar-nonmetricity formulation, a scalar mode in $f(Q)$ gravity has a negative kinetic energy. This conclusion holds regardless of the coincident gauge frequently used in STEGR and $f(Q)$ gravity. To study the scalar mode, we further consider the covariant $f(Q)$ gravity as a special class in higher-order scalar tensor (HOST) theory and rewrite the four scalar fields, which play a role of the St\"{u}eckelberg fields associated with the diffeomorphism, by vector fields. Applying the standard Arnowitt-Deser-Misner (ADM) formulation to the new formulation of the $f(Q)$ gravity, we demonstrate that the ghost scalar mode can be eliminated by the second-class constraints, thus ensuring that $f(Q)$ gravity is a healthy theory., Comment: 31 pages, 0 figures

We reexamine the static and spherical symmetric compact star configuration in the $R^2$ model of the $F(R)$ gravity theory. With asymptotic solutions for the additional scalar degrees of freedom, we refine analysis on the external geometry and settle the scalar-hair problem argued in previous works. Performing the numerical integration of the modified Tolman-Oppenheimer-Volkoff equations as a two-boundaries-value problem, we further discuss the scalar-field distribution inside the compact stars and its influence on the mass-radius relation. We show that the chameleon potential plays an essential role in determining the scalar-field profile inside the star. The scalar field often behaves as a quintessential field that effectively decreases the mass of compact stars with lower central energy density., Comment: 37 pages, 22 figures, 1 table. Version to appear in PRD

Since the discovery of the accelerated expansion of the present Universe, significant theoretical developments have been made in the area of modified gravity. In the meantime, cosmological observations have been providing more high-quality data, allowing us to explore gravity on cosmological scales. To bridge the recent theoretical developments and observations, we present an overview of a variety of modified theories of gravity and the cosmological observables in the cosmic microwave background and large-scale structure, supplemented with a summary of predictions for cosmological observables derived from cosmological perturbations and sophisticated numerical studies. We specifically consider scalar-tensor theories in the Horndeski and DHOST family, massive gravity/bigravity, vector-tensor theories, metric-affine gravity, and cuscuton/minimally-modified gravity, and discuss the current status of those theories with emphasis on their physical motivations, validity, appealing features, the level of maturity, and calculability. We conclude that the Horndeski theory is one of the most well-developed theories of modified gravity, although several remaining issues are left for future observations. The paper aims to help to develop strategies for testing gravity with ongoing and forthcoming cosmological observations., Comment: 115 pages, 8 figures

$R^2$-corrected dark energy (DE) models in $F(R)$ gravity have been widely investigated in recent years, which not only removes the weak singularity potentially present in DE models but also provide us with a unified picture of the cosmic history, including the inflationary and DE epochs. Towards the unified interpretation of dynamical DE all over the cosmic history in the class of $R^2$-corrected DE models, we explore the universal features of the scalaron dynamics in the radiation-dominated epoch, along with the chameleon mechanism, by keeping our eyes on the inflationary and DE epochs. We show that the scalaron evolution does not follow a \textit{surfing solution} and is mostly adiabatic before big bang nucleosynthesis (BBN), even properly including the \textit{kick} by the nonperturbative QCD phase transition, hence a catastrophic consequence claimed in the literature is not applied to this class of DE models. This is due to the presence of the gigantic scale hierarchy between $R^2$ correction and DE, so is the universal feature for the class of $R^2$-corrected DE models. The prospects for the post- or onset-inflationary epoch would be pretty different from what the standard $R^2$ inflationary scenario undergoes due to the presence of the chameleon mechanism., Comment: 24 pages, 10 figures, 1 data file; Version to appear in Chinese Physics C with few references added

$f(Q)$ gravity is an extension of the symmetric teleparallel equivalent to general relativity. We demonstrate the Hamiltonian analysis of $f(Q)$ gravity with fixing the coincident gauge condition. Using the standard Dirac-Bergmann algorithm, we show that $f(Q)$ gravity has 8 physical degrees of freedom. This result reflects that the diffeomorphism symmetry of $f(Q)$ gravity is completely broken due to the gauge fixing. Moreover, in terms of the perturbations, we discuss the possible mode decomposition of these degrees of freedom., Comment: 19 pages

