Tag Archives: #inflation

How Primordial Black Holes Forms From Inflation With Solo or Multiple Bumps? (Cosmology / Quantum Physics)

Ruifeng Zheng and colleagues investigated the formation of primordial black holes (PBHs) from inflation model with bumpy potential, which has multiple bumps. They found that, the potential can give rise to power spectrum with single or multiple peaks in small scales, which can in turn predict the production of primordial black holes. Their study recently appeared in Arxiv.

There are several inflation models which discuss the possibility of the production of primordial black holes in inflation process of the early universe. But, the production of PBHs requires the violation of slow-roll condition. For this reason, slow-roll violating models become an interesting alternative, including ultra-slow-roll (USR) inflation, inflation with inflection points or bumps and others.

Previous studies have already discussed the case of potential with one bump. Now, Ruifeng and colleagues discussed the extended case of multiple bumps, which can generate PBHs at different mass ranges.

Fig 1: The evolution of φ with the parameter N, which enters the USR-like stage three times near N = 20, N = 35 and N = 50. © Zheng et al.

Specifically, they considered the power-law potential as the basic potential, and add one or several bumps of Gaussian type which makes the inflaton roll from the slow-roll stage to USR-like stage.

“These multiple bumps are quite different from the solo-bumpy ones, we have to take care of not only the shape of each bump like height, width, etc., but also the relative distance of the bumps. This is important because, when the inflaton field passes through one bump, it will lose kinetic energy, and if the bumps are far from each other, it may not have enough energy to pass through the next ones. For this reason, we set the bumps close to each other.”

With the potential, they constructed the power spectrum with single or multiple peaks in small scales, while keeping the large scale power spectrum consistent with CMB data. Later, they numerically calculated the abundances of PBHs (fraction to dark matter) at the mass range given by the solo-bumpy potential, as well as three mass ranges given by the multi-bumpy potential. Finally, they found that, PBHs can be formed at different mass ranges, including asteroid mass range (10¯16 − 10¯14M), planet mass range (10¯6 − 10¯3M) and solar mass range (around 1M), some of which can reach significant abundance.

FIG. 2: They plot fP BH for potential (21) given in paper with p = 2 using different threshold densities δc, where the yellow line corresponds to δc = 0.41, the purple line corresponds to δc = 0.46, and the blue line corresponds to δc = 0.486. Their results are consistent with the constraints from current observations. © Zheng et al.

They also found that, the larger threshold energy density (δc) is, the smaller the abundance will be, and this is easy understanding: the larger the threshold energy is, the more difficult it is to form black holes. For the small value of threshold energy density, the abundance of PBHs can reach around 10% of dark matter. The mass range of the PBHs formed is around 10¯15 M, namely the asteroid mass.

Moreover, they also considered the possibility of formation of primordial black holes (PBHs) in the early universe, through ellipsoidal collapse instead of spherical collapse. The difference between these two collapse models is that the threshold density for forming PBH is different. Because compared with the spherical collapse, the PBHs formed by the ellipsoidal collapse will increase the ellipticity of the formed PBHs, which will lead to the correction of the threshold density. Thus, abudance of ellipsoidal PBHs is lower than that of spherical PBHs, due to difference in their threshold densities.

FIG. 3: The figures above show the constraints on primordial black holes acting as dark matter, in which the colored region is excluded by various observations. The blue line correspond to fPBH, and the red line correspond to fe-PBH. The plot is for potential and δc = 0.465. From left to right, the masses of PBHs are 3.6975 × 10¯27 M, 5.8601 × 10¯16 M and 3.6975 × 10¯3 M respectively. Constraints are obtained from the publicly available Python code PBHbounds. © Zheng et al.

Finally, it has been suggested that, considering the age of the universe, PBHs with initial mass less than 1015g (∼ 10¯18 M) has been completely evaporated today. But, the PBHs of mass 3.6975 × 10¯27 (as shown in figure 3 above) may actually be vanishing, and cannot explain the dark matter today. But, although they can’t explain today’s dark matter they may still have a significant impact on the early universe, such as the process of Big Bang Nucleosynthesis, reheating, baryogenesis and so on.

Ruifeng and colleagues suggested that, we can be able to detect the traces left by such PBHs with future observation techniques, to find more evidence of their existence. Meanwhile, for other mass ranges, the PBHs are hardly evaporated till now and thus can act as dark matter.

“We will explore further details on the influences of the PBHs in our model in the future work.”

— concluded authors of the study

Reference: Ruifeng Zheng, Jiaming Shi, Taotao Qiu, “On Primordial Black Holes generated from inflation with solo/multi-bumpy potential”, Arxiv, pp. 1-14, 2021. https://arxiv.org/abs/2106.04303


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Can Non-minimal Gravitational Coupling Form Q-balls and Produce Gravitational Waves? (Quantum Physics)

Summary:

  • Fei and Rui proposed to introduce non-minimal gravitational coupling of AD field to Ricci scalar and discuss its impacts on the Q-balls formation and the associated gravitational wave production.
  • They obtained new form of scalar potential for AD field in the einstein frame.
  • Through simulations, they showed that the AD condensate can fragment efficiently into Q-balls when the fluctuations produced by linear parametric resonance become significant and the dynamics become highly nonlinear.
  • They also found that unless the effects of non-minimal gravitational couplings are taken into account, the Q-balls can not form with positive K parameter.
  • Moreover, they discussed the associated gravitational wave (GW) productions as well as their dependences on the ξ parameter and showed that the peak frequency fP is not sensitive to the choices of ξ while the peak value of Ω (sys. gw, stat. 0)h²  depends on the choices of ξ. Larger ξ will lead to larger peak value of Ω (sys. gw, stat. 0)h². The peak frequency for GW power spectrum lies around a few KHz with their choice of m3/2 = 100TeV. Therefore, the stochastic GW backgrounds can not be observed by the current and upcoming interferometer based GW experiments.

Observations of the gravitational waves (GWs) from black hole mergers by the Advanced LIGO/VIGO detectors open a new era in astrophysics and cosmology. Many experiments plan to further explore GWs, including both the transient GW signals and stochastic GW backgrounds, in a broader range of frequencies and with more accuracy in the coming decades. The stochastic GW backgrounds could reveal certain interesting properties of the very early universe, including the information of the baryogenesis stage, because the relevant dynamics can be potential sources of the stochastic GW backgrounds.

The origin of the baryon asymmetry, which make up 5 percent of the total energy density of the universe, is still an unsolved puzzle today. Sakharov suggested that current baryon density might be understandable in terms of microphysical laws instead of some sort of initial condition. His famous three conditions include the baryon number violation, C and CP violation, the departure from thermal equilibrium. The coherent production of baryons or leptons by the Affleck-Dine (AD) fields can satisfy Sakharov’s conditions and act as a viable baryogenesis mechanism other than the electroweak baryogenesis, the leptogenesis etc. According to the AD mechanism, the AD field starts oscillating around its origin and gives rise to rotational motion when the Hubble parameter becomes as small as the AD scalar mass after inflation, making the baryon number of the universe. The instability of AD field oscillations under small perturbations, which are inevitably introduced by quantum fluctuations of the field, will drive the condensate to fragment into non-topological solitons called Q-balls. The existence and stability of such nontopological solitons are guaranteed by the conserved charge related to a global symmetry. Many numerical studies simulate the formation of Q-balls.

The formation of AD condensate is fairly generic, relying only on the assumptions of inflation and flat directions in supersymmetry (SUSY). SUSY is widely regarded as one of the most promising candidates for new physics beyond the standard model. SUSY gauge theories often possess a remarkable vacuum degeneracy at the classical level, which can be parameterized by some gauge invariant combinations of squarks and sleptons. The flat directions can be lifted by SUSY breaking terms and higher order terms in the superpotential. Such flat directions can act as the AD fields for baryogenesis.

It was shown that significant GWs can be emitted during the Q-balls formation associated with AD mechanism of baryogenesis because the formation of Q-balls is inhomogeneous and not spherical. The formation of Q-balls depend on the effective potential of the AD field, which had been discussed for different SUSY breaking types. On the other hand, it is possible for the AD field to have a direct coupling to the Ricci scalar R, which can change the shape of the effective potential and amend the GW signals. So, it is interesting to discuss the impact of such non-minimal couplings of AD fields to gravity in the AD mechanism and know the new predictions of this scenario and thats what Fei and Rui have discussed in their recent paper.

They proposed to introduce non minimal gravitational coupling of AD field to Ricci scalar and discuss its impacts on the Q-balls formation and the associated gravitational wave productions.

