An effective theory of gravity in the infrared is proposed, which involves the determinant of the metric relative to the determinant of a prior metric taken to be that of Minkowski spacetime. This effective theory can be interpreted as a generalization of unimodular gravity. In a cosmological context with ultrarelativistic or cold matter, the resulting field equations have only one solution, empty Minkowski spacetime (selected by the prior metric of the theory). The introduction of energy exchange between vacuum and matter gives rise to nonstatic cosmic solutions. It is found that Minkowski spacetime (from the prior metric) appears as an attractor of the dynamic equations. A further result is that energy-momentum conservation of any localized material system is violated in a nonconstant gravitational background. The impact for experiment appears, however, negligible if the vacuum-energy mass scale is of order meV.
BRST-invariant action of general relativity in the unimodular gauge proposed by Baulieu is studied without using perturbative expansions. The expression for the path integral in the unimodular gauge is reduced to a form in which a functional measure is defined by a norm invariant under Transverse Diffeomorphism. It is shown that general relativity in the unimodular gauge with this action and the quantum unimodular gravity are equivalent. It is also shown that Vacuum Expectation Values (VEVs) of Diff invariant operators in the unimodular gauge and other gauge such as the harmonic gauge take dis…
We propose a unimodular version of the Brans-Dicke theory designed with a constrained Lagrangian formulation. The resulting field equations are traceless. The vacuum solutions in the cosmological background reproduce the corresponding solutions of the usual Brans-Dicke theory but with a cosmological constant term. A perturbative analysis of the scalar modes is performed and stable and unstable configurations appear in contrast with the Brans-Dicke case for which only stable configurations occur. On the other hand, tensorial modes in this theory remains the same as in the traditional Brans-Dick…
Unimodular time in JT gravity: a holographic clock
School of Mathematical Sciences and STAG Research Centre, University of Southampton（南安普顿大学数学科学学院和STAG研究中心）；School of Physics and Astronomy and Nottingham Centre of Gravity, University of Nottingham（诺丁汉大学物理与天文学院和诺丁汉引力中心）
给出了D（1 \le D \le 11）维单模引力理论的局部超对称形式，即具有行列式为1的度规张量的超引力理论.在这样一个公式中，不再需要对宇宙学常数进行通常的微调，但它的值被理解为一个初始条件。此外，基于有效真空泛函，得出宇宙学常数为零是最可能的组态。我们还证明了超对称规范代数的封闭性与度规上的么模条件是一致的。
We discuss the weight of vacuum energy in various contexts. First, we compute the vacuum energy for flat spacetimes of the form $\mathbb{T}^3 \times \mathbb{R}$, where $\mathbb{T}^3$ stands for a general 3-torus. We discover a quite simple relationship between energy at radius $R$ and energy at radius $\frac{l_s^2}{ R}$. Then we consider quantum gravity effects in the vacuum energy of a scalar field in $\mathbb{M}_3 \times S^1$ where $\mathbb{M}_3$ is a general curved spacetime, and the circle $S^1$ refers to a spacelike coordinate. We compute it for General Relativity and generic transverse {…
Unimodular gravity is an appealing approach to address the cosmological constant problem. In this scenario, the vacuum energy density of quantum fields does not gravitate and the cosmological constant appears merely as an integration constant. Recently, it has been shown that energy diffusion that may arise in quantum gravity and in theories with spontaneous collapse is compatible with this framework by virtue of its restricted diffeomorphism invariance. New studies suggest that this phenomenon could lead to higher-order equations in the context of homogeneous and isotropic Universe, affecting…
We examine the dynamics of FLRW cosmologies in which the vacuum interacts with a perfect fluid through an energy exchange, focusing on the exploration of nonsingular configurations, including cyclic and bouncing models. We consider two specific choices for the energy transfer. In the first case, the energy transfer is proportional to a linear combination of the vacuum and fluid energy densities which makes the conservation equations exactly integrable. The resulting Friedmann equation can be interpreted as an energy constraint equation with an effective potential for the scale factor that may …