We investigate a compact star in the general $F(R)$ gravity. Developing a novel formulation in the spherically symmetric and static space-time with the matter, we confirm that an arbitrary relation between the mass $M$ and the radius $R_s$ of the compact star can be realized by adjusting the functional form of $F(R)$. Such a degeneracy with a choice of the equation of state (EOS) suggests that only mass-radius relation is insufficient to constrain the $F(R)$ gravity. Furthermore, by solving the differential equation for $\left. \frac{dF(R)}{dR}\right|_{R=R(r)}$ near and inside the surface of the compact star with the polytropic EOS, the boundary condition demands a weak curvature correction to the Einstein gravity could be non-integer power of the scalar curvature, which gives a stringent constraint on the functional form of $F\left(R\right)$. This consequence follows that the equation of motion in $F(R)$ gravity includes the fourth-order derivative of metric, and thus, it is applicable to general $F(R)$ models., Comment: 14 pages. Typos are corrected

f(Q) gravity is the extension of symmetric teleparallel general relativity (STGR), in which both curvature and torsion vanish, and gravity is attributed to nonmetricity. This work performs theoretical analyses of static and spherically symmetric solutions with an anisotropic fluid for general f(Q) gravity. We find that the off-diagonal component of the field equation due to a coincident gauge leads to stringent restrictions on the functional form of f(Q) gravity. In addition, although the exact Schwarzschild solution only exists in STGR, we obtain Schwarzschild-like solutions in nontrivial f(Q) gravity and study its asymptotic behavior and deviation from the exact one., Comment: 7 pages,version to appear in Physical Review D

Toward understanding of dark energy, we propose a novel method to directly produce a chameleon particle and force its decay under controlled gas pressure in a laboratory-based experiment. {\it Chameleon gravity}, characterized by its varying mass depending on its environment, could be a source of dark energy, which is predicted in modified gravity. A remarkable finding is a correspondence between the varying mass and a characteristic pressure dependence of a stimulated photon-photon scattering rate in a dilute gas surrounding a focused photon-beam spot. By observing a steep pressure dependence in the scattering rate, we can directly extract the characteristic feature of the chameleon mechanism. As a benchmark model of modified gravity consistent with the present cosmological observations, a reduced $F(R)$ gravity is introduced in the laboratory scale. We then demonstrate that the proposed method indeed enables a wide-ranging parameter scan of such a chameleon model with the varying mass around $(0.1-1)~[\mu \mathrm{eV}]$ by controlling pressure values., Comment: 13 pages, 11 figures; Version to appear in Physical Review D

The recent observations from CMB have imposed a very stringent upper-limit on the tensor/scalar ratio $r$ of inflation models, $r < 0.064$, which indicates that the primordial gravitational waves (PGW), even though possible to be detected, should have a power spectrum of a tiny amplitude. However, current experiments on PGW is ambitious to detect such a signal by improving the accuracy to an even higher level. Whatever their results are, it will give us much information about the early Universe, not only from the astrophysical side but also from the theoretical side, such as model building for the early Universe. In this paper, we are interested in analyzing what kind of inflation models can be favored by future observations, starting with a kind of general action offered by the effective field theory (EFT) approach. We show a general form of $r$ that can be reduced to various models, and more importantly, we show how the accuracy of future observations can put constraints on model parameters by plotting the contours in their parameter spaces., Comment: 19 pages, 9 figures with title changed and contents improved

We study spherically symmetric solutions with a scalar field in the shift-symmetric subclass of the Horndeski theory. Constructing an effective energy-momentum tensor of the scalar field based on the two-fluid model, we decompose the scalar field into two components: dark matter and dark energy.We find the dark-matter fluid is pressure-less, and its distribution of energy density obeys the inverse-square law. We show the scalar field dark matter can explain the galaxy rotation curve and discuss the time evolution of the dark matter in the cosmic background., Comment: 25 pages,revtex4-1