“The AD field can develop a large Vaccum expectation value (VEV) during inflation, and it starts to oscillate after inflation when the cosmic expansion rate becomes comparable to its mass. Soon after the onset of oscillations, the AD field experiences spatial instabilities and deforms into clumpy Q-ball. From the equations of motion for the homogeneous modes and the fluctuations, one can check if the fluctuations can grow exponentially so as to go nonlinear and eventually form Q-balls, given the explicit form of the AD scalar potential.”

— wrote authors of the study

The non-linear property of the Q-ball formation and the subsequent evolution necessitates a numerical simulation. So, they used the public code HLATTICE to simulate numerically the fragmentation of AD fields and the formation of Q-balls with the potential of the form given below.

This is the new form of scalar potential they obtained, for AD fields in the Einstein frame © Fei and Rui

They also solved, the evolution of the equation of motion for the homogeneous mode and the small perturbations δR and δΘ numerically, on a three dimensional cubic N3 lattice with N = 128. In the HLATTICE package, the equations of motion are re-cast in a different form in order to make use of more accurate, stable symplectic integrators.

The initial small fluctuations of the AD condensate come dominantly from the primordial quantum fluctuations, which exited the horizon during inflation and re-entered the horizon afterwards. From the inflationary cosmology, it can be expected to be |δφ/φ| ∼ 10¯5. The final amplitude of the gravity waves is proved to be independent of the size of the initial perturbation in the flat direction.

In addition, they discussed the Q-balls formation process and the emitted GWs with non-vanishing ξ, especially the most interesting K ≥ 0, ξ > 0 case. Their numerical results for fiducial points K = 0, ξ = 10 and K = 0.01, ξ = 10 are shown in Fig.1. In the simulation of this fiducial points, the gravitino mass m3/2 in the scalar potential is chosen to be 100 TeV and the initial value of the homogeneous mode Φ0 is chosen to be 1017 GeV, which may correspond to the flat direction lifted by n = 9. They found that the AD condensate can fragment efficiently into Q-balls when the fluctuations produced by linear parametric resonance become significant and the dynamics become highly nonlinear.

Figure 1: The fragmentation of AD condensate, the formation of Q-balls and the evolution of the GW power spectrum in the case of K = 0, ξ = 10 and K = 0.01, ξ = 10, respectively. The corresponding time scales are labeled with m3/2t. The input parameters are chosen as m3/2 = 100TeV, φ0 = 1017 GeV, δφ/φ0 = 10¯5, dx = 50dt, LH = 0.5. The average energy density is normalized to 1. © Fei and Rui

They showed the process of the Q-balls formation in the panels of Fig.1. From the panels, we can see the stages for AD fragmentation, the emerging of Q-balls and the further evolution of Q-balls, respectively. The maximum values of the energy density within the formed Q-balls are not large for positive K. It can be understood that, unless the effects of non-minimal gravitational couplings are taken into account, the Q-balls can not form with positive K. As such effects are not large, the maximum values of the energy density in the Q-balls should not be large either.

“We find that, with non-minimal gravitational coupling to AD field, Q-balls can successfully form even with the choice of non-negative K parameter for ξ > 0”

— wrote authors of the study

They also showed that the fragmentation process is not isotropic and non-spherical motions of the condensate can generate a quadrupole moment, which will emit GWs during Q-balls formation. The corresponding GW productions associated with the fragmentation of AD field in the case K > 0 and K = 0 can reveal the information of evolution. The evolution of GWs as a function of the evolution time m3/2 t are shown in the upper and lower right panels of Fig.1, respectively.

Figure 2: Benchmark point with K = – 0.1, ξ = 3. The form of the final-stage massive Q-balls in this case is shown in the left panel. The evolution of the GW power spectrum and its dependence on the choices of ξ are shown in the middle and right panels, respectively. The input parameters are chosen as m3/2 = 100TeV, φ0 = 1016GeV, δφ/φ0 = 10¯5, dx = 50dt, LH = 0.5. © Fei and Rui

