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Register a new userGravitational Constraints on a Lightlike boundary
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We analyse the boundary structure of General Relativity in the coframe formalism in the case of a lightlike boundary, i.e., when the restriction of the induced Lorentzian metric to the boundary is degenerate. We describe the associated reduced phase space in terms of constraints on the symplectic space of boundary fields. We explicitly compute the Poisson brackets of the constraints and identify the first- and second-class ones. In particular, in the 3+1 dimensional case, we show that the reduced phase space has two local degrees of freedom, instead of the usual four in the non-degenerate case.
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An explicit, geometric description of the first-class constraints and their Poisson brackets for gravity in the Palatini-Cartan formalism (in space-time dimension greater than three) is given. The corresponding Batalin- Fradkin-Vilkovisky (BFV) formulation is also developed.
We show that it is impossible to improve the high-energy behavior of the tree-level four-point amplitude of a massive spin-2 particle by including the exchange of any number of scalars and vectors in four spacetime dimensions. This constrains possible weakly coupled ultraviolet extensions of massive gravity, ruling out gravitational analogues of the Higgs mechanism based on particles with spins less than two. Any tree-level ultraviolet extension that is Lorentz invariant and unitary must involve additional massive particles with spins greater than or equal to two, as in Kaluza-Klein theories and string theory.
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Gravitational waves (GW) produced in the early Universe contribute to the number of relativistic degrees of freedom, $N_{rm eff}$, during Big Bang Nucleosynthesis (BBN). By using the constraints on $N_{rm eff}$, we present a new bound on how much the Universe could have expanded between horizon exit of the largest observable scales today and the end of inflation. We discuss the implications on inflationary models and show how the new constraints affect model selection. We also discuss the sensitivities of the current and planned GW observatories such as LIGO and LISA, and show that the constraints they could impose are always less stringent than the BBN bound.
Cosmological constraints on the scalar-tensor theory of gravity by analyzing the angular power spectrum data of the cosmic microwave background (CMB) obtained from the Planck 2015 results are presented. We consider the harmonic attractor model, in which the scalar field has a harmonic potential with curvature ($beta$) in the Einstein frame and the theory relaxes toward the Einstein gravity with time. Analyzing the {it TT}, {it EE}, {it TE} and lensing CMB data from Planck by the Markov chain Monte Carlo method, we find that the present-day deviation from the Einstein gravity (${alpha_0}^2$) is constrained as ${alpha_0}^2<2.5times10^{-4-4.5beta^2} (95.45% {rm C.L.})$ and ${alpha_0}^2<6.3times10^{-4-4.5beta^2} (99.99% {rm C.L.})$ for $0<beta<0.4$. The time variation of the effective gravitational constant between the recombination and the present epochs is constrained as $G_{rm rec}/G_0<1.0056 (95.45% {rm C.L.})$ and $G_{rm rec}/G_0<1.0115 (99.99 %{rm C.L.})$. We also find that the constraints are little affected by extending to nonflat cosmological models because the diffusion damping effect revealed by Planck breaks the degeneracy of the projection effect.
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