The general relativistic perturbations of scalar-tensor theories (STT) of gravity are studied in a manifestly gauge invariant Hamiltonian formalism. After the derivation of the Hamiltonian equations of motion in this framework, the gauge invariant formalism is used to compute the evolution equations of linear perturbations around a general relativistic spacetime background in the Jordan frame. These equations are then specialized to the case of a flat FRW cosmological background. Furthermore, the equivalence between the Jordan frame and the Einstein frame of STT in the manifestly gauge invariant Hamiltonian formalism is analyzed, and it is shown that also in this framework they can be related by a conformal transformation. Finally, the obtained evolution equations for the linear perturbations in our formalism are compared with those in the standard cosmological perturbation theory. It turns out that the perturbation equations in the two different formalisms coincide with each other in a suitable limit. *
In the spatially flat case of loop quantum cosmology, the connectionk is usually replaced by the holonomy sin(μk) µ in the effective theory. In this paper, instead of the standardμ scheme, we use a generalised, undertermined function g(k,p) to represent the holonomy and by using the approach of anomaly free constraint algebra we fix all the counter terms in the constraints and find the restriction on the form of g(k,p), then we derive the gauge invariant equations of motion of the scalar, tensor and vector perturbations and study the inflationary power spectra with generalised holonomy correction. † To be precise, there are actually three different approaches: the "hybrid models" developed by Marugán et al. , the "dressed metric" developed by Ashtekar et al. and the "anomaly free algebra" developed by Bojowald et al., however, the key ideas of the former two are quite similar, and for convenience of statement we put them together with a common name "dressed effective metric".
A first-order action for scalar-tensor theories of gravity is proposed. The Hamiltonian analysis of the action gives the desired connection dynamical formalism, which was derived from the geometrical dynamics by canonical transformations. It is shown that this connection formalism in Jordan frame is equivalent to the alternative connection formalism in Einstein frame. Therefore, the action principle underlying loop quantum scalar-tensor theories is recovered.
The successful detection of the binary neutron star merger GW 170817 and its electromagnetic counterparts has provided an opportunity to explore the joint effect of the host galaxy and the Milky Way (MW) on the weak equivalence principle (WEP) test. In this paper, using the Navarro–Frenk–White profile and the Hernquist profile, we present an analytic model to calculate the galactic potential, in which the possible locations of the source from the observed angle offset and the second supernova kick are accounted for. We show that the upper limit of Δγ is 10−9 for the comparison between GW 170817 and a gamma-ray burst (GRB 170817A), and it is 10−4 for the comparison between GW 170817 and a bright optical transient (SSS 17a, now with the IAU identification of AT 2017gfo). These limits are more stringent by one to two orders of magnitude than those determined solely using the measured MW potential in the literature. We demonstrate that the WEP test is strengthened by the contribution from the host galaxy to the Shapiro time delay. Meanwhile, we also find that large natal kicks produce a maximum deviation of about 20% from the results with a typical kick velocity of 400 to ∼500 km s−1. Finally, we analyze the impact from the halo mass of NGC 4993 with a typical 0.2 dex uncertainty and find that the upper limit of Δγ, with a maximum mass , is nearly two times more stringent than that of the minimum mass .
The effective dynamics of scalar-tensor theory (STT) in the Jordan frame is studied in the context of loop quantum cosmology with holonomy corrections. After deriving the effective Hamiltonian from the connection dynamics formulation, we obtain the holonomy-corrected evolution equations of STT on spatially flat Friedmann-Robterson-Walker background, which exhibit some interesting features unique to the Jordan frame of STT. In particular, the linear term of the cosine function appearing in the equations could lead to dynamics much different from the classical theory in the low-energy limit. In the latter part of this paper, we choose a particular model in STT -the Brans-Dicke theory to specifically illustrate these features. It is found that in Brans-Dicke theory the effective evolution equations can be classified into four different cases. Exact solutions of the Friedmann equation in terms of the internal time are obtained in these cases. Moreover, the solutions in terms of the proper time describing the late time evolution of the Universe are also obtained under certain approximation; in two cases the solutions coincide with the existing solutions in classical Brans-Dicke theory while in the other two cases the solutions do not.
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