Moreover, they have also given the associated GW productions as well as their dependences on the ξ parameter. They showed the form of the final-stage massive Q-balls and the frequencies of the GW power spectrum in the case K = −0.1 and ξ = 3 in Fig.2. The GW power spectrum for K = −0.1 and various value of ξ are also shown in Fig. 2. We can see that the peak frequency fP is not sensitive to the choices of ξ while the peak value of Ω (sys. gw, stat. 0)h² depends on the choices of ξ. Larger ξ will lead to larger peak value of Ω (sys. gw, stat. 0)h². The peak frequency for GW power spectrum lies around a few KHz with their choice of m3/2 = 100TeV. Therefore, the stochastic GW backgrounds can not be observed by the current and upcoming interferometer based GW experiments. It was shown in Shuang-Yong Zhou that the peak position of the GW power spectrum depends on the value of m3/2 . Larger values of m3/2 lead to higher GW frequencies. Choosing a lower value of m3/2 can shift the spectrum to lower frequency. However, they found that such a small-shifted GW power spectrum can still not be detected by the upcoming interferometer based GW experiments. As the gravitino mass is given by m3/2 = F/√ 3MP , low SUSY breaking scale F may cause low GW frequencies. If such stochastic GW signal are detected, it may give interesting information on SUSY breaking scale.


Reference: Fei Wang, Rui Wang, “Q-balls Formation and the Production of Gravitational Waves With Non-minimal Gravitational Coupling”, ArXiv, pp. 1-11, 2021. https://arxiv.org/abs/2104.04682


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When Dark Matter Could Be Produced? (Cosmology / Thermodynamics / Astronomy)

Mambrini and Olive proposed the production of dark matter through the gravitational scattering of the inflaton. They found that sufficient GeV-ZeV dark matter can be obtained with reasonable values of reheating temperature (TRH) and maximum temperature (Tmax) by pure gravitational production through inflaton scattering. Their study recently published in ArXiv on dated 11 Feb 2021.

Inflation is a period of supercooled expansion, when the temperature drops by a factor of 100,000 or so. This relatively low temperature is maintained during the inflationary phase. When inflation ends, the temperature returns to the pre-inflationary temperature; this is called reheating or thermalization because the large potential energy of the inflaton field decays into particles and fills the Universe with Standard Model particles, including electromagnetic radiation, starting the radiation dominated phase of the Universe.

Illustration of the production of dark matter through the gravitational scattering of the inflaton. © Mambrini and Olive

They showed that the final abundance of dark matter depends not only on the reheating temperature, but also on the maximum temperature attained and hence on the detailed evolution of the reheating process.

We saw that GeV-ZeV dark matter can be obtained with reasonable values of TRH and Tmax by pure gravitational production through inflaton scattering

— said Olive

As per Mambrini and Olive, during reheating, a thermal bath is quickly generated with a maximum temperature Tmax, and the temperature decreases as the inflaton continues to decay until the energy densities of radiation and inflaton oscillations are equal, at TRH. During these oscillations, s-channel gravitational production of dark matter occurs.

During these oscillations, the inflaton density is high and the leading contribution to dark matter production occurs at the start of reheating at Tmax. This represents an absolute minimal amount of dark matter production and it contributes independent of any interactions the dark matter may have with the Standard Model (or another dark sector if present).

— said Mambrini.

Reference: Yann Mambrini, Keith A. Olive, “Gravitational Production of Dark Matter during Reheating”, Astronomical Journal, pp. 1-6, 2021. https://arxiv.org/abs/2102.06214


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Is It A Wormhole Which Is Expanding?: PART 2: Blackhole Collapse vs. Inflation (Astronomy)

Previously on “Is it a wormhole which is expanding?: PART 1”, we saw that in 1999, Sean hayward proposed a concept that if wormhole negative energy source fails it may collapse into a black hole. He used 3-step penrose diagrams in order to explain this process. Along with all these concepts, he also proposed that if you want to transport matter to another universe through black hole, you need additional negative energy and suggested that:

It is useful for theoretical purposes to have a simple matter model which allows negative energy.

— Said Hayward.

One such suggestion given by Hayward is a Klein-Gordon field whose gravitational coupling takes the opposite sign to normal. That is, the Lagrangian and therefore energy tensor take the new sign, while the Klein-Gordon equation itself is therefore preserved. This may be thought of as a simple model of negative-energy matter or radiation, respectively in the massive and massless cases.

