Tag Archives: #branes

How Would Be Thick Branes In Mimetic Gravity? (Quantum)

Qun-Ying Xie and colleagues investigated thick branes generated by a scalar field in mimetic gravity theory, which is inspired by considering the conformal symmetry under the conformal transformation of an auxiliary metric. They obtained a series of analytical thick brane solutions and found that, perturbations of the brane system are stable and the effective potentials for the tensor and scalar perturbations are dual to each other. Findings of this study recently appeared in the Journal Symmetry.

Mimetic gravity is a Weyl-symmetric extension of General Relativity, related to the latter by a singular disformal transformation, wherein the appearance of a dust-like perfect fluid can mimic cold dark matter at a cosmological level. Within this framework, it is possible to provide an unified geometrical explanation for dark matter, the late-time acceleration, and inflation, making it a very attractive theory. This theory was also extended to Horava-like theory and applied to galactic rotation curves. It was also applied to other gravity theories such as f(R) gravity, Horndeski gravity and Gauss–Bonnet gravity.

On the other hand, Lisa Randall and Raman Sundrum proposed that our four-dimensional world could be a brane embedded in five-dimensional space-time, in order to solve gauge hierarchy problem and the cosmological constant problem. With the warped extra dimension, it was further found that the size of extra dimension can be infinitely large without conflicting with Newtonian gravitational law. This charming idea has attracted substantial researches in particle physics, cosmology, gravity theory, and other related fields. In the RS model, the brane is geometrically thin, therefore the space-time is singular at the brane. Although in the thin brane approximation many interesting results have been obtained, in some situations the effects of the brane thickness cannot be neglected.

“In five-dimensional problems, the thin brane approximation is valid as long as the brane thickness cannot be resolved, in other words, if the energy scale of the brane thickness is much higher than those in the bulk and on the brane. In contrast, when thickness becomes as large as the scale of interest, its effect is no longer negligible.”

Now, Qun-Ying Xie and colleagues investigated the super-potential method with which the second-order equations can be reduced to the first-order ones for thick brane models in modified gravity with Lagrange multiplier. The main step of this method is to introduce a pair of auxiliary super-potentials, i.e., W(φ) and Q(φ). With these two super-potentials, the field equations are rewritten as Equations (1)–(5).

Then, they used this method to find a series of analytical thick brane solutions via some polynomial super-potentials, period super-potentials, and mixed super-potentials.

Finally, they analyzed the tensor and scalar perturbations of the brane system. It was shown that both equations of motion of the perturbations can be transformed into Schrodinger-like equations. They added that, both perturbations are stable and the effective potentials for the tensor and scalar perturbations are dual to each other. Moreover, the tensor zero mode can be localized on the brane while the scalar zero mode cannot. Thus, the four-dimensional Newtonian potential can be recovered on the brane and there is no additional fifth force contradicting with the experiments.

Featured image: The effective potential VS(z(y)) for solution I. The parameter is set as n = 1 (red solid thick lines), n = 3 (blue dashed lines), and n = 5 (black solid thin lines). © Xie et al.

Reference: Xie, Q.-Y.; Fu, Q.-M.; Sui, T.-T.; Zhao, L.; Zhong, Y. First-Order Formalism and Thick Branes in Mimetic Gravity. Symmetry 2021, 13, https://doi.org/10.3390/sym13081345

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How To Form A Wormhole? (Cosmology / Astronomy)

Stojkovic and colleagues in their very recent paper provided a simple but very useful description of the process of wormhole formation.

Fig. 1 A: A wormhole connecting two points in the same universe. B: In brane world models, the 3 + 1-dimensional universe is confined on a brane that can be twisted or folded. The wormhole structure can connect two spacetime points on brane through the bulk. C: Two completely disconnected branes are connected by a wormhole. This and the previous option are locally equivalent. © Stojkovic et al.
Fig. 2 A: Two branes represented by the solid lines are initially parallel (in the distance they could be twisted or bent). B: Massive objects placed on each brane attract each other gravitationally. The branes bend to balance the force. C: If the gravitational force overcomes the brane tensions, the contact is made and a wormhole like structure is created.

According to authors, if we place two massive objects in two parallel universes (modeled by two branes). Gravitational attraction between the objects competes with the resistance coming from the brane tension. For sufficiently strong attraction, the branes are deformed, objects touch and a wormhole is formed.

“Our analysis indicated that more massive and compact objects are more likely to fulfill the conditions for wormhole formation. This implies that we should be looking for wormholes either in the background of black holes and compact stars, or massive microscopic relics.”, said Skojkovic.

To get some feeling for the orders of magnitude, they calculated that two solar mass objects can form a wormhole like structure for reasonable values of brane tension and distance between the branes.

Strictly speaking, what they discuss in their paper are, wormhole-like structures rather than wormholes in strict sense. They make this distinction because they deal with some global properties of the space-time rather than local geometry. The precise metric of the wormhole-like structure would depend on the concrete massive objects researchers are talking about. If objects located in two parallel universes exerting gravitational force on each other are black holes, then the resulting wormhole would not be traversable due to the presence of the horizon. If the objects in question are neutron stars of other horizon-less objects, then the wormhole would be traversable.

They also note that the role of negative energy density which provides repulsion that counteracts gravity is played by the brane tension. Thus they do not need extra source of negative energy density in their setup to support gravity. However, this still does not guarantee stability of the whole construct. It could happen that a very long wormhole throat breaks into smaller pieces in order to minimize its energy. To verify this, a full stability analysis would be required. They leave this question for further investigation.

“There is a huge range in parameter space that allows for wormhole creation in our setup. Since the balance between the brane tension and mass (and size) of the objects is required, from Equation

we see that if the brane tension is zero, any non-zero mass would be sufficient to form a wormhole. Similarly, if the brane tension is infinite, one would need an infinitely massive object to form a wormhole. Thus, apriory there is no minimal nor maximal max required to form a wormhole.”, said Djordje Minic.

However, from the plot in Fig. given below they saw that for a fixed brane tension and fixed mass more compact objects are more likely to form wormholes.

© Minic et al.

They concluded that, “related issues reserved for future investigation that could possibly be answered in the same or similar framework including the question whether wormholes are produced before or after (brane of bulk) inflation, and whether they are stable on cosmological timescales.

References: De-Chang Dai, Djordje Minic, Dejan Stojkovic, “How to form a wormhole”, ArXiv, pp. 1-6, 2020. https://arxiv.org/abs/2010.03947v2

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Time Maybe Slowing Down – And Will Eventually Stop (Physics)

The universe is expanding at an ever-accelerating rate. At least, that’s what the vast majority of scientists would have you believe. But according to a team of Spanish physicists, it may not be the expansion of the universe that’s changing rate, but time itself. Time might be slowing down, and that means that it could eventually stop altogether.

To illustrate what José Senovilla and his team at the University of the Basque Country in Bilbao, Spain are getting at, think about what it sounds like when an ambulance passes you on the street, sirens blazing. As it drives away from you, the siren begins to drop in pitch. This is known as the Doppler effect, and it happens because the sound waves ever so slightly stretch as the ambulance drives away from you, meaning they reach you at a slower rate (i.e. a lower frequency).

But what if the laws of physics changed when that ambulance passed, and instead of its speed causing that drop in frequency, it was the passage of time? If time were slowing down, that would also make the sound waves reach you at a lower frequency. That’s essentially what Senovilla’s team is suggesting. We “know” the universe is expanding at an accelerating rate because galaxies further away from us have a greater redshift — light’s version of that ambulance Doppler effect — than galaxies closer to us, meaning they’re moving faster. But if time were slowing down, the light would just reach us at a lower frequency. We’d see the redshift, but it would be for a different reason.

This theory sounds outlandish, but it fixes some nagging problems. For the universe’s expansion to be accelerating, you need to come up with something to cause it. That’s where so-called “dark energy” comes in. This mysterious force is supposed to make up 68 percent of the universe, but we’ve never actually observed it. If time is slowing down instead, you don’t need dark energy at all. The mystery of dark energy is fixed since it never existed in the first place.

This theory sounds outlandish, but it fixes some nagging problems. For the universe’s expansion to be accelerating, you need to come up with something to cause it. That’s where so-called “dark energy” comes in. This mysterious force is supposed to make up 68 percent of the universe, but we’ve never actually observed it. If time is slowing down instead, you don’t need dark energy at all. The mystery of dark energy is fixed since it never existed in the first place.

But this theory gets weirder. That’s because it’s based on a principle in string theory that says our universe exists on the surface of a membrane — a “brane,” in string-theory speak — that itself exists inside a higher-dimensional space called the “bulk,” aka hyperspace. All branes can have different numbers of dimensions; ours happens to have three spatial dimensions and one time dimension, but others could have no time dimensions or multiple time dimensions. Dimensions in those other branes could even swing between different versions: space could become time and vice versa. That’s what the researchers think might be happening to our time dimension: It’s slowly turning into a space dimension. If it succeeded, our universe would be frozen in time and exist in four-dimensional space.

We’d experience this as a gradual slowing of time — so gradual, in fact, that for the first billion years or so, we’d only see its evidence in grand scales, like the movement of faraway galaxies. “Our calculations show that we would think that the expansion of the universe is accelerating,” Senovilla told New Scientist. “[Any] observation of dark energy could be evidence that our brane is changing signature and that time is disappearing.”

But if this sounds alarming, don’t worry: This won’t happen for billions of years. In the meantime, buck up! Life is longer than you thought.