String Theory Can Now Describe a Universe That Has Dark Energy

Scientists have struggled to make string theory compatible with the expanding universe.

科学家们一直在努力使弦理论与不断膨胀的宇宙兼容。

In 1998, astronomers discovered dark energy.

1998年，天文学家发现了暗能量。

The finding, which transformed our conception of the cosmos, came with a little-known consequence: It threw a wrench into the already daunting task of finding a version of string theory that describes the universe we live in.

这一发现改变了我们对宇宙的概念，但也带来了一个鲜为人知的后果：它给寻找描述我们所生活的宇宙的弦理论版本这一本已艰巨的任务带来了困难。

Dark energy is a “positive” energy that causes our universe to expand at an accelerating rate.

暗能量是一种“正”能量，它会导致我们的宇宙加速膨胀。

But the best-understood models of string theory describe universes with energy that is either negative or zero.

但最容易理解的弦理论模型描述的宇宙能量要么为负，要么为零。

Of the various criticisms made of string theory through the years — that it only works in a 10-dimensional universe, that its fundamental constituents, tiny strings, are too small to ever be observed — this was perhaps the most troubling.

多年来对弦理论提出的各种批评——弦理论只适用于 10 维宇宙，其基本组成部分，微小的弦，太小而无法被观察到——这可能是最令人不安的。

String theory appeared to be useful only for describing a universe with a negative “anti-de Sitter” geometry, whereas we live in a universe with a positive “de Sitter” geometry.

弦理论似乎只适用于描述具有负“反德西特”几何形状的宇宙，而我们生活在具有正“德西特”几何形状的宇宙中。

Then last year, two physicists offered a stripped-down but precise formula for how string theory could give rise to a universe similar to ours — a de Sitter universe undergoing accelerated expansion.

去年，两位物理学家提出了一个简洁但精确的公式，说明弦理论如何产生一个与我们的宇宙相似的宇宙——一个正在加速膨胀的德西特宇宙。

“It is the very first example [from string theory] of an explicit de Sitter space,” said Thomas Van Riet of KU Leuven in Belgium.

比利时鲁汶大学的托马斯·范里特 (Thomas Van Riet) 表示：“这是第一个（来自弦理论的）显式德西特空间的例子。”

The new work, by Bruno Bento and Miguel Montero of the Institute for Theoretical Physics in Madrid, describes a universe with a dark energy that should weaken over time — a result that matches preliminary cosmic observations from the past few years.

马德里理论物理研究所的布鲁诺·本托和米格尔·蒙特罗的新研究描述了一个具有暗能量的宇宙，这种暗能量会随着时间的推移而减弱——这一结果与过去几年的初步宇宙观测结果相符。

But the universe they describe is not exactly like ours.

但他们描述的宇宙并不完全像我们的宇宙。

While their original hope was to reduce the high-dimensional world of string theory to our own four-dimensional world, they ended up with an extra dimension.

虽然他们最初的希望是将弦理论的高维世界简化为我们自己的四维世界，但他们最终得到了一个额外的维度。

“What they have found is a 5D de Sitter solution, and we don’t live in 5D,” said Antonio Padilla of the University of Nottingham.

“他们找到的是 5D de Sitter 解决方案，而我们并不生活在 5D 中，”诺丁汉大学的 Antonio Padilla 说。

Bruno Bento (left) and Miguel Montero published work that connects the hidden dimensions of string theory to the positive energy of our universe.

布鲁诺·本托（左）和米格尔·蒙特罗发表了将弦理论的隐藏维度与宇宙的正能量联系起来的著作。

Still, the work is expected to launch a new era in matching the mathematical elegance of string theory to the actual world we live in.

尽管如此，这项工作预计将开启一个新时代，将弦理论的数学优雅与我们生活的现实世界相匹配。

“What they have done,” Padilla said, “is open up a new frontier to finding explicit de Sitter solutions in string theory.”

帕迪拉说：“他们所做的是开辟了在弦理论中寻找明确的德西特解的新领域。”

The new work was inspired by a bizarre feature of quantum theory first predicted over 75 years ago.

这项新工作的灵感来自于 75 多年前首次预测的量子理论的一个奇异特征。

In a vacuum, space is never completely empty.

在真空中，空间永远不会完全是空的。

Particles pop in and out of existence, and tiny fluctuations cause quantum fields to do the same.

粒子会突然出现或消失，微小的波动也会导致量子场发生同样的情况。

In 1948, the Dutch physicist Hendrik Casimir recognized that in the narrow space between two conducting plates, not all quantum fields can pop into existence.

1948 年，荷兰物理学家亨德里克·卡西米尔 (Hendrik Casimir) 认识到，在两个导电板之间的狭窄空间中，并非所有量子场都能突然出现。

In this region, the long wavelengths get cut off.

在这个区域，长波长被切断。

This leads to a lower energy density inside the plates than outside.

这导致板内部的能量密度低于外部。

The mismatch of energies creates a force that tries to push the plates together.