And that’s what Shinkai and Hayward studied in their next paper. They studied dynamical perturbations of static wormhole, using the spherically symmetric Einstein system with the exotic matter model, the massless ghost Klein-Gordon field. They developed a numerical code based on a dual-null coordinate system, in order to follow the horizon dynamics and radiation propagation clearly. Their main experiment involves, adding or subtracting Gaussian pulses in the ghost field, i.e. respectively with negative or positive energy. They also considered Gaussian pulses in a normal Klein-Gordon field, to see the effect on the wormhole of normal matter, like a human being traversing the wormhole.

© Shinkai and Hayward et al.

They found that the dynamical structure will be characterized by the total mass or energy of the system, the Bondi energy. For the static wormhole, the Bondi energy is everywhere positive, maximal at the throat and zero at infinity, i.e. the Bondi energy is zero. Generally, the Bondi energy-loss property, that it should be non-increasing for matter satisfying the null energy condition, is reversed for the ghost field.

FIG. 1: Areal radius r of the “throat” x+ = x–, plotted as a function of proper time. Additional negative energy causes inflationary expansion, while reduced negative energy causes collapse to a black hole and central singularity © Shinkai and Hayward et al.

As a physical measure of the size of the perturbation, they took the initial Bondi energy, scaled by the initial throat radius ‘a’. In practice, they took E(20, 0) and subtract the corresponding value for the static wormhole. Some data are presented in Table I. They found that positive Bondi energy, E0 will cause collapse to a black hole, while negative Bondi energy E0 will cause explosion to an inflationary universe. Also, the speed of the horizon bifurcation increases with the energy. One could also scale the total energy by the maximal initial energy E, but this occurs at the throat and is a/2. In either case, the perturbations are small, down to 1% in energy, yet the final structure is dramatically different. Thus they concluded that the static wormhole is unstable.

FIG. 2: Energy E(x+, x–) as a function of x–, for x+ = 12, 16, 20. Here ca is (a) 0.05, (b1) – 0.1 and (b2) – 0.01. The energy for different x+ coincides at the final horizon location xH–, indicating that the horizon quickly attains constant mass M = E(∞, xH–). This is the final mass of the black hole. The values are shown in Table I. © Shinkai and Hayward et al.

They plot the energy E(x+, x–) as a function of x–, for x+ = 12, 16, 20 for the three cases. In each case, the mass increases rapidly in x– as the horizon ϑ± = 0 forms, but rapidly approaches a constant value in x+ at the horizon. This value M = E(∞, xH–) is the final mass of the black hole. The values are shown in Table I. The graphs indicated that an observer at infinity will see a burst of radiation as the wormhole collapses or explodes. For collapse, a certain fraction of the field energy radiates away, the rest being captured by the black hole, constituting its mass. For explosion, the radiated energy continues to rise in an apparently self-supporting way as the universe inflates.

FIG. 3: Temporary wormhole maintenance. After a normal scalar pulse representing a traveller, they beamed in an additional ghost pulse to extend the life of the wormhole. Horizon locations ϑ+ = 0 are plotted for three cases: (A) no maintenance, which results in a black hole; (B) with a maintenance pulse which results in an inflationary expansion; (C) with a more finely tuned maintenance pulse, which keeps the static structure up to the end of the range. © Shinkai and Hayward et al.

Similarly, they next considered adding a small amount of conventional scalar field to the static wormhole solution. Just refer fig. 3 above you will get the idea. To extend the life of wormhole, they used additional pulse which they sent with scalar pulse. With this maintainance pulse, you will get inflation i.e. Expansion of universe. But, if you avoid to add this ghost pulse you will get a black hole.

FIG. 4: Evolution of a wormhole perturbed by a normal scalar field. Horizon locations: dashed lines and solid lines are ϑ+ = 0 and ϑ– = 0 respectively. © Shinkai and Hayward et al.

In simple terms, just assume normal field pulse as an actual traveller of the traversible wormhole, then he, she or it may go through the wormhole and exit safely into the other universe if the speed is high enough, as can be seen from the Penrose diagram obtained from Fig. 4. However the wormhole itself will collapse to a black hole, ending its usefulness for travellers by killing them.

