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Register a new userTheoretical and observational constraints on regularized 4$D$ Einstein-Gauss-Bonnet gravity
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Regularized Einstein-Gauss-Bonnet (EGB) theory of gravity in four dimensions is a new attempt to include nontrivial contributions of Gauss-Bonnet term. In this paper, we make a detailed analysis on possible constraints of the model parameters of the theory from recent cosmological observations, and some theoretical constraints as well. Our results show that the theory with vanishing bare cosmological constant, $Lambda_0$, is ruled out by the current observational value of $w_{de}$, and the observations of GW170817 and GRB 170817A as well. For nonvanishing bare cosmological constant, instead, our results show that the current observation of the speed of GWs measured by GW170817 and GRB 170817A would place a constraints on $tilde{alpha}$, a dimensionless parameter of the theory, as $-7.78times10^{-16}le tilde{alpha} leq 3.33times10^{-15}$.
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In this paper we study the observational constraints that can be imposed on the coupling parameter, $hat alpha$, of the regularized version of the 4-dimensional Einstein-Gauss-Bonnet theory of gravity. We use the scalar-tensor field equations of this theory to perform a thorough investigation of its slow-motion and weak-field limit, and apply our results to observations of a wide array of physical systems that admit such a description. We find that the LAGEOS satellites are the most constraining, requiring $| hat alpha | lesssim 10^{10} ,{rm m}^2$. This constraint suggests that the possibility of large deviations from general relativity is small in all systems except the very early universe ($t<10^{-3}, {rm s}$), or the immediate vicinity of stellar-mass black holes ($Mlesssim100, M_{odot}$). We then consider constraints that can be imposed on this theory from cosmology, black hole systems, and table-top experiments. It is found that early universe inflation prohibits all but the smallest negative values of $hat alpha$, while observations of binary black hole systems are likely to offer the tightest constraints on positive values, leading to overall bounds $0 lesssim hat alpha lesssim 10^8 , {rm m}^2$.
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 $Dto4$ Einstein-Gauss-Bonnet gravity with the rescaled Gauss-Bonnet coupling constant $tilde{alpha}$. 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) $Drightarrow 4$ 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 $tilde{alpha}>0$ and $dot{H}<0$, perturbations are free of any pathologies so that we can implement the setup to construct early and/or late time cosmological models. Interestingly, a $k^4$ 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) $Dto 4$ limit. Taking into account the $k^4$ term, the observational constraint on the propagation of gravitational waves yields the bound $tilde{alpha} lesssim (10,{rm meV})^{-2}$. This is the first bound on the only parameter (besides the Newtons constant and the choice of a constraint that stems from a temporal gauge fixing) in the consistent theory of $Dto 4$ Einstein-Gauss-Bonnet gravity.
We study the slow-roll single field inflation in the context of the consistent $Dto4$ Einstein-Gauss-Bonnet gravity that was recently proposed in cite{Aoki:2020lig}. In addition to the standard attractor regime, we find a new attractor regime which we call the Gauss-Bonnet attractor as the dominant contribution comes from the Gauss-Bonnet term. Around this attractor solution, we find power spectra and spectral tilts for the curvature perturbations and gravitational waves (GWs) and also a model-independent consistency relation among observable quantities. The Gauss-Bonnet term provides a nonlinear $k^4$ term to the GWs dispersion relation which has the same order as the standard linear $k^2$ term at the time of horizon crossing around the Gauss-Bonnet attractor. The Gauss-Bonnet attractor regime thus provides a new scenario for the primordial GWs which can be tested by observations. Finally, we study non-Gaussianity of GWs in this model and estimate the nonlinear parameters $f^{s_1s_2s_3}_{rm NL,;sq}$ and $f^{s_1s_2s_3}_{rm NL,;eq}$ by fitting the computed GWs bispectra with the local-type and equilateral-type templates respectively at the squeezed limit and at the equilateral shape. For helicities $(+++)$ and $( -- )$, $f^{s_1s_2s_3}_{rm NL,;sq}$ is larger while $f^{s_1s_2s_3}_{rm NL,;eq}$ is larger for helicities $(++-)$ and $(--+)$.
We provide a refined and much more simplified Einstein-Gauss-Bonnet inflationary theoretical framework, which is compatible with the GW170817 observational constraints on the gravitational wave speed. As in previous works, the constraint that the gravitational wave speed is $c_T^2=1$ in natural units, results to a constraint differential equation that relates the coupling function of the scalar field to the Gauss-Bonnet invariant $xi(phi)$ and the scalar potential $V(phi)$. Adopting the slow-roll conditions for the scalar field and the Hubble rate, and in contrast to previous works, by further assuming that $kappa frac{xi }{xi}ll 1$, which is motivated by slow-roll arguments, we succeed in providing much more simpler expressions for the slow-roll indices and for the tensor and scalar spectral indices and for the tensor-to-scalar ratio. We exemplify our refined theoretical framework by using an illustrative example with a simple power-law scalar coupling function $xi(phi)sim phi^{ u}$ and as we demonstrate the resulting inflationary phenomenology is compatible with the latest Planck data. Moreover, this particular model produces a blue-tilted tensor spectral index, so we discuss in brief the perspective of describing the NANOGrav result with this model as is indicated in the recent literature.
We study the properties of compact objects in a particular 4D Horndeski theory originating from higher dimensional Einstein-Gauss-Bonnet gravity. Remarkably, an exact vacuum solution is known. This compact object differs from general relativity mostly in the strong field regime. We discuss some properties of black holes in this framework and investigate in detail the properties of neutron stars, both static and in slow rotation. We find that for relatively modest deviations from general relativity, the secondary object in GW190814 is compatible with being a slowly-rotating neutron star, without resorting to very stiff or exotic equations of state. For larger deviations from general relativity, the equilibrium sequence of neutron stars matches asymptotically to the black hole limit, closing the mass gap between neutron stars and black holes of same radius, but the stability of equilibrium solutions has yet to be determined. In light of our results and of current observational constraints, we discuss specific constraints on the coupling constant that parametrizes deviations from general relativity in this theory.
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