The present paper extends two previous one's on pure gravity dealing with Einstein-Hilbert and higher derivatives by including a massless scalar field as representative of matter. We study the renormalization to all orders of perturbation theory, provide the Slavnov-Taylor identity, symmetric partial differential equations and derive finiteness properties in the Landau gauge. It is shown that beginning with one-loop negative norm states originating from higher derivatives disappear.
One-loop counterterms are computed in the first order formalism for the Einstein-Hilbert action with a minimally coupled scalar field using the background field method and the heat kernel technique. The {\em off-shell} divergent piece in the harmonic gauge is {\em exactly} the same as the one first found by 't Hooft and Veltman.
In a perturbative approach Einstein-Hilbert gravity is quantized about a flat background. In order to render the model power counting renormalizable, higher order curvature terms are added to the action. They serve as Pauli-Villars type regulators and require an expansion in the number of fields in addition to the standard expansion in the number of loops. Renormalization is then performed within the BPHZL scheme, which provides the action principle to construct the Slavnov-Taylor identity and invariant differential operators. The final physical state space of the Einstein-Hilbert theory is re…
We construct the pure gravity Becchi-Rouet-Stora-Tyutin (BRST) Einstein-Hilbert Lagrangian, to cubic order, using the BRST convolution product of two Yang-Mills theories, in conjunction with the Bern-Carrasco-Johansson (BCJ) double-copy.
We present a systematic technique to expand the Einstein-Hilbert Lagrangian in inverse powers of the speed of light squared. The corresponding result for the non-relativistic gravity Lagrangian is given up to next-to-next-to-leading order. The techniques are universal and can be used to expand any Lagrangian theory whose fields are a function of a given parameter.
Peculiarities of the Canonical Analysis of the First Order Form of the Einstein-Hilbert Action in Two Dimensions in Terms of the Metric Tensor or the Metric Density
We consider the curvatures 2 form asociated with AdSL4 valued one-form gauge connetion, and then we construct a four-dimensional action that generalize the Einstein-Hilbert gravity. It is shown that the Maxwell extension of Einstein gravity can be obtained from AdSL4-gravity making use of the Inonu-Wigner contraction method. In the same way, by gauging the AdSL5 spacetime algebra, the Einstein-Hilbert gravity is extended including the vector fields kab and ha which are associated with non-Abelian tensors and non Abelian vectors charges in the AdSL5 algebra. The B5 extension of Einstein gravity…
We consider cosmological and black hole solutions in the Einstein and higher-derivative gravity in two dimensions where the theory is formulated first in $D$ dimensions. In the limit that $D$ tends to $2$ with simultaneous singular rescaling of the scalar curvature coupling constant as $1/(D-2)$, we get the novel Einstein and higher-derivative gravity. Due to non-trivial contribution of scalar curvature which is topological invariant in exactly two dimensions to gravitational equations in the two-dimensional limit one gets novel cosmological and black hole solutions.In particular, the de Sitte…
We examine how the Einstein-Hilbert action is renormalized by adding the usual counterterms and additional corner counterterms when the boundary surface has corners. A bulk geometry asymptotic to $H^{d+1}$ can have boundaries $S^k \times H^{d-k}$ and corners for $0\leq k<d$. We show that the conformal anomaly when $d$ is even is independent of $k$. When $d$ is odd the renormalized action is a finite term that we show is independent of $k$ when $k$ is also odd. When $k$ is even we were unable to extract the finite term using the counterterm method and we address this problem using instead the K…
The neutrino behavior in the Einstein$\text{-}$Hilbert$\text{-}$Bumblebee gravity around global monopole field
College Pharmacy, Guizhou University of Traditional Chinese Medicine（贵州中医药大学药学院）；School of Science, Guiyang University（贵阳学院理学院）；College of Physics, Guizhou University（贵州大学物理学院）
In this work we shall study a class of $f(R,ϕ)$ gravity models which during the inflationary era, which is the large curvature regime, result to an effective inflationary Lagrangian that contains a rescaled Einstein-Hilbert term $αR$ in the presence of a canonical minimally coupled scalar field. The dimensionless parameter $α$ is chosen to take values in the range $0<α<1$ and the main motivation for studying these rescaled Einstein-Hilbert $f(R,ϕ)$ gravities, is the fact that the rescaled action may render an otherwise incompatible canonical scalar field theory with the Swampland criteria, to …
