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Register a new userHyperbolicity in Spherical Gravitational Collapse in a Horndeski Theory
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We numerically study spherical gravitational collapse in shift symmetric Einstein dilaton Gauss Bonnet (EdGB) gravity. We find evidence that there are open sets of initial data for which the character of the system of equations changes from hyperbolic to elliptic type in a compact region of the spacetime. In these cases evolution of the system, treated as a hyperbolic initial boundary value problem, leads to the equations of motion becoming ill-posed when the elliptic region forms. No singularities or discontinuities are encountered on the corresponding effective Cauchy horizon. Therefore it is conceivable that a well-posed formulation of EdGB gravity (at least within spherical symmetry) may be possible if the equations are appropriately treated as mixed-type.
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We analyze the polarization content of gravitational waves in Horndeski theory. Besides the familiar plus and cross polarizations in Einsteins General Relativity, there is one more polarization state which is the mixture of the transverse breathing and longitudinal polarizations.The additional mode is excited by the massive scalar field. In the massless limit, the longitudinal polarization disappears, while the breathing one persists. The upper bound on the graviton mass severely constrains the amplitude of the longitudinal polarization, which makes its detection highly unlikely by the ground-based or space-borne interferometers in the near future. However, pulsar timing arrays might be able to detect the polarization excited by the massive scalar field. Since additional polarization states appear in alternative theories of gravity, the measurement of the polarizations of gravitational waves can be used to probe the nature of gravity. In addition to the plus and cross states, the detection of the breathing polarization means that gravitation is mediated by massless spin 2 and spin 0 fields, and the detection of both the breathing and longitudinal states means that gravitation is propagated by the massless spin 2 and massive spin 0 fields.
We investigate the propagation of primordial gravitational waves within the context of the Horndeski theories, for this, we present a generalized transfer function quantifying the sub-horizon evolution of gravitational waves modes after they enter the horizon. We compare the theoretical prediction of the modified primordial gravitational waves spectral density with the aLIGO, Einstein telescope, LISA, gLISA and DECIGO sensitivity curves. Assuming reasonable and different values for the free parameters of the theory (in agreement with the event GW170817 and stability conditions of the theory), we note that the gravitational waves amplitude can vary significantly in comparison with general relativity. We find that in some cases the gravitational primordial spectrum can cross the sensitivity curves for DECIGO detector with the maximum frequency sensitivity to the theoretical predictions around 0.05 - 0.30 Hz. From our results, it is clear that the future generations of space based interferometers can bring new perspectives to probing modifications in general relativity.
We present results from a numerical study of spherical gravitational collapse in shift symmetric Einstein dilaton Gauss-Bonnet (EdGB) gravity. This modified gravity theory has a single coupling parameter that when zero reduces to general relativity (GR) minimally coupled to a massless scalar field. We first show results from the weak EdGB coupling limit, where we obtain solutions that smoothly approach those of the Einstein-Klein-Gordon system of GR. Here, in the strong field case, though our code does not utilize horizon penetrating coordinates, we nevertheless find tentative evidence that approaching black hole formation the EdGB modifications cause the growth of scalar field hair, consistent with known static black hole solutions in EdGB gravity. For the strong EdGB coupling regime, in a companion paper we first showed results that even in the weak field (i.e. far from black hole formation), the EdGB equations are of mixed type: evolution of the initially hyperbolic system of partial differential equations lead to formation of a region where their character changes to elliptic. Here, we present more details about this regime. In particular, we show that an effective energy density based on the Misner-Sharp mass is negative near these elliptic regions, and similarly the null convergence condition is violated then.
Using the classical top-hat profile, we study the non-linear growth of spherically symmetric density perturbation and structure formation in $f(T)$ gravities. In particular, three concrete models, which have been tested against the observation of large-scale evolution and linear perturbation of the universe in the cosmological scenario, are investigated in this framework, covering both minimal and nonminimal coupling cases of $f(T)$ gravities. Moreover, we consider the virialization of the overdense region in the models after they detach from the background expanding universe and turn around to collapse. We find that there are constraints in the magnitude and occurring epoch of the initial perturbation. The existence of these constraints indicates that a perturbation that is too weak or occurs too late will not be able to stop the expanding of the overdense region. The illustration of the evolution of the perturbation shows that in $f(T)$ gravities, the initial perturbation within the constraints can eventually lead to clustering and form structure. The evolution also shows that nonminimal coupling models collapse slower than the minimal coupling one.
Studying the effects of dark energy and modified gravity on cosmological scales has led to a great number of physical models being developed. The effective field theory (EFT) of cosmic acceleration allows an efficient exploration of this large model space, usually carried out on a phenomenological basis. However, constraints on such parametrized EFT coefficients cannot be trivially connected to fundamental covariant theories. In this paper we reconstruct the class of covariant Horndeski scalar-tensor theories that reproduce the same background dynamics and linear perturbations as a given EFT action. One can use this reconstruction to interpret constraints on parametrized EFT coefficients in terms of viable covariant Horndeski theories. We demonstrate this method with a number of well-known models and discuss a range of future applications.
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