So, Hayward and Shinkai demonstrated a kind of temporary maintenance of the wormhole, by sending in an additional ghost pulse just after the passing of the traveller. In Fig. 3 they showed the results for pulse parameters (ca’, cb’, cc’) = (0.1, 6.0, 2.0) for the normal field representing the traveller, combined with a balancing pulse, (ca’, cb’, cc’) = (0.02390, 6.0, 3.0), case B, or (ca’, cb’, cc’) = (0.02385, 6.0, 3.0), case C. If they do not send the balancing pulse, the wormhole collapses to a black hole with horizons given by case A in the plot. The case B ends up with an inflationary expansion, while the case C keeps the wormhole structure at least until x’ = 10. Since the final fate of the wormhole is either a black hole or an inflationary expansion, to keep the throat as it was requires a fine-tuning of the parameters, and may not be realistic. However, it shows how the wormhole life may be extended.

This indicates that the wormhole might be maintained by continual adjustments to the radiation level, though it would be a never-ending project.

You might think Hayward’s idea is weird but he let us think alot deeper than anyone ever have been. If proved someday, this will change the way we look at our universe today.


Reference: Hisa-aki Shinkai and Sean A. Hayward, “Fate of the first traversible wormhole: Black-hole collapse or inflationary expansion”, Phys. Rev. D 66, 044005 – Published 16 August 2002. DOI: https://doi.org/10.1103/PhysRevD.66.044005 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.66.044005


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Does Scalar Field and Gravitational Waves Helps in Expansion Of the Universe? (Cosmology / Astronomy / Maths)

Summary:

–> By obtaining de Sitter solutions for isotropic homogeneous on average scalar field, gravitational waves (GW) and gravitons for the empty Universe, Marochnik and colleagues showed that the scalar field and quantum gravitational waves generate the de Sitter expansion of the empty (with no matter) space-time i.e. at the start and by the end of its cosmological evolution the Universe is empty.

–> To get the de Sitter accelerated expansion of the empty space-time under influence of scalar fields, gravitons and classical and quantum gravitational waves, one needs to make a mandatory Wick rotation, i.e. one needs to make a transition to the Euclidean space of imaginary time [means from where the Universe started to the end (which will be imaginary)].

–> In short, in order to get the exponentially fast expansion of the empty FLRW space-time one must use time as a complex variable.

____________________________________________________

Inflation and dark energy are two unsolved puzzles of modern cosmology. The idea of the necessity of inflation (exponentially fast expansion of the very early Universe) does not yet have direct reliable observational confirmation but it seems very attractive due to its ability to solve three known major cosmological paradoxes (flatness, horizon and monopoles). On the other hand, the existence of dark energy (exponentially fast expansion of the modern very late Universe) is an established observational fact. In case of inflation, it is almost generally accepted that the acceleration of expansion is due to a hypothetical scalar field. Choosing a different form of the potential of this field, the authors attempt to reconcile the theory with a number of e-foldings needed to ensure the flatness of the modern Universe to solve the horizon and monopole problems and get an agreement with the CMB observations. In the case of dark energy, for the lack of a better choice, the cosmological constant and the quintessence ( evolving scalar field) are considered as the popular candidates to provide an acceleration, although both ideas meet insuperable difficulties like one of these is a so-called “old cosmological constant problem”: Why is the Λ -value measured from observations is of the order of 10−¹²² vacuum energy density? The second one is a “coincidence problem”: Why is the acceleration happening during the contemporary epoch of matter domination?

© Gettyimages

A common feature of both effects is exponentially rapid expansion of the Universe, and this is an accepted fact. Another common feature is the fact that both effects occur in an empty (or nearly empty) Universe. If an empty space should expand with acceleration then such a mechanism of acceleration should be common for both very early and very late Universe. The crucial importance of this fact was mentioned by Marochnik in his last paper. The modern Universe is about 70% empty, so that we are in the emptying expanding Universe, which asymptotically must become completely empty, i.e. contain no matter. As a result of such emptiness, we observe the dark energy effect. If before the birth of matter the Universe was empty, this empty space-time was to expand in accordance with the de Sitter law. It could explain the origin of inflation. The space-time without matter is not really empty as it always has the natural quantum and Classical fluctuations of its geometry, i.e. gravitons and classical gravitational waves. The question arises: Could not gravitons and/or classical gravitational waves, filling the empty (or nearly empty) Universe, lead to its accelerated expansion?

