弦理论现可描述包含暗能量的宇宙。
内容总结：
弦论首次成功构建含暗能量的宇宙模型，理论物理迎来重大突破
近日，国际物理学界在弦论研究领域取得里程碑式进展。西班牙马德里理论物理研究所的布鲁诺·本托与米格尔·蒙特罗合作，首次在弦论框架下构建出一个明确描述“德西特宇宙”的数学模型。该宇宙类型与人类实际所处的膨胀加速的宇宙特征相符，且模型中暗能量呈现随时间减弱的动态特性，与近年天文观测的初步迹象一致。
自1998年天文学家发现暗能量以来，如何使弦论兼容这种驱动宇宙加速膨胀的“正能量”，一直是理论物理的核心难题。此前弦论最成熟的模型仅适用于能量为负或为零的“反德西特宇宙”，与真实宇宙的几何结构存在根本矛盾。
本托与蒙特罗的研究创新性地借鉴了量子力学中的“卡西米尔效应”——即真空中量子涨落会受到边界限制而产生可观测力。他们将此原理应用于弦论的“紧致化”过程：在将理论中额外的六维空间卷曲成微观流形时，其内部量子涨落受到类似限制，产生内向的“卡西米尔力”。研究团队通过引入弦论中常见的“通量”场产生反向膨胀力与之平衡，最终计算出微小且为正的暗能量数值。
尽管该模型仍存在显著局限——例如最终得到的是一个五维时空解，而非真实四维宇宙；且解本身具有不稳定性，暗能量无法永久恒定——但学界普遍认为其开辟了关键的新研究方向。英国诺丁汉大学安东尼奥·帕迪利亚评价称，这项工作“开启了在弦论中寻找明确德西特解的新前沿”。
值得关注的是，模型预测的暗能量衰减趋势，与2024年以来暗能量光谱仪（DESI）等观测设备发布的初步数据相互呼应。蒙特罗指出，若这些观测结果被进一步确认，可能意味着爱因斯坦提出的“宇宙学常数”并非恒定，而是动态变化的。
研究人员下一步将全力攻克维度难题，尝试将模型降至四维。法国国家科学研究中心的戴维·安德里奥表示，尽管未来可能仍有障碍，但此项突破已为弦论与真实宇宙的对接奠定了重要基础。
中文翻译：
弦理论如今能够描述一个含有暗能量的宇宙
引言
1998年，天文学家发现了暗能量。这一发现不仅彻底改变了我们对宇宙的认知，还带来了一个鲜为人知的后果：它给本就艰巨的弦理论研究增添了新的障碍——我们亟需找到一个能描述现实世界的弦理论版本。
暗能量是一种“正”能量，它导致宇宙加速膨胀。然而，现有最完善的弦理论模型所描述的宇宙，其能量要么为负，要么为零。多年来，弦理论面临诸多批评：它只能在十维宇宙中成立；其基本构成单元“弦”过于微小而无法观测。但最令人困扰的或许是：弦理论似乎仅适用于描述具有负曲率的“反德西特”几何宇宙，而我们实际生活的宇宙却具有正曲率的“德西特”几何结构。
直到去年，两位物理学家提出了一个简化而精确的公式，首次论证弦理论如何能够推导出与我们宇宙相似的德西特宇宙——一个经历加速膨胀的宇宙。比利时鲁汶大学的托马斯·范·里特评价道：“这是弦理论首次给出明确的德西特空间实例。”
马德里理论物理研究所的布鲁诺·本托和米格尔·蒙特罗提出的新理论，描述了一个暗能量随时间逐渐衰减的宇宙——这与过去几年的初步宇宙观测结果相吻合。但他们描述的宇宙并非与我们完全一致。虽然他们最初希望将弦理论的高维世界简化为我们熟悉的四维世界，最终却得到了一个额外维度。诺丁汉大学的安东尼奥·帕迪利亚指出：“他们发现的是五维德西特解，而我们并不生活在五维空间。”
尽管如此，这项研究仍被视为开启了一个新时代，有望将弦理论的数学优雅性与我们生活的现实世界相统一。帕迪利亚认为：“他们的工作开辟了新前沿，为在弦理论中寻找明确的德西特解提供了新路径。”
截断效应
这项研究的灵感来源于量子理论中一个早在75年前就被预言的奇特现象。真空中并非空无一物，粒子会不断产生与湮灭，量子场也存在微小涨落。1948年，荷兰物理学家亨德里克·卡西米尔发现：在两块导体板之间的狭窄空间里，并非所有量子场都能产生。该区域的长波涨落会被截断，导致板内能量密度低于外部，这种能量差会产生使导体板相互靠近的作用力。
本托和蒙特罗将这一思路应用于“紧致化”过程——即弦理论的十维物理结构转化为我们生存的四维世界的过程。紧致化的基本前提是：额外维度会收缩卷曲成极其微小的形状，以至于沿其移动几乎瞬间就会回到起点。容纳这些额外维度的“流形”的具体形态，将决定自然界中所有粒子和力的特性。
在新模型中，六维流形内部空间取代了卡西米尔导体板之间的区域。流形内部的涨落同样受到限制，从而产生类卡西米尔力。研究人员通过弦理论紧致化的标准要素——“通量”产生的力来平衡卡西米尔效应。通量由贯穿弦理论额外维度的场线构成，与试图压缩流形内部体积的卡西米尔力不同，通量会产生试图扩张该体积的反向作用力。法国国家科学研究中心的戴维·安德里奥指出：“这是他们理论的关键要素。”
本托和蒙特罗成功计算出暗能量的具体数值：该值为正且微小，在普朗克单位制下为10⁻¹⁵。虽然距离实际观测值10⁻¹²⁰仍有差距，但蒙特罗表示这已“走上正确轨道”。他解释道，该解具有明确性：“意味着我们可以阐明所有细节及其协调机制，能计算出接近精确结果的暗能量值。其他物理学家拿到我们的模型后，可以精确计算任何可观测量。”
这一寻找类卡西米尔效应的原始构想，源自斯坦福大学伊娃·西尔弗斯坦与两位合作者2021年的论文。但本托和蒙特罗的目标从一开始就是寻找比前人更简明的紧致化方案。例如在选择紧致额外维度的几何结构时，他们采用了环面状空间。本托解释说：“这是简单形状。”甜甜圈就是二维环面的例子，因其可由平面卷曲成管状再连接两端构成，故被视为“平坦”结构。他们选用这类被称为“六维黎曼平坦流形”的几何结构来容纳模型中的额外维度，该六维空间赋予了他们所需的物理特性。
相比之下，西尔弗斯坦团队选择了更为复杂的负曲率双曲流形，这使其计算难度大幅增加。在本托和蒙特罗论文发表后不久，帕多瓦大学的詹圭多·达拉加塔与法比奥·兹维纳也发表论文，他们采用类似框架（同样涉及黎曼平坦流形）计算卡西米尔效应强度，并论证其产生暗能量的机制。兹维纳表示：“我们使用了互补的不同技术。”蒙特罗则指出，至少在实现完整弦理论紧致化方面，他们的研究比帕多瓦团队更进一步，但“两种方法结论一致令人欣慰，这为总体思路提供了有效验证”。
现实局限
本托和蒙特罗的研究存在若干重要限制，作者对此予以承认。首先，他们的德西特解具有不稳定性：暗能量虽为正，但会随时间衰减。安德里奥指出，与爱因斯坦1917年提出的恒定“宇宙学常数”概念相比，这种可变的动态暗能量“更容易从弦理论中获得”。对物理学家而言，“不稳定”在此特指暗能量的稳定期不应超过哈勃时间（约140亿年，即宇宙当前估算年龄）。
长期以来，多数观测数据支持暗能量恒定的宇宙模型。但最新研究显示暗能量可能正在变化。2024年4月，暗能量光谱仪提供初步证据表明暗能量正在减弱，该发现于一年后得到进一步支持。蒙特罗表示：“如果这些结论成立，它们确实暗示宇宙学常数并非恒定。”
为寻求德西特解，本托和蒙特罗从M理论（有时被称为“弦理论之母”）入手以简化研究。多数弦理论版本要求宇宙存在六个额外维度，而M理论要求七个。尽管维度更多，但M理论的构成要素少于弦理论，这显著降低了计算难度。然而从M理论的十一维总量中减去卷曲在流形内的六个额外维度后，理论家得到的是五维宇宙——多出了一个维度。
在四维宇宙中获得五维解绝非小事，本托和蒙特罗将解决此问题列为首要任务。本托坦言：“若无法找到四维解，我们的工作就不能成为最终答案。”安德里奥表示：“希望他们能成功实现四维构建。”但他同时提醒，鉴于弦理论家过去几十年面临的重重挑战，即使德西特问题再设新障也不足为奇。
英文来源：
String Theory Can Now Describe a Universe That Has Dark Energy
Introduction
In 1998, astronomers discovered dark energy. 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.
Dark energy is a “positive” energy that causes our universe to expand at an accelerating rate. But the best-understood models of string theory describe universes with energy that is either negative or zero.
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. 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.
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.
“It is the very first example [from string theory] of an explicit de Sitter space,” said Thomas Van Riet of KU Leuven in Belgium.
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.
But the universe they describe is not exactly like ours. 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. “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.
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.
“What they have done,” Padilla said, “is open up a new frontier to finding explicit de Sitter solutions in string theory.”
The Cutoff
The new work was inspired by a bizarre feature of quantum theory first predicted over 75 years ago.
In a vacuum, space is never completely empty. Particles pop in and out of existence, and tiny fluctuations cause quantum fields to do the same.
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. In this region, the long wavelengths get cut off. This leads to a lower energy density inside the plates than outside. The mismatch of energies creates a force that tries to push the plates together.
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. 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. The precise shape of the “manifold” that houses these extra dimensions would dictate the properties of all the particles and forces observed in nature.
In the new scenario, the space enclosed within a six-dimensional manifold takes the place of the space between Casimir’s conducting plates. Inside the manifold’s interior, fluctuations are similarly restricted, which generates a Casimir-like force.
The researchers counterbalanced the Casimir effect with a force generated by a flux. Fluxes are standard elements in string theory compactifications. They’re made up of field lines that wind through string theory’s extra dimensions. 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. “That’s their key ingredient,” said David Andriot of France’s National Center for Scientific Research.
Bento and Montero were able to calculate a specific value for dark energy that was both positive and small. 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.
The solution is considered explicit, he explained, which “means we can tell you every detail involved and how it fits together. 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 … with precision.”
The original idea to look for a Casimir-like effect came from a 2021 paper by Eva Silverstein of Stanford University and two collaborators. But Bento and Montero’s goal from the outset was to find a simpler recipe for compactification than previous researchers had.
In selecting a geometry for the compact extra dimensions, for instance, they chose a space that resembles a torus. “It’s a simple shape,” Bento said. 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. Bento and Montero picked shapes of this general type, called 6D Riemann-flat manifolds, to house the extra dimensions in their model. Using this 6D space for the compactification gave them the physical properties they sought.
In comparison, the Silverstein team selected a much more complicated geometry to work with: negatively curved hyperbolic manifolds. That made their calculations dramatically harder.
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. “We use different techniques that are complementary,” Zwirner said.
Bento and Montero took things further than the Padua team, at least in terms of carrying out a full-fledged string compactification. But, Montero said, “it was nice that these two approaches agreed, because that provided a good check on the general idea.”
A Dose of Reality
The work of Bento and Montero comes with some substantial caveats, as the authors acknowledge.
First, their de Sitter solution is unstable; its dark energy, though positive, will diminish over time. 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.”
“Unstable,” in this case, has a specific meaning to physicists. 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.
Until recently, most observations have been consistent with a universe containing a constant amount of dark energy. But recent results suggest that dark energy may be changing. In April 2024, the Dark Energy Spectroscopic Instrument presented tentative evidence that dark energy is weakening, and the finding was bolstered a year later. “If those results are here to stay, they are really hinting that the cosmological constant is not a constant,” Montero said.
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”). Whereas most versions of string theory require our universe to have six extra dimensions, M-theory requires it to have seven. 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. 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.
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. “If we cannot find the four-dimensional solution,” Bento said, “our work cannot be the final answer.”
“I hope it works, and they manage to get it [to work] in four dimensions,” Andriot said. 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.