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We investigate the possibility of reducing the number of degrees of freedom (d.o.f.) starting from generic metric theories of gravity by introducing multiple auxiliary constraints (ACs), under the restriction of retaining spatial covariance as a gauge symmetry. Arbitrary numbers of scalar-, vector- and tensor-type ACs are considered a priori, yet we find that no vector- and tensor-type constraints should be introduced, and that scalar-type ACs should be no more than four for the purpose of constructing minimally modified gravity (MMG) theories which propagate only two tensorial d.o.f., like general relativity (GR). Through a detailed Hamiltonian analysis, we exhaust all the possible classifications of ACs and find out the corresponding minimalizing and symmetrizing conditions for obtaining the MMG theories. In particular, no condition is required in the case of four ACs, hence in this case the theory can couple with matter consistently and naturally. To illustrate our formalism, we build a concrete model for this specific case by using the Cayley-Hamilton theorem and derive the dispersion relation of the gravitational waves, which is subject to constraints from the observations., 15 pages, 1 table, no figure

Bigravity is one of the natural extensions of general relativity and contains an additional massive spin-2 field which can be a good candidate for dark matter. To discuss the production of spin-2 dark matter, we study fixed point solutions of the background equations for axisymmetric Bianchi type-I Universes in two bigravity theories without Boulware-Deser ghost, i.e., Hassan-Rosen bigravity and Minimal Theory of Bigravity. We investigate the local and global stability of the fixed points and classify them. Based on the general analysis, we propose a new scenario where spin-2 dark matter is produced by the transition from an anisotropic fixed point solution to isotropic one. The produced spin-2 dark matter can account for all or a part of dark matter and can be directly detected by laser interferometers in the same way as gravitational waves., Comment: 15 pages, 3 figures

In the former part, we study the gravitational collapse of pressureless dust and find special solutions, where, in both the physical and fiducial sectors, the exterior and interior spacetime geometries are given by the Schwarzschild spacetimes and the Friedmann-Lema\^itre-Robertson-Walker universes dominated by pressureless dust, respectively, with specific time slicings. In the case where the Lagrange multipliers are trivial and have no jump across the matter interfaces in both the physical and fiducial sectors, the junction conditions across them remain the same as those in general relativity (GR). For simplicity, we foliate the interior geometry by homogeneous and isotropic spacetimes. For a spatially flat interior universe, we foliate the exterior geometry by a time-independent flat space, while for a spatiallycurved interior universe, we foliate the exterior geometry by a time-independent space with deficit solid angle. Despite the rather restrictive choice of foliations, we find interesting classes of exact solutions that represent gravitational collapse in MTBG. In the spatially flat case, under a certain tuning of the initial condition, we find exact solutions of matter collapse in which the two sectors evolve independently. In the spatially closed case, once the matter energy densities and the Schwarzschild radii are tuned between the two sectors, we find exact solutions that correspond to the Oppenheimer-Snyder model in GR. In the latter part, we study odd-parity perturbations of the Schwarzschild$-$de Sitter solutions written in the spatially flat coordinates. For the higher-multipole modes $\ell\geq2$, we find that, in general, the system reduces to that of four physical modes, where two of them are dynamical and the remaining two are shadowy, i.e., satisfying only elliptic equations., Comment: 28 pages, published version

We investigate a generic quadratic higher-order scalar-tensor theory with a scordatura term, which is expected to provide a consistent perturbative description of stealth solutions with a timelike scalar field profile. In the DHOST subclass, exactly stealth solutions are known to yield perturbations infinitely strongly coupled and thus cannot be trusted. Beyond DHOST theories with the scordatura term, such as in ghost condensation and U-DHOST, we show that stealth configurations cannot be realized as exact solutions but those theories instead admit approximately stealth solutions where the deviation from the exactly stealth configuration is controlled by the mass scale $M$ of derivative expansion. The approximately stealth solution is time-dependent, which can be interpreted as the black hole mass growth due to the accretion of the scalar field. From observed astrophysical black holes, we put an upper bound on $M$ as $\hat{c}_{\rm D1}^{1/2} M\lesssim 2\times 10^{11}$ GeV, where $\hat{c}_{\rm D1}$ is a dimensionless parameter of order unity that characterizes the scordatura term. As far as $M$ is sufficiently below the upper bound, the accretion is slow and the approximately stealth solutions can be considered as stealth at astrophysical scales for all practical purposes while perturbations are weakly coupled all the way up to the cutoff $M$ and the apparent ghost is as heavy as or heavier than $M$., 10 pages

In minisuperspace quantum cosmology, the Lorentzian path integral formulations of the no-boundary and tunneling proposals have recently been analyzed. But it has been pointed out that the wave function of linearized perturbations around a homogeneous and isotropic background is of an inverse Gaussian form and thus that their correlation functions are divergent. In this paper, we revisit this issue and consider the problem of perturbations in Lorentzian quantum cosmology by modifying the dispersion relation based on trans-Planckian physics. We consider two modified dispersion relations, the generalized Corley-Jacobson dispersion relation with higher momentum terms and the Unruh dispersion relation with a trans-Planckian mode cut-off, as examples. We show that the inverse Gaussian problem of perturbations in Lorentzian quantum cosmology is hard to overcome with the trans-Planckian physics modifying the dispersion relation at short distances., 25 pages, 11 figures, v2: final published version

In this work, we introduce a class of extended Minimal Theories of Massive Gravity (eMTMG), without requiring a priori that the theory should admit the same homogeneous and isotropic cosmological solutions as the de Rham-Gabadadze-Tolley massive gravity. The theory is constructed as to have only two degrees of freedom in the gravity sector. In order to perform this step we first introduce a precursor theory endowed with a general graviton mass term, to which, at the level of the Hamiltonian, we add two extra constraints as to remove the unwanted degrees of freedom, which otherwise would typically lead to ghosts and/or instabilities. On analyzing the number of independent constraints and the properties of tensor mode perturbations, we see that the gravitational waves are the only propagating gravitational degrees of freedom which do acquire a non-trivial mass, as expected. In order to understand how the effective gravitational force works for this theory we then investigate cosmological scalar perturbations in the presence of a pressureless fluid. We then restrict the whole class of models by imposing the following conditions at all times: 1) it is possible to define an effective gravitational constant, $G_{{\rm eff}}$; 2) the value $G_{\text{eff}}/G_{N}$ is always finite but not always equal to unity (as to allow some non-trivial modifications of gravity, besides the massive tensorial modes); and 3) the square of mass of the graviton is always positive. These constraints automatically make also the ISW-effect contributions finite at all times. Finally we focus on a simple subclass of such theories, and show they already can give a rich and interesting phenomenology., Comment: 20 pages+appendices, 1 figure

The cosmological memory effect is a permanent change in the relative separation of test particles located in a FLRW spacetime due to the passage of gravitational waves. In the case of a spatially flat FLRW spacetime filled with a perfect fluid in general relativity, it is known that only tensor perturbations contribute to the memory effect while scalar and vector perturbations do not. In this paper, we show that in the context of scalar-tensor theories, the scalar perturbations associated to the scalar graviton contribute to the memory effect as well. We find that, depending on the mass and coupling, the influence of cosmic expansion on the memory effect due to the scalar perturbations can be either stronger or weaker than the one induced by the tensor perturbations. As a byproduct, in an appendix, we develop a general framework which can be used to study coupled wave equations in any curved spacetime region which admits a foliation by time slices., Comment: 8+11 pages (two-column), 5 appendices; v2: the differences/similarities between the cosmological scalar and tensor memory effects are clarified in more detail

Black hole spectroscopy with gravitational waves is an important tool to measure the mass and spin of astrophysical black holes and to test their Kerr nature. Next-generation ground- and space-based detectors will observe binary black hole mergers with large signal-to-noise ratios and perform spectroscopy routinely. It was recently shown that small perturbations due, e.g., to environmental effects (the "flea") to the effective potential governing gravitational-wave generation and propagation in black hole exteriors (the "elephant") can lead to arbitrarily large changes in the black hole's quasinormal spectrum, including the fundamental mode, which is expected to dominate the observed signal. This raises an important question: is the black hole spectroscopy program robust against perturbations? We clarify the physical behavior of time-domain signals under small perturbations in the potential, and we show that changes in the amplitude of the fundamental mode in the prompt ringdown signal are parametrically small. This implies that the fundamental quasinormal mode extracted from the observable time-domain signal is stable against small perturbations. The stability of overtones deserves further investigation., 10 pages, 7 figures. Matches published version on PRD