We study the chameleon field dark matter, dubbed \textit{scalaron}, in $F(R)$ gravity in the Big Bang Nucleosynthesis (BBN) epoch. With an $R^{2}$-correction term required to solve the singularity problem for $F(R)$ gravity, we first find that the scalaron dynamics is governed by the $R^{2}$ term and the chameleon mechanism in the early universe, which makes the scalaron physics model-independent regarding the low-energy scale modification. In viable $F(R)$ dark energy models including the $R^{2}$ correction, our analysis suggests the scalaron universally evolves in a way with a bouncing oscillation irrespective of the low-energy modification for the late-time cosmic acceleration. Consequently, we find a universal bound on the scalaron mass in the BBN epoch, to be reflected on the constraint for the coupling strength of the $R^2$ term, which turns out to be more stringent than the one coming from the fifth force experiments. It is then shown that the scalaron naturally develops a small enough fluctuation in the BBN epoch, hence can avoid the current BBN constraint placed by the latest Planck 2018 data, and can also have a large enough sensitivity to be hunted by the BBN, with more accurate measurements for light element abundances as well as the baryon number density fraction., Comment: 29 pages, 7 figures, Prepared for submission to JHEP

We discuss the scalar mode of gravitational waves emerging in the context of $F(R)$ gravity by taking into account the chameleon mechanism. Assuming a toy model with a specific matter distribution to reproduce the environment of detection experiment by a ground-based gravitational wave observatory, we find that chameleon mechanism remarkably suppresses the scalar wave in the atmosphere of Earth, compared with the tensor modes of the gravitational waves. We also discuss the possibility to detect and constrain scalar waves by the current gravitational observatories and advocate a necessity of the future space-based observations., Comment: 15 pages, 5 figures, accepted version in Physical Review D

We study the static and spherical symmetric (SSS) configurations in the non-minimal model of the de Rham-Gabadadze-Tolley (dRGT) massive gravity with a flat reference metric. Considering the modified Tolman-Oppenheimer-Volkoff (TOV) equation, the Bianchi identity, and energy-momentum conservation, we find a new algebraic equation for the radial coordinate of the reference metric. We demonstrate that this equation suggests an absence of the Vainshtein mechanism in the minimal model of the dRGT massive gravity, while it has two branches of solutions where one connects with the Schwarzschild space-time and another implies the significant deviation from the asymptotically flat space-time in the non-minimal model. We also briefly discuss the boundary conditions for the relativistic stars in the dRGT massive gravity and a potential relation with the mass-radius relation of the stars., Comment: 22 pages

It is widely believed that the screening mechanism is an essential feature for the modified gravity theory. Although this mechanism has been examined thoroughly in the past decade, their analyses are based on the classical configuration of the matter fields. In this paper, we demonstrate a new formulation of the chameleon mechanism in $F(R)$ gravity theory, to shed light on quantum-field theoretical effects on the chameleon mechanism as well as the related scalaron physics, induced by the matter sector. We show a potential absence of the chameleon mechanism in the cosmic history based on a scale-invariant-extended scenario beyond the standard model of particle physics, in which a realistic electroweak phase transition, possibly yielding the right amount of baryon asymmetry of Universe today, simultaneously breaks the scale invariance in the early Universe. Remarkably enough, the matter sector contribution to the trace of energy-momentum tensor turns out to be on the same order of magnitude as that computed in the classical perfect-fluid approximation, even though the theory involves the nontrivial electroweak-phase transition environment. We also briefly discuss the oscillation of the scalaron field and indirect generation of non-tensorial gravitational waves induced by the electroweak phase transition., Comment: 17 pages, 4 figures, version accepted in Chinese Physics C