Now, University of Maryland’s researchers Leonid Marochnik and colleagues have shown that the answer to this question is yes. In their paper, they showed that in the FLRW metric on the average, homogeneous and isotropic scalar field and on the average homogeneous and isotropic ensembles of classical and quantum gravitational waves generate the de Sitter expansion of the empty (with no matter) space-time. i.e. friends, at the start and by the end of its cosmological evolution the Universe is empty.

“The de Sitter solutions for isotropic homogeneous on average scalar field, gravitational waves (GW) and gravitons are obtained for the empty Universe, i.e. they are applicable to the beginning of the Universe evolution (before matter was born) and to the end of it (after the matter disappears).”, said Marochnik.

According to authors, to get the de Sitter accelerated expansion of the empty space-time under influence of scalar fields, gravitons and classical and quantum gravitational waves, one needs to make a mandatory Wick rotation, i.e. one needs to make a transition to the Euclidean space of imaginary time. In other words, to get the exponentially fast expansion of the empty FLRW space-time one must use time as a complex variable.

“As is shown in this paper, the de Sitter accelerated expansion of the empty FLRW space under backreaction of quantum metric fluctuations, classical gravitational waves and/or scalar field require a mandatory transition to the Euclidean space of imaginary time and then return to the Lorentzian space of real time.”, wrote Marochnik in his paper.

On the other hand, they confirmed the de Sitter accelerated expansion of the empty space at the beginning and end of the evolution of the Universe by observational data (dark energy and inflation). One can assume that the very existence of these two effects is the observable evidence to the fact that time by its nature could be a complex value in the empty spacetime of the Universe. If time is a complex variable, what is the physical meaning of its imaginary part?

“I am indebted to Daniel Usikov profound remark that the observable could be only the real part of time, and the imaginary part, for whatever reasons, is unobservable (by analogy with quantum mechanics).”, said Marochnik.

Reference: Marochnik, L. Cosmological acceleration from a scalar field and classical and quantum gravitational waves (Inflation and dark energy). Gravit. Cosmol. 23, 201–207 (2017). https://doi.org/10.1134/S0202289317030082 https://link.springer.com/article/10.1134/S0202289317030082

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Does Dark Worm Hole Exists? If Yes, Then Where?

Ali Ovgun and colleagues studied the evolving wormhole, using dark matter and dark energy. They have obtained the evolving dark wormhole with interesting results.

A wormhole in spacetime is a gravitational quantum fluctuation or bridge, connecting different points and creating a short-cut. Einstein and Rosen first elaborate on wormhole in 1935 using the theory of general relativity. Then, main contributions on traversable wormholes are done by Morris, Thorne and Yurtsever in 1980s. However, since then, no one has discovered a wormhole to date, it is pure theoretical research area. To understand the nature of the Universe with its mysterious is an one of the puzzle of the human’s life.

Artist impression of wormhole © Credit: Mark Garlick Getty Images

Now, Ali Ovgun and colleagues have obtained the evolving dark wormhole with interesting results. Their solutions of the dark wormhole showed that it is located in the early universe and it decays during the inflation. On the other hand, evolving dark wormhole is inflated and continues to accelerated expansion.

The importance of their work is that the matter has two components: cosmological part (only time dependent) and wormhole part (only space dependent). To do so, they used the Chaplygin gas as an equation of state for
cosmic part,

where B, A and α are free parameters. © Ali Ovgun et al.

and Navarro-Frenk-White dark matter density profile to form dark wormhole.

They revealed more interesting results that evolving dark wormhole is located between the Big Bang and inflation. During inflation, it decays, and then there is no dark wormhole i.e. it vanished. It showed that wormhole behaves similarly to the inflation.

©Ali Ovgun et al.

Moreover, in the Fig. (1-5), they plot the scale factor R(t) versus time t, scale factor R(t) versus α with different configurations to show behavior of the evolving wormhole in the inflation era. The figures showed that, first evolving wormhole begun with negative α till inflation, then it was periodically expanding at an accelerating rate and then decelerating rate. The α has a role of fine tuning.

“We have also addressed some open questions to the Kim’s arguments that one might raise. For example, the scale factor of the universe has two components complex and real. We wonder that how it is possible, and how we can explain it. Another issue is that wormhole shall be small as a scale of the Planck length at the Big bang, but then expands too much greater and decays smaller than the Planck length. One may wonder whether wormholes make phase transition to black hole in fact contribute significantly to inflation. On the other hand, if it is correct, this proposal renew in basis our aspiration of understanding how Nature works as parallel of evolving wormhole in universe.”, concluded authors of the study.

Reference: Ali Ovgun et al., “Evolving wormhole supported by dark matter and dark energy”, ArXiv, pp. 1-6, 2018. https://arxiv.org/abs/1803.04256v2

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S-Branes Can Make Ekpyrotic Theory At least Somewhat Respectable (Quantum / Astronomy)

Guys, we know that we live in an expanding universe, in which galaxies and stars are flying away from us at an ever-increasing speed. Scientists can tell that by using different types of techniques to calculate how fast galaxies at different distances from us are moving away. We also have pictures of the baby universe, when it was just 380,000 years old.

Within that baby picture, we see interesting patterns — tiny splotches and blotches that reveal the existence of slight temperature and pressure differences in that young universe.

We are able to explain all these observations with what’s called ‘Big Bang cosmology’, plus an additional idea known as inflation, which is a process that we think happened when the universe was less than a second old. During that process, the universe became much, much larger, taking quantum differences and making them bigger in the process. Those differences eventually grew, as slightly denser patches had slightly stronger gravity, making them bigger. Over time, those differences became large enough to imprint themselves as splotches in the baby picture of the universe.

Big bang cosmology

Tired of the Big Bang Theory and want another version of cosmology? That’s fine, but we’ll have to explain things like the expansion of the universe and the splotches in the baby picture of cosmos. In other words, we have to do a better job at explaining the universe than inflation does.

This seems easy, but it isn’t. The pressure, density and temperature differences in the universe’s early years has bedeviled many alternative cosmologies, including one of the most popular let’s-go-bigger-than-the-big-bang ideas, known as Ekpyrotic universe. The word ekpyrotic comes from the Greek for word for “conflagration,” which refers to an ancient philosophical idea of a constantly repeating universe.

In the Ekpyrotic scenario, the universe … constantly repeats. Under that perspective, we are currently in a “bang” phase, which will eventually slow down, stop, reverse, and crunch back down to incredibly high temperatures and pressures. Then, the universe will somehow bounce back and re-ignite in a new big bang phase.

The trouble is, it’s hard to replicate the blotches and splotches in the baby picture of the universe in an Ekpyrotic universe. When we attempt to put together some vague physics to explain the crunch-bounce-bang cycle (and I do emphasize “vague” here, because these processes involve energies and scales that we aren’t even coming close to understanding with known physics), everything just comes out too … smooth. No bumps. No wiggles. No splotches. No differences in temperature, pressure or density.

And that doesn’t just mean the theories don’t match observations of the early universe. It means that these cosmologies don’t lead to a universe filled with galaxies, stars or even people.

So that’s kind of a bummer.

But, in the latest study, researchers tried attempt to overcome this hurdle and make Ekpyrotic cosmologies at least somewhat respectable, they invoke none other than the S-brane.

Right. S-branes. So you’ve heard of string theory, right? That’s the universe of fundamental physics where every particle is really a tiny, vibrating string. But a few years ago, theorists realized that the strings don’t have to be one-dimensional. And the name they give to a multidimensional string? A brane.

As for the “S” part? Well most branes in string theory can roam around freely through both space and time, but the hypothetical S-brane can exist only in one instant in time, under very special conditions.

In this new Ekpyrotic scenario, when the universe was at its smallest and densest configuration possible, an S-brane appeared, triggering the re-expansion of a cosmos filled with matter and radiation.. Yeah, a Big Bang and with small variations in temperature and pressure, it had given rise to the well-known splotches in the baby pictures of the universe. That’s what three physicists proposed in their new paper.

Is this idea correct? Who knows. String theory is on thin theoretical ice recently, as experiments like those at the Large Hadron Collider have failed to find any hints of a theory known as supersymmetry, which is a critical underpinning of String theory. And the concept of S-branes is itself a controversial idea within the String Theory community, as it’s not exactly known if branes would be allowed to exist only in one moment in time.

There’s also the fact that not only is the universe as we know it expanding, but it’s accelerating in its expansion, with no sign whatsoever of it slowing down (let alone collapsing) anytime soon. Figuring out what could make it hit the brakes and reverse course, then, is tricky.

Still, Ekpyrotic (and other) ideas are worth exploring, because the earliest moments of the universe provide some of the most puzzling and challenging questions to modern physics.