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arXiv 2005.06052gr-qcastro-ph.COhep-th
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单模引力中的扩散:解析解、后期加速度和宇宙学约束

Diffusion in unimodular gravity: Analytical solutions, late-time acceleration, and cosmological constraints

Cristóbal Corral, Norman Cruz, Esteban González

摘要:

幺模引力是解决宇宙学常数问题的一种有吸引力的方法。在这种情况下,量子场的真空能量密度不受引力的影响,宇宙学常数仅仅表现为一个积分常数。最近,它已被证明,能量扩散,可能会出现在量子引力和自发坍缩的理论是兼容的,凭借其限制的非同态不变性与这个框架。新的研究表明,这种现象可能导致在均匀和各向同性宇宙的背景下高阶方程,影响其柯西初值问题的适定性。在这项工作中,我们表明,这个问题可以通过假设一个状态方程,涉及的能量密度的功能,其特征在于扩散规避。作为一个应用,我们解决了场方程解析各向同性和均匀的宇宙在正压模型和质量比例连续自发定位(CSL)的情况下,假设只有暗物质发展能量扩散。利用Ia型超新星的宇宙学数据和Hubble观测数据对两个模型的自由参数进行了约束,得到了具有从减速膨胀到加速膨胀的相变的不同解。结果表明,很小但非平凡的能量不守恒与正压模式是相容的。然而,对于CSL模型,我们发现最佳拟合值与以前的实验室实验不兼容。我们评论这一事实,并提出未来的方向,探索宇宙学中的能量扩散。

英文摘要:

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 the well-posedness of their Cauchy initial-value problem. In this work, we show that this issue can be circumvented by assuming an equation of state that relates the energy density to the function that characterizes the diffusion. As an application, we solve the field equations analytically for an isotropic and homogeneous Universes in a barotropic model and in the mass-proportional continuous spontaneous localization (CSL) scenario, assuming that only dark matter develops energy diffusion. Different solutions possessing phase transition from decelerated to accelerated expansion are found. We use cosmological data of type Ia Supernovae and observational Hubble data to constrain the free parameters of both models. It is found that very small but nontrivial energy nonconservation is compatible with the barotropic model. However, for the CSL model, we find that the best-fit values are not compatible with previous laboratory experiments. We comment on this fact and propose future directions to explore energy diffusion in cosmology.

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