We make a theoretical prediction for the ratio of the dark energy to other components in the Universe based on the scenario of the sequestering mechanism which was recently proposed as one possible way to solve the cosmological constant problem. In order to evaluate the value of dark energy and the others, we assume a specific scale factor which describes the Big-Crunch scenario in the scalar-tensor theory. We specify the parameter region where the one can explain the observed dark energy-matter ratio., Comment: LaTeX 14 pages, small corrections

We study the cosmic history of the scalaron in $F(R)$ gravity with constructing the time evolution of the cosmic environment and discuss the chameleonic dark matter based on the chameleon mechanism in the early and current Universe. We then find that the scalaron can be a dark matter. We also propose an interesting possibility that the $F(R)$ gravity can address the coincidence problem., Comment: 33 pages, 10 figures, 1 table, some comments and references added, minor typos corrected

We explore a new horizon of modified gravity from the viewpoint of the particle physics. As a concrete example, we take the $F(R)$ gravity to raise a question: can a scalar particle ("scalaron") derived from the $F(R)$ gravity be a dark matter candidate? We place the limit on the parameter in a class of $F(R)$ gravity model from the constraint on the scalaron as a dark matter. The role of the screening mechanism and compatibility with the dark energy problem are addressed., Comment: 11 pages, 3 figures, version accepted in PRD

We study relativistic stars in the simplest model of the de Rham-Gabadadze-Tolley massive gravity which describes the massive graviton without ghost propagating mode. We consider the hydrostatic equilibrium, and obtain the modified Tolman-Oppenheimer-Volkoff equation and the constraint equation coming from the potential terms in the gravitational action. We give analytical and numerical results for quark and neutron stars and discuss the deviations compared with General Relativity and $F(R)$ gravity. It is shown that theory under investigation leads to small deviation from the General Relativity in terms of density profiles and mass-radius relation. Nevertheless, such deviation may be observable in future astrophysical probes., Comment: 15 pages, 5 figures, PRD version

We study the stability under the perturbation and the related anti-evaporation of the Nariai space-time in bigravity. If we impose specific condition for the solutions and parameters, we obtain asymptotically de Sitter space-time, and show the existence of the Nariai space-time as a background solution. Considering the perturbation around the Nariai space-time up to first order, we investigate the behavior of black hole horizon. We show that the anti-evaporation does not occur on the classical level in the bigravity., Comment: 9 pages, 1 figure

We consider the Palatini formalism of the Born-Infeld gravity. In the Palatini formalism, the propagating mode is only graviton, whose situation is different from that in the metric formalism. We discuss about the FRW cosmology by using an effective potential. Especially we consider the condition that the bouncing could occur. We also give some speculations about the black hole formation, Comment: LaTeX 10 pages, title is changed, the differences from the previous works are clarified, version to appear in Physics Letters B

We consider the properties of solutions in the bigravity theory for general models, which are parametrized by two parameters $\alpha_{3}$ and $\alpha_{4}$. Assuming that two metric tensors $g_{\mu \nu}$ and $f_{\mu \nu}$ satisfy the condition $f_{\mu \nu}=C^{2}g_{\mu \nu}$ where $C$ is a constant, we investigate the conditions for the parameters so that the solutions with $C\neq1$ could exist. We also discuss the magnitude and the sign of corresponding cosmological constants. For the black hole solution, we consider the black hole entropy to which the massive spin-$2$ field contributes. In order to obtain the black hole entropy, we take an approach which uses the Virasoro algebra and the central charge corresponding to the surface term in the action., Comment: 12 pages, 7 figures

We consider the static, spherically symmetric black hole solutions in bigravity theory for minimal model with a condition $f_{\mu \nu} = C^{2} g_{\mu \nu}$ and evaluate the entropy for black holes. In this condition, we show that there exists the Schwarzschild solution for $C^{2} = 1$, which is unique consistent solution. We examine how the massive spin-2 field contributes and affects to the Bekenstein-Hawking entropy corresponding to Einstein gravity. In order to obtain the black hole entropy, we use a recently proposed approach which use Virasoro algebra and central charge corresponding to surface term in the gravitational action., Comment: 7 pages, version to appear in Physical Review D