能量的不匹配产生了一种力，试图将板块推到一起。

Bento and Montero applied this line of thinking to the process of “compactification,” in which the 10-dimensional physics of string theory becomes the four-dimensional realm we inhabit.

本托和蒙特罗将这种思路应用到“紧化”过程中，其中弦理论的十维物理变成了我们居住的四维领域。

The basic premise of compactification is that the extra dimensions should shrink down and curl up into a shape so tiny that if you were to travel along one of them, you would almost instantly come back to the starting point.

紧凑化的基本前提是，额外的维度应该缩小并卷曲成一个非常小的形状，以至于如果你沿着其中一个维度移动，你几乎会立即回到起点。

The precise shape of the “manifold” that houses these extra dimensions would dictate the properties of all the particles and forces observed in nature.

容纳这些额外维度的“流形”的精确形状将决定自然界中观察到的所有粒子和力的特性。

In the new scenario, the space enclosed within a six-dimensional manifold takes the place of the space between Casimir’s conducting plates.

在新的场景中，六维流形内封闭的空间取代了卡西米尔导电板之间的空间。

Inside the manifold’s interior, fluctuations are similarly restricted, which generates a Casimir-like force.

在歧管内部，波动同样受到限制，从而产生类似卡西米尔的力。

“That’s their key ingredient,” said David Andriot of France’s National Center for Scientific Research.

“这是它们的关键成分，”法国国家科学研究中心的大卫·安德里奥说。

The researchers counterbalanced the Casimir effect with a force generated by a flux.

研究人员用通量产生的力来平衡卡西米尔效应。

Fluxes are standard elements in string theory compactifications.

通量是弦理论紧化中的标准元素。

They’re made up of field lines that wind through string theory’s extra dimensions.

它们由蜿蜒穿过弦理论额外维度的场线组成。

Unlike the Casimir force, which works toward reducing the volume of the manifold’s interior, a flux creates a countervailing effect that tries to expand that volume.

与卡西米尔力不同，卡西米尔力致力于减少歧管内部的体积，而通量会产生试图扩大该体积的抵消效应。

Bento and Montero were able to calculate a specific value for dark energy that was both positive and small.

本托和蒙特罗能够计算出暗能量的特定值，该值既正又小。

The value they arrived at, 10 − 15 in Planck units, is still far from the actual, even smaller value of 10 − 120 , but it is “going down the right path,” Montero said.

他们得出的值（普朗克单位为 10 − 15）仍然与实际值 10 − 120 相距甚远，甚至更小，但它“正在沿着正确的道路前进，”蒙特罗说。

The solution is considered explicit, he explained, which “means we can tell you every detail involved and how it fits together.

他解释说，该解决方案被认为是明确的，这“意味着我们可以告诉您所涉及的每个细节以及它们如何组合在一起。

We can compute a precise value for the dark energy that is close to the exact result.” And if you give your model to other physicists, he said, “they can compute the value of any observable …

我们可以计算出接近准确结果的暗能量的精确值。”他说，如果你把你的模型提供给其他物理学家，“他们可以计算任何可观察到的值……

with precision.”

精确。”

The original idea to look for a Casimir-like effect came from a 2021 paper by Eva Silverstein of Stanford University and two collaborators.

寻找类卡西米尔效应的最初想法来自于斯坦福大学 Eva Silverstein 和两位合作者 2021 年发表的一篇论文。

But Bento and Montero’s goal from the outset was to find a simpler recipe for compactification than previous researchers had.

但本托和蒙特罗从一开始的目标就是找到一种比以前的研究人员更简单的压缩方法。

Eva Silverstein, photographed at Stanford University in 2017, co-authored the paper that inspired Bento and Montero’s solution.

伊娃·西尔弗斯坦 (Eva Silverstein) 于 2017 年在斯坦福大学拍摄，她是这篇论文的共同作者，为 Bento 和 Montero 的解决方案提供了灵感。

In selecting a geometry for the compact extra dimensions, for instance, they chose a space that resembles a torus.

例如，在为紧凑的额外维度选择几何形状时，他们选择了一个类似于环面的空间。

“It’s a simple shape,” Bento said.

“这是一个简单的形状，”本托说。

A doughnut is an example of a 2D torus; it is considered “flat” because it can be made by rolling a flat sheet into a tube and then fastening the ends.

甜甜圈是 2D 环面的一个例子；它被认为是“扁平”的，因为它可以通过将平板卷成管子然后紧固两端来制成。

Bento and Montero picked shapes of this general type, called 6D Riemann-flat manifolds, to house the extra dimensions in their model.

Bento 和 Montero 选择了这种通用类型的形状，称为 6D 黎曼平坦流形，以在模型中容纳额外的维度。

Using this 6D space for the compactification gave them the physical properties they sought.

利用这个 6D 空间进行压缩，为他们提供了他们所寻求的物理特性。

In comparison, the Silverstein team selected a much more complicated geometry to work with: negatively curved hyperbolic manifolds.

相比之下，西尔弗斯坦团队选择了一种更复杂的几何形状来处理：负弯曲双曲流形。

That made their calculations dramatically harder.