We investigate static and spherically symmetric solutions in the Minimal Theory of Bigravity (MTBG). First, we show that a pair of Schwarzschild-de Sitter spacetimes with different cosmological constants and black hole masses written in the spatially-flat Gullstrand-Painlev\'e (GP) coordinates is a solution in the self-accelerating branch of MTBG, while it cannot be a solution in the normal branch. We then illustrate how Schwarzschild-de Sitter solutions can become compatible with the normal branch when using different coordinates. We also confirm that the self-accelerating branch of MTBG admits static and spherically symmetric general relativity solutions with matter written in the spatially-flat coordinates, including neutron stars with arbitrary matter equations of state. Finally, we show that in the self-accelerating branch nontrivial solutions are given by the Schwarzschild-de Sitter metrics written in nonstandard coordinates., Comment: 19 pages

Modified gravity theories can accommodate exact solutions, for which the metric has the same form as the one in general relativity, i.e., stealth solutions. One problem with these stealth solutions is that perturbations around them exhibit strong coupling when the solutions are realized in degenerate higher-order scalar-tensor theories. We show that the strong coupling problem can be circumvented in the framework of the so-called U-DHOST theories, in which the degeneracy is partially broken in such a way that higher-derivative terms are degenerate only in the unitary gauge. In this sense, the scordatura effect is built-in in U-DHOST theories in general. There is an apparent Ostrogradsky mode in U-DHOST theories, but it does not propagate as it satisfies a three-dimensional elliptic differential equation on a spacelike hypersurface. We also clarify how this nonpropagating mode, i.e., the "shadowy" mode shows up at the nonlinear level.

In this article, we develop the formalism for singular hypersurfaces and junction conditions in generalized coupling theories using a variational approach. We then employ this formalism to examine the behavior of sharp matter density gradients in generalized coupling theories. We find that such gradients do not necessarily lead to the pathologies present in other theories of gravity with auxiliary fields. A detailed example, based on a simple instance of a generalized coupling theory called the MEMe model, is also provided. In the static case, we show that sharp boundaries do not generate singularities in the dynamical frame despite the presence of an auxiliary field. Instead, in the case of a collapsing spherical density distribution with a general profile an additional force compresses over-densities and expands underdensities. These results can also be used to deduce additional constraints on the parameter of this model., 17 pages, 7 figures

We present a simple class of mechanical models where a canonical degree of freedom interacts with another one with a negative kinetic term, i.e., with a ghost. We prove analytically that the classical motion of the system is completely stable for all initial conditions, notwithstanding that the conserved Hamiltonian is unbounded from below and above. This is fully supported by numerical computations. Systems with negative kinetic terms often appear in modern cosmology, quantum gravity, and high energy physics and are usually deemed as unstable. Our result demonstrates that for mechanical systems this common lore can be too naive and that living with ghosts can be stable.

We present a well-tempered DeWitt wave function, which vanishes at the classical big-bang singularity, in Ho\v{r}ava-Lifshitz (HL) cosmology with tensor perturbation, both analytically and numerically. In general relativity, the DeWitt wave function is ill-behaved once the tensor perturbation is taken into account. This is essentially because the amplitude of the perturbation diverges at the singularity and the perturbative expansion completely breaks down. On the other hand, in HL gravity it is known that the higher dimensional operators required by the perturbative renormalizability render the tensor perturbation scale-invariant and regular all the way up to the singularity. In this paper we analytically show that in $d+1$ dimensional HL gravity the DeWitt wave function for tensor perturbation is indeed well-defined around the classical big-bang singularity. Also, we numerically demonstrate the well-behaved DeWitt wave function for tensor perturbation from the big-bang to a finite size of the Universe., Comment: 20 pages, 4 figures

We construct an asymmetric bouncing scenario within the VCDM model - also known as type-II minimally modified gravity -, a modified gravity theory with two local physical degrees of freedom. The scenario is exempt of any ghost or gradient instability, ad-hoc matching conditions or anisotropic stress issue (BKL instability). It moreover succeeds in generating the cosmological perturbations compatible with the observations. The scalar spectral index can be adapted by the choice of the equation of state of the matter sector and the form of the VCDM potential leading to an almost scale-invariant power spectrum. Satisfying the CMB bounds on the tensor-to-scalar ratio leads to a blue tensor spectrum., Comment: 15 pages, 8 figures; accepted version

We investigate a systematic formulation of vector-tensor theories based on the effective field theory (EFT) approach. The input of our EFT is that the spacetime symmetry is spontaneously broken by the existence of a preferred timelike direction in accordance with the cosmological principle. After clarifying the difference of the symmetry breaking pattern from the conventional EFT of inflation/dark energy, we find an EFT description of vector-tensor theories around the cosmological background. This approach not only serves as a unified description of vector-tensor theories but also highlights universal differences between the scalar-tensor theories and the vector-tensor theories. The theories having different symmetry breaking patterns are distinguished by a phenomenological function and consistency relations between the EFT coefficients. We study the linear cosmological perturbations within our EFT framework and discuss the characteristic properties of the vector-tensor theories in the context of dark energy. In particular, we compute the effective gravitational coupling and the slip parameter for the matter density contrast in terms of the EFT coefficients., Comment: 39 pages + appendices, 1 figure, published version

In quantum cosmology the DeWitt boundary condition is a proposal to set the wave function of the universe to vanish at the classical big-bang singularity. In this Letter, we show that in many gravitational theories including general relativity, the DeWitt wave function does not take a desired form once tensor perturbations around a homogeneous and isotropic closed universe are taken into account: anisotropies and inhomogeneities due to the perturbations are not suppressed near the classical singularity. We then show that Ho\v{r}ava-Lifshitz gravity provides a satisfactory DeWitt wave function. In particular, in the limit of $z=3$ anisotropic scaling, we find an exact analytic expression for the DeWitt wave function of the universe with scale-invariant perturbations. In general cases with relevant deformations, we show that the DeWitt wave function can be systematically expanded around the classical big-bang singularity with perturbations under control., Comment: 7 pages, v2: final published version

We study U-DHOST theories, i.e., higher-order scalar-tensor theories which are degenerate only in the unitary gauge and yield an apparently unstable extra mode in a generic coordinate system. We show that the extra mode satisfies a three-dimensional elliptic differential equation on a spacelike hypersurface, and hence it does not propagate. We clarify how to treat this "shadowy" mode at both the linear and the nonlinear levels., 10 pages

We present a cosmological model of an early-time scenario that incorporates a relaxation process of the would-be large vacuum energy, followed by a reheating era connecting to the standard hot big bang universe. Avoiding fine-tuning the cosmological constant is achieved by the dynamics of a scalar field whose kinetic term is modulated by an inverse power of spacetime curvature. While it is at work against radiative corrections to the dark energy, this mechanism alone would wipe out not only the vacuum energy but also all other matter contents. Our present work aims to complete the scenario by exploiting a null-energy-condition violating sector whose energy is eventually transferred to a reheating sector. We provide an explicit example of this process and thus a concrete scenario of the cosmic onset that realizes the thermal history of the Universe with a negligible cosmological constant., 36 pages, 10 figures

We study spherically symmetric spacetimes in Einstein-aether theory in three different coordinate systems, the isotropic, Painlev\`e-Gullstrand, and Schwarzschild coordinates, in which the aether is always comoving, and present both time-dependent and time-independent exact vacuum solutions. In particular, in the isotropic coordinates we find a class of exact static solutions characterized by a single parameter $c_{14}$ in closed forms, which satisfies all the current observational constraints of the theory, and reduces to the Schwarzschild vacuum black hole solution in the decoupling limit ($c_{14} = 0$). However, as long as $c_{14} \not= 0$, a marginally trapped throat with a finite non-zero radius always exists, and in one side of it the spacetime is asymptotically flat, while in the other side the spacetime becomes singular within a finite proper distance from the throat, although the geometric area is infinitely large at the singularity. Moreover, the singularity is a strong and spacetime curvature singularity, at which both of the Ricci and Kretschmann scalars become infinitely large., Comment: revtex4-1, one figure and no tables. Some typos are corrected. Universe 7 (2021) 272

We study a theory of massive tensor gravitons which predicts blue-tilted and largely amplified primordial gravitational waves. After inflation, while their mass is significant until it diminishes to a small value, gravitons are diluted as non-relativistic matter and hence their amplitude can be substantially amplified compared to the massless gravitons which decay as radiation. We show that such gravitational waves can be detected by interferometer experiments, even if their signal is not observed on the CMB scales., 6 pages, 2 figures

