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In a very recent paper [1], we have proposed a novel 4-dimensional gravitational theory with two dynamical degrees of freedom, which serves as a consistent realization of D→4 Einstein-Gauss-Bonnet gravity with the rescaled Gauss-Bonnet coupling constant ̃α. This has been made possible by breaking a part of diffeomorphism invariance, and thus is consistent with the Lovelock theorem. In the present paper, we study cosmological implications of the theory in the presence of a perfect fluid and clarify the similarities and differences between the results obtained from the consistent 4-dimensional theory and those from the previously considered, naive (and inconsistent) D→ 4 limit. Studying the linear perturbations, we explicitly show that the theory only has tensorial gravitational degrees of freedom (besides the matter degree) and that for 0̃α> and 0Ḣ<, perturbations are free of any pathologies so that we can implement the setup to construct early and/or late time cosmological models. Interestingly, a k4 term appears in the dispersion relation of tensor modes which plays significant roles at small scales and makes the theory different than not only general relativity but also many other modified gravity theories as well as the naive (and inconsistent) D→ 4 limit. Taking into account the k4 term, the observational constraint on the propagation of gravitational waves yields the bound ̃α ≲ 𝒪(1) eV−2. This is the first bound on the only parameter (besides the Newton's constant and the choice of a constraint that stems from a temporal gauge fixing) in the consistent theory of D→ 4 Einstein-Gauss-Bonnet gravity.

We study canonical transformations of general relativity (GR) to provide a novel matter coupling to gravity. Although the transformed theory is equivalent to GR in vacuum, the equivalence no longer holds if a matter field minimally couples to the canonically transformed gravitational field. We find that a naive matter coupling to the transformed field leads to the appearance of an extra mode in the phase space, rendering the theory inconsistent. We then find a consistent and novel way of matter coupling: after imposing a gauge fixing condition, a matter field can minimally couple to gravity without generating an unwanted extra mode. As a result, the way matter field couples to the gravitational field determines the preferred time direction and the resultant theory has only two gravitational degrees of freedom. We also discuss the cosmological solution and linear perturbations around it, and confirm that their dynamics indeed differ from those in GR. The novel matter coupling can be used for a new framework of modified gravity theories. * katsuki-a12@gravity.phys.waseda.ac.jp † Chunshan.Lin@fuw.edu.pl ‡ shinji.mukohyama@yukawa.kyoto-u.ac.jp Recently, the paper [18] provided new class of modi-

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We study cosmology in a class of minimally modified gravity (MMG) with two local gravitational degrees of freedom. We classify modified gravity theories into type-I and type-II: theories of type-I have an Einstein frame and can be recast by change of variables as general relativity (GR) with a nonminimal matter coupling, while theories of type-II have no Einstein frame. Considering a canonical transformation of the lapse, the 3-dimensional induced metric and their conjugate momenta we generate type-I MMG. We then show that phenomenological deviations from GR, such as the speed of gravitational waves cT and the effective gravitational constant for scalar perturbations G eff , are characterized by two functions of an auxiliary variable. We study the phenomenology of several models all having cT = 1. We obtain a scenario with cT = 1 in which the effective equation-of-state parameter of dark energy is different from −1 even though the cosmic acceleration is caused by a bare cosmological constant, and we find that it is possible to reconstruct the theory on choosing a selected time-evolution for the effective dark energy component.

We consider the possibility that the massive graviton is a viable candidate of dark matter in the context of bimetric gravity. We first derive the energy-momentum tensor of the massive graviton and show that it indeed behaves as that of dark matter fluid. We then discuss a production mechanism and the present abundance of massive gravitons as dark matter. Since the metric to which ordinary matter fields couple is a linear combination of the two mass eigenstates of bigravity, production of massive gravitons, i.e. the dark matter particles, is inevitably accompanied by generation of massless gravitons, i.e. the gravitational waves. Therefore, in this scenario some information about dark matter in our universe is encoded in gravitational waves. For instance, if LIGO detects gravitational waves generated by the preheating after inflation then the massive graviton with the mass of ∼ 0.01 GeV is a candidate of the dark matter.

We study the validity of positivity bounds in the presence of a massless graviton, assuming the Regge behavior of the amplitude. Under this assumption, the problematic t-channel pole is canceled with the UV integral of the imaginary part of the amplitude in the dispersion relation, which gives rise to finite corrections to the positivity bounds. We find that low-energy effective field theories (EFT) with “wrong” sign are generically allowed. The allowed amount of the positivity violation is determined by the Regge behavior. This violation is suppressed by $$ {M}_{\mathrm{pl}}^{-2}\alpha^{\prime } $$ M pl − 2 α ′ where α′ is the scale of Reggeization. This implies that the positivity bounds can be applied only when the cutoff scale of EFT is much lower than the scale of Reggeization. We then obtain the positivity bounds on scalar-tensor EFT at one-loop level. Implications of our results on the degenerate higher-order scalar-tensor (DHOST) theory are also discussed.

We classify the metric-affine theories of gravitation, in which the metric and the connections are treated as independent variables, by use of several constraints on the connections. Assuming the Einstein-Hilbert action, we find that the equations for the distortion tensor (torsion and nonmetricity) become algebraic, which means that those variables are not dynamical. As a result, we can rewrite the basic equations in the form of Riemannian geometry. Although all classified models recover the Einstein gravity in the Palatini formalism (in which we assume there is no coupling between matter and the connections), but when matter field couples to the connections, the effective Einstein equations include an additional hyper energy-momentum tensor obtained from the distortion tensor. Assuming a simple extension of a minimally coupled scalar field in metricaffine gravity, we analyze an inflationary scenario. Even if we adopt a chaotic inflation potential, certain parameters could satisfy observational constraints. Furthermore, we find that a simple form of Galileon scalar field in metric-affine could cause G-inflation.