这使得他们的计算变得更加困难。

Shortly after Bento and Montero published their paper, Gianguido Dall’Agata and Fabio Zwirner of the University of Padua published their own paper , in which they used a similar setup — also involving Riemann-flat manifolds — to compute the strength of the Casimir effect and show how it can be used to produce dark energy.

本托和蒙特罗发表论文后不久，帕多瓦大学的吉安吉多·达亚加塔 (Gianguido Dall’Agata) 和法比奥·兹维尔纳 (Fabio Zwirner) 发表了自己的论文，其中他们使用类似的设置（也涉及黎曼平坦流形）来计算卡西米尔效应的强度，并展示如何使用它来产生暗能量。

“We use different techniques that are complementary,” Zwirner said.

“我们使用不同的互补技术，”卓纳说。

Bento and Montero took things further than the Padua team, at least in terms of carrying out a full-fledged string compactification.

本托和蒙特罗比帕多瓦团队走得更远，至少在进行全面的弦压缩方面是这样。

But, Montero said, “it was nice that these two approaches agreed, because that provided a good check on the general idea.”

但是，蒙特罗说，“这两种方法达成一致真是太好了，因为这可以很好地检查总体想法。”

The work of Bento and Montero comes with some substantial caveats, as the authors acknowledge.

正如作者承认的那样，本托和蒙特罗的工作带有一些重要的警告。

First, their de Sitter solution is unstable; its dark energy, though positive, will diminish over time.

首先，他们的德西特解不稳定；它的暗能量虽然是积极的，但会随着时间的推移而减弱。

A changeable, dynamical dark energy of this sort, Andriot pointed out, “is much easier to get from string theory” than a dark energy that remains fixed — a notion Einstein introduced in 1917 as the “cosmological constant.”

安德里奥特指出，这种可变的动态暗能量“比保持固定的暗能量更容易从弦理论中获得”——这是爱因斯坦在 1917 年提出的“宇宙常数”概念。

“Unstable,” in this case, has a specific meaning to physicists.

在这种情况下，“不稳定”对于物理学家来说具有特定的含义。

It indicates that the period of stability, or constancy, of dark energy shouldn’t last much longer than a Hubble time — the estimated age of the universe, or about 14 billion years.

它表明暗能量的稳定期或恒定期不应比哈勃时间（宇宙的估计年龄，即大约 140 亿年）持续太久。

Until recently, most observations have been consistent with a universe containing a constant amount of dark energy.

直到最近，大多数观测结果都一致认为宇宙含有恒定量的暗能量。

But recent results suggest that dark energy may be changing.

但最近的结果表明暗能量可能正在发生变化。

In April 2024, the Dark Energy Spectroscopic Instrument presented tentative evidence that dark energy is weakening , and the finding was bolstered a year later .

2024年4月，暗能量光谱仪提出了暗能量正在减弱的初步证据，一年后这一发现得到了证实。

“If those results are here to stay, they are really hinting that the cosmological constant is not a constant,” Montero said.

蒙特罗说：“如果这些结果一直存在，那么它们确实暗示宇宙常数不是一个常数。”

In their pursuit of a de Sitter solution, Bento and Montero simplified their task by starting from M-theory (sometimes called “ the mother of all string theories ”).

在寻求德西特解的过程中，本托和蒙特罗从 M 理论（有时被称为“所有弦理论之母”）出发，简化了他们的任务。

Whereas most versions of string theory require our universe to have six extra dimensions, M-theory requires it to have seven.

大多数版本的弦理论要求我们的宇宙有六个额外维度，而 M 理论则要求它有七个。

Despite the larger number of dimensions, M-theory has fewer ingredients than string theory, so starting with M-theory made Bento and Montero’s calculations markedly easier.

尽管维数较多，但 M 理论的成分比弦理论少，因此从 M 理论开始使本托和蒙特罗的计算明显更容易。

But subtracting the six extra dimensions curled into their manifold from the 11 total dimensions of M-theory left the theorists with a universe in 5D — one “D” too many.

但是，从 M 理论的 11 个总维度中减去卷曲到其流形中的 6 个额外维度，理论家们就得到了一个 5D 的宇宙——多了一个“D”。

The issue of landing on a 5D solution in a 4D universe is no small matter, and Bento and Montero consider resolving it a top priority.

在 4D 宇宙中落地 5D 解决方案的问题不是小问题，Bento 和 Montero 认为解决它是首要任务。

“If we cannot find the four-dimensional solution,” Bento said, “our work cannot be the final answer.”

“如果我们找不到四维解决方案，”本托说，“我们的工作就不能成为最终答案。”

“I hope it works, and they manage to get it [to work] in four dimensions,” Andriot said.

“我希望它能起作用，他们设法让它在四个维度上起作用，”安德里奥说。

However, he cautioned, given the myriad challenges string theorists have faced over the past few decades, he wouldn’t be surprised if the de Sitter problem threw at least a few more obstacles in their path.

然而，他警告说，考虑到弦理论学家在过去几十年中面临的无数挑战，如果德西特问题至少给他们的道路带来了更多障碍，他不会感到惊讶。

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