We investigate the relativistic effective field theory (EFT) describing a non-dissipative gravitating continuum. In addition to ordinary continua, namely solids and fluids, we find an extraordinary more symmetric continuum, aether. In particular, the symmetry of the aether concludes that a homogeneous and isotropic state behaves like a cosmological constant. We formulate the EFT in the unitary/comoving gauge in which the dynamical degrees of freedom of the continuum (phonons) are eaten by the spacetime metric. This gauge choice, which is interpreted as the Lagrangian description in hydrodynamics, offers a neat geometrical understanding of continua. We examine a thread-based spacetime decomposition with respect to the four-velocity of the continuum which is different from the foliation-based Arnowitt-Deser-Misner one. Our thread-based decomposition respects the symmetries of the continua and, therefore, makes it possible to systematically find invariant building blocks of the EFT for each continuum even at higher orders in the derivative expansion. We also discuss the linear dynamics of the system and show that both gravitons and phonons acquire "masses" in a gravitating background., 41 pages + appendices, 1 figure, 3 tables, added explanations, published version

Deci-hertz Interferometer Gravitational Wave Observatory (DECIGO) is the future Japanese space mission with a frequency band of 0.1 Hz to 10 Hz. DECIGO aims at the detection of primordial gravitational waves, which could be produced during the inflationary period right after the birth of the universe. There are many other scientific objectives of DECIGO, including the direct measurement of the acceleration of the expansion of the universe, and reliable and accurate predictions of the timing and locations of neutron star/black hole binary coalescences. DECIGO consists of four clusters of observatories placed in the heliocentric orbit. Each cluster consists of three spacecraft, which form three Fabry-Perot Michelson interferometers with an arm length of 1,000 km. Three clusters of DECIGO will be placed far from each other, and the fourth cluster will be placed in the same position as one of the three clusters to obtain the correlation signals for the detection of the primordial gravitational waves. We plan to launch B-DECIGO, which is a scientific pathfinder of DECIGO, before DECIGO in the 2030s to demonstrate the technologies required for DECIGO, as well as to obtain fruitful scientific results to further expand the multi-messenger astronomy., Comment: 10 pages, 3 figures

The detections of gravitational waves (GW) by the LIGO/Virgo collaborations provide various possibilities for both physics and astronomy. We are quite sure that GW observations will develop a lot, both in precision and in number, thanks to the continuous work on the improvement of detectors, including the expected new detector, KAGRA, and the planned detector, LIGO-India. On this occasion, we review the fundamental outcomes and prospects of gravitational wave physics and astronomy. We survey the development, focusing on representative sources of gravitational waves: binary black holes, binary neutron stars, and supernovae. We also summarize the role of gravitational wave observations as a probe of new physics.

We propose a covariant entropy bound in gravitational theories beyond general relativity (GR), using Wald-Jacobson-Myers entropy instead of Bekenstein-Hawking entropy. We first extend the proof of the bound known in 4-dimensional GR to D-dimensional GR, f(R) gravity and canonical scalar-tensor theory. We then consider Einstein-Gauss-Bonnet (EGB) gravity as a more non-trivial example and, under a set of reasonable assumptions, prove the bound in the GR branch of spherically symmetric configurations. As a corollary, it is shown that under the null and dominant energy conditions, the generalized second law holds in the GR branch of spherically symmetric configurations of EGB gravity at the fully nonlinear level., Comment: 11 pages

We investigate the ringdown waveform and reflectivity of a Lifshitz scalar field around a fixed Schwarzschild black hole. The radial wave equation is modified due to the Lorentz breaking terms, which leads to a diversity of ringdown waveforms. Also, it turns out that Lifshitz waves scattered by the Schwarzschild black hole exhibits superradiance. The Lorentz breaking terms lead to superluminal propagation and high-frequency modes can enter and leave the interior of the Killing horizon where negativity of energy is not prohibited. This allows the Lifshitz waves to carry out additional positive energy to infinity while leaving negative energy inside the Killing horizon, similar to the Penrose process in the ergosphere of a Kerr spacetime. Another interesting phenomenon is emergence of long-lived quasinormal modes, associated with roton-type dispersion relations. These effects drastically modify the greybody factor of a microscopic black hole, whose Hawking temperature is comparable with or higher than the Lifshitz energy scale., Comment: 25 pages, 14 figures

In this paper, we systematically study gravitational waves (GWs) produced by remote compact astrophysical sources. To describe such GWs properly, we introduce three scales, $\lambda, \; L_c$ and $L$, denoting, respectively, the typical wavelength of GWs, the scale of the cosmological perturbations, and the size of the observable universe. For GWs to be detected by the current and foreseeable detectors, the condition $\lambda \ll L_c \ll L$ holds, and such GWs can be well approximated as high-frequency GWs. In order for the backreaction of the GWs to the background to be negligible, we must assume that $\left|h_{\mu\nu}\right| \ll 1$, in addition to the condition $\epsilon \ll 1$, which are also the conditions for the linearized Einstein field equations for $h_{\mu\nu}$ to be valid, where $g_{\mu\nu} = \gamma_{\mu\nu} + \epsilon h_{\mu\nu}$, and $\gamma_{\mu\nu}$ denotes the background. To simplify the field equations, we show that the spatial, traceless, and Lorentz gauge conditions can be imposed simultaneously, even when the background is not vacuum, as long as the high-frequency GW approximation is valid. However, to develop the formulas that can be applicable to as many cases as possible, we first write down explicitly the linearized Einstein field equations by imposing only the spatial gauge. Applying the general formulas together with the geometrical optics approximation to such GWs, we find that they still move along null geodesics and its polarization bi-vector is parallel-transported, even when both the cosmological scalar and tensor perturbations are present. In addition, we also calculate the gravitational integrated Sachs-Wolfe effects, whereby the dependences of the amplitude, phase and luminosity distance of the GWs on these two kinds of perturbations are read out explicitly., Comment: revtex4, one figure, no tables. Typos are corrected. Phys. Rev. D103, 123021 (2021)

Following the path of minimalism in alternative theories of gravity, we construct the "Minimal Theory of Bigravity" (MTBG), a theory of two interacting spin-2 fields that propagates only four local degrees of freedom instead of the usual seven ones and that allows for the same homogeneous and isotropic cosmological solutions as in Hassan-Rosen bigravity (HRBG). Starting from a precursor theory that propagates six local degrees of freedom, we carefully choose additional constraints to eliminate two of them to construct the theory. Investigating the cosmology of MTBG, we find that it accommodates two different branches of homogeneous and isotropic background solutions, equivalent on-shell to the two branches that are present in HRBG. Those branches in MTBG differ however from the HRBG ones at the perturbative level, are both perfectly healthy and do not exhibit strong coupling issues nor ghost instabilities. In the so-called self-accelerating branch, characterized by the presence of an effective cosmological constant, the scalar and vector sectors are the same as in General Relativity (GR). In the so-called normal branch, the scalar sector exhibits non-trivial phenomenology, while its vector sector remains the same as in GR. In both branches, the tensor sector exhibits the usual HRBG features: an effective mass term and oscillations of the gravitons. Therefore MTBG provides a stable nonlinear completion of the cosmology in HRBG., Comment: 23 pages

Static, spherically symmetric solutions representing stars made of barotropic perfect fluid are studied in the context of two theories of type-II minimally modified gravity, VCDM and VCCDM. Both of these theories share the property that no additional degree of freedom is introduced in the gravity sector, and propagate only two gravitational waves besides matter fields, as in General Relativity (GR). We find that, on imposing physical boundary conditions on the Misner-Sharp mass of the system, the solutions in V(C)CDM exactly coincide with the ones in GR, namely they also satisfy the Tolman-Oppenheimer-Volkoff equation., Comment: 11 pages, no figures, uses revtex

We show how a class of multi-field scalar-field theories in a Lorentz-breaking background imposes consistency conditions on its effective theory of a single field and provides an example of order-unity violation of a naively applied positivity bound, assuming a large hierarchy between the masses of the lightest field and the others., Comment: 50 pages, 3 figures, 1 table, v2: improved explanations, new section VF added, references added, to appear in JCAP

We examine the post-Newtonian limit of the minimal exponential measure (MEMe) model presented in [J. C. Feng, S. Carloni, Phys. Rev. D 101, 064002 (2020)] using an extension of the parameterized post-Newtonian (PPN) formalism which is also suitable for other type-I minimally modified Gravity theories. The new PPN expansion is then used to calculate the monopole term of the post-Newtonian gravitational potential and to perform an analysis of circular orbits within spherically symmetric matter distributions. The latter shows that the behavior does not differ significantly from that of general relativity for realistic values of the MEMe model parameter $q$. Instead the former shows that one can use precision measurements of Newton's constant $G$ to improve the constraint on $q$ by up to $10$ orders of magnitude., 14 pages, 3 figures. Matches published version

The accumulated energy density of the excited entropy modes in multiple field inflationary scenarios can play the role of dark matter. In the usual case of a flat field space without any turning trajectory, only light superhorizon entropy modes can be excited through the gravitational instability. In the case of a negatively curved field space, we show that subhorizon entropy modes can be excited as well through the tachyonic instability induced by the negative curvature of the field space. The latter allows for production of entropy modes with masses larger than or at the order of the Hubble expansion rate during inflation, leading to a new dark matter scenario. Due to the contribution of subhorizon modes, the corresponding spectral density has a peak at a scale smaller than its counterpart in the models based on a flat field space. This difference makes our model observationally distinguishable., Comment: 26+7 pages, 8 figures, 2 appendices, matches published version

Disformal transformation provides a map relating different scalar-tensor and vector-tensor theories and gives access to a powerful solution-generating method in modified gravity. In view of the vast family of new solutions one can achieve, it is crucial to design suitable tools to guide their construction. In this work, we address this question by revisiting the Petrov classification of disformally constructed solutions in modified gravity theories. We provide close formulas which relate the principal nulls directions as well as the Weyl scalars before and after the disformal transformation. These formulas allow one to capture if and how the Petrov type of a given seed geometry changes under a disformal transformation. Finally, we apply our general setup to three relevant disformally constructed solutions for which the seeds are respectively homogeneous and isotropic, static spherically symmetric and stationary axisymmetric. For the first two cases, we show that the Petrov type O and Petrov type D remain unchanged after a disformal transformation while we show that disformed Kerr black hole is no longer of type D but of general Petrov type I. The results presented in this work should serve as a new toolkit when constructing and comparing new disformal solutions in modified gravity., Comment: 26+11 pages, 2 tables, matches the published version

We investigate cosmological signatures of the minimal theory of massive gravity (MTMG). To this aim, we simulate the normal branch of the MTMG by employing the \textsc{Ramses} \mbox{$N$-body} code and extending it with an effective gravitational constant $G_{\rm eff}$. We implement an environment-dependent $G_{\rm eff}$ as a function of the graviton mass and the local energy density as predicted by MTMG. We find that halo density profiles are not a good probe for MTMG, because deviations from general relativity (GR) are quite small. Similarly, the matter power spectra show deviations only at the percentage level. However, we find a clear difference between MTMG and GR in that voids are denser in MTMG than in GR. As measuring void profiles is quite a complex task from an observational point of view, a better probe of MTMG would be the halo abundances. In this case, MTMG creates a larger amount of massive halos, while there is a suppression in the abundance of small halos., 8 pages, 7 figures. Updated to reflect peer-reviewed version for publication

Working directly with a general Hamiltonian for the spacetime metric with the $3+1$ decomposition and keeping only the spatial covariance, we investigate the possibility of reducing the number of degrees of freedom by introducing an auxiliary constraint. The auxiliary constraint is considered as part of the definition of the theory. Through a general Hamiltonian analysis, we find the conditions for the Hamiltonian as well as for the auxiliary constraint, under which the theory propagates two tensorial degrees of freedom only. The class of theories satisfying these conditions can be viewed as a new construction for the type-II minimally modified gravity theories, which propagate the same degrees of freedom of but are not equivalent to general relativity in the vacuum. We also illustrate our formalism by a concrete example, and derive the dispersion relation for the gravitational waves, which can be constrained by observations., 11 pages

The $k$-essence theory is a prototypical class of scalar-field models that already gives rich phenomenology and has been a target of extensive studies in cosmology. General forms of shift-symmetric $k$-essence are known to suffer from formation of caustics in a planar-symmetric configuration, with the only exceptions of canonical and DBI-/cuscuton-type kinetic terms. With this in mind, we seek for multi-field caustic-free completions of a general class of shift-symmetric $k$-essence models in this paper. The field space in UV theories is naturally curved, and we introduce the scale of the curvature as the parameter that controls the mass of the heavy field(s) that would be integrated out in the process of EFT reduction. By numerical methods, we demonstrate that the introduction of a heavy field indeed resolves the caustic problem by invoking its motion near the would-be caustic formation. We further study the cosmological application of the model. By expanding the equations with respect to the curvature scale of the field space, we prove that the EFT reduction is successfully done by taking the limit of infinite curvature, both for the background and perturbation, with gravity included. The next leading-order computation is consistently conducted and shows that the EFT reduction breaks down in the limit of vanishing sound speed of the perturbation., 24 pages, 4 figures (10 plots)