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Register a new userCosmology in a Higher-Curvature Gravity
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We investigated the cosmology in a higher-curvature gravity where the dimensionality of spacetime gives rise to only quantitative difference, contrary to Einstein gravity. We found exponential type solutions for flat isotropic and homogeneous vacuum universe for the case in which the higher-curvature term in the Lagrangian density is quadratic in the scalar curvature, $xi R^2$. The solutions are classified according to the sign of the cosmological constant, $Lambda$, and the magnitude of $Lambdaxi$. For these solutions 3-dimensional space has a specific feature in that the solutions are independent of the higher curvature term. For the universe filled with perfect fluid, numerical solutions are investigated for various values of the parameter $xi$. Evolutions of the universes in different dimensionality of spacetime are compared.
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Following the method of Buchbinder and Lyahovich, we carry out a canonical formalism for a higher-curvature gravity in which the Lagrangian density ${cal L}$ is given in terms of a function of the salar curvature $R$ as ${cal L}=sqrt{-det g_{mu u}}f(R)$. The local Hamiltonian is obtained by a canonical transformation which interchanges a pair of the generalized coordinate and its canonical momentum coming from the higher derivative of the metric.
We study the polarizations of gravitational waves (GWs) in two classes of extended gravity theories. First, we formulate the polarizations in linear massive gravity (MG) with generic mass terms of non-Fierz-Pauli type by identifying all the independent variables that obey Klein-Gordon-type equations. The dynamical degrees of freedom (dofs) in the generic MG consist of spin-2 and spin-0 modes, the former breaking down into two tensor (helicity-2), two vector (helicity-1) and one scalar (helicity-0) components, while the latter just corresponding to a scalar. We find convenient ways of decomposing the two scalar modes of each spin into distinct linear combinations of the transverse and longitudinal polarizations with coefficients directly expressed by the mass parameters, thereby serving as a useful tool in measuring the masses of GWs. Then we analyze the linear perturbations of generic higher-curvature gravity (HCG) whose Lagrangian is an arbitrary polynomial of the Riemann tensor. On a flat background, the linear dynamical dofs in this theory are identified as massless spin-2, massive spin-2, and massive spin-0 modes. As its massive part encompasses the identical structure to the generic MG, GWs in the generic HCG provide six massive polarizations on top of the ordinary two massless modes. In parallel to MG, we find convenient representations for the scalar-polarization modes directly connected to the parameters of HCG. In this analysis, we employ two distinct methods; One takes full advantage of the partial equivalence between the generic HCG and MG at the linear level, whereas the other relies upon a gauge-invariant formalism. We confirm that the two results agree. We also discuss methods to determine the theory parameters by GW-polarization measurements. Our method does not require measuring the propagation speeds or the details of the waveforms of the GWs. [Abridged]
Four-dimensional black hole solutions generated by the low energy string effective action are investigated outside and inside the event horizon. A restriction for a minimal black hole size is obtained in the frame of the model discussed. Intersections, turning points and other singular points of the solution are investigated. It is shown that the position and the behavior of these particular points are definded by various kinds of zeros of the main system determinant. Some new aspects of the $r_s$ singularity are discussed.
Gravitational wave observations of compact binaries allow us to test general relativity (and modifications thereof) in the strong and highly-dynamical field regime of gravity. Here we confront two extensions to general relativity, dynamical Chern-Simons and Einstein-dilaton-Gauss-Bonnet theories, against the gravitational wave sources from the GWTC-1 and GWTC-2 catalogs by the LIGO-Virgo Collaboration. By stacking the posterior of individual events, we strengthen the constraint on the square root of the coupling parameter in Einstein-dilaton-Gauss-Bonnet gravity to $sqrt{alpha_{rm tiny EdGB}} < 1.7$ km, but we are unable to place meaningful constraints on dynamical Chern-Simons gravity. Importantly, we also show that our bounds are robust to (i) the choice of general-relativity base waveform model, upon which we add modifications, (ii) unknown higher post-Newtonian order terms in the modifications to general relativity, (iii) the small-coupling approximation, and (iv) uncertainties on the nature of the constituent compact objects.
It is necessary to make assumptions in order to derive models to be used for cosmological predictions and comparison with observational data. In particular, in standard cosmology the spatial curvature is assumed to be constant and zero (or at least very small). But there is, as yet, no fully independent constraint with an appropriate accuracy that gaurentees a value for the magnitude of the effective normalized spatial curvature $Omega_{k}$ of less than approximately $0.01$. Moreover, a small non-zero measurement of $Omega_{k}$ at such a level perhaps indicates that the assumptions in the standard model are not satisfied. It has also been increasingly emphasised that spatial curvature is, in general, evolving in relativistic cosmological models. We review the current situation, and conclude that the possibility of such a non-zero value of $Omega_k$ should be taken seriously.
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