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Supermassive cosmic string compactifications

Blanco-Pillado, Jose J., Reina, Borja, Sousa, Kepa, Urrestilla, Jon·2014·Journal of Cosmology and Astroparticle Physics
DOI 10.1088/1475-7516/2014/06/001
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Figures

Figure 1 Space-time geometry and profile functions for a subcritical cosmic string of winding number n = 1 with β = 11 . 1, γ = 0 . 19 and ∆ = 0 . 66 π . LEFT: The lower (blue) surface represents the embedding diagram of the spatial metric on the directions transverse to the string, with the string ( r = 0) placed at the top of the figure. The distance between the lower and the upper (green) surfaces represents the magnetic field density on the transverse space. RIGHT: Scalar condensate f ( r ) (solid blue line), magnetic field B ( r ), reescaled from B (0) = 2 . 03 to 1 / 2 at r = 0 to fit nicely in the plot (dashed red), and metric profile function N ( r ) (dotted green).
Figure 1 Space-time geometry and profile functions for a subcritical cosmic string of winding number n = 1 with β = 11 . 1, γ = 0 . 19 and ∆ = 0 . 66 π . LEFT: The lower (blue) surface represents the embedding diagram of the spatial metric on the directions transverse to the string, with the string ( r = 0) placed at the top of the figure. The distance between the lower and the upper (green) surfaces represents the magnetic field density on the transverse space. RIGHT: Scalar condensate f ( r ) (solid blue line), magnetic field B ( r ), reescaled from B (0) = 2 . 03 to 1 / 2 at r = 0 to fit nicely in the plot (dashed red), and metric profile function N ( r ) (dotted green).CC-BY · From the PDF
Figure 2 Space-time geometry and profile functions for a supermassive cosmic string of winding n = 3 with β = 11 . 1 and γ = 0 . 19 (∆ = 2 . 84 π ). LEFT: The inner (blue) surface represents the embedding diagram of the spatial metric on the directions transverse to the strings. The cosmic string is at the top of the figure ( r = 0), and the conical singularity at the bottom ( r ∗ = 3 . 9). The distance between the inner and the outer (green) surfaces represents the magnetic field density on the transverse space. RIGHT: Scalar condensate f ( r ) (solid blue line), magnetic field B ( r ) (dashed red), and metric profile function N ( r ) (dotted green). The radial coordinate is measured in units of r ∗ . As in the previous plot the magnetic field is rescaled from B (0) = 2 . 2 to 1 / 2 at r = 0.
Figure 2 Space-time geometry and profile functions for a supermassive cosmic string of winding n = 3 with β = 11 . 1 and γ = 0 . 19 (∆ = 2 . 84 π ). LEFT: The inner (blue) surface represents the embedding diagram of the spatial metric on the directions transverse to the strings. The cosmic string is at the top of the figure ( r = 0), and the conical singularity at the bottom ( r ∗ = 3 . 9). The distance between the inner and the outer (green) surfaces represents the magnetic field density on the transverse space. RIGHT: Scalar condensate f ( r ) (solid blue line), magnetic field B ( r ) (dashed red), and metric profile function N ( r ) (dotted green). The radial coordinate is measured in units of r ∗ . As in the previous plot the magnetic field is rescaled from B (0) = 2 . 2 to 1 / 2 at r = 0.CC-BY · From the PDF
Figure 3 Space-time geometry and profile functions for a configuration (1 , 1) with β = γ = 1, and an inter-string distance is r ∗ = 9 . 4. LEFT: Embedding diagram of the transverse space metric (inner blue surface) and magnetic field density over it (outer green surface). The two strings are located at the top and bottom ends of the figure. RIGHT: Profile functions: scalar field profile function f ( r ) (solid blue line), the magnetic field (dashed red) and L ( r ) (dot-dashed yellow). The radial coordinate is measured in units of r ∗ , and the magnetic field is rescaled from B (0) = 1 to 1 / 2 at r = 0.
Figure 3 Space-time geometry and profile functions for a configuration (1 , 1) with β = γ = 1, and an inter-string distance is r ∗ = 9 . 4. LEFT: Embedding diagram of the transverse space metric (inner blue surface) and magnetic field density over it (outer green surface). The two strings are located at the top and bottom ends of the figure. RIGHT: Profile functions: scalar field profile function f ( r ) (solid blue line), the magnetic field (dashed red) and L ( r ) (dot-dashed yellow). The radial coordinate is measured in units of r ∗ , and the magnetic field is rescaled from B (0) = 1 to 1 / 2 at r = 0.CC-BY · From the PDF
Figure 4 Space-time geometry and profile functions for a configuration (3 , 1) with β = 11 . 1 and γ = 0 . 19. The conical singularity has been resolved by a second cosmic string at r ∗ = 3 . 3. LEFT: Embedding diagram of the transverse space metric (inner blue surface) and magnetic field density over it (outer green surface). The higher and lower winding strings are located at the top and bottom ends of the figure respectively. RIGHT: Profile functions: condensate size f ( r ) (solid blue line), magnetic field (dashed red), and the gravitational potential N ( r ) (dotted green). The radial coordinate is measured in units of r ∗ , and the magnetic field is rescaled from B (0) = 1 . 9 to 1 / 2 at r = 0.
Figure 4 Space-time geometry and profile functions for a configuration (3 , 1) with β = 11 . 1 and γ = 0 . 19. The conical singularity has been resolved by a second cosmic string at r ∗ = 3 . 3. LEFT: Embedding diagram of the transverse space metric (inner blue surface) and magnetic field density over it (outer green surface). The higher and lower winding strings are located at the top and bottom ends of the figure respectively. RIGHT: Profile functions: condensate size f ( r ) (solid blue line), magnetic field (dashed red), and the gravitational potential N ( r ) (dotted green). The radial coordinate is measured in units of r ∗ , and the magnetic field is rescaled from B (0) = 1 . 9 to 1 / 2 at r = 0.CC-BY · From the PDF
Figure 5 LEFT: The lines represent the possible regular supermassive solutions in the ( γ, 1 /β ) plane for the configurations ( n 1 , n 2 ) = (2 , 1) (bottom) and (3 , 1)( top ). RIGHT: Inter-string distance r ∗ (also related to the size of the transverse space T ) as function of beta on a (3 , 1) configuration. It decays as r ∗ ∼ 5 . 4 β -0 . 2 for β →∞ .
Figure 5 LEFT: The lines represent the possible regular supermassive solutions in the ( γ, 1 /β ) plane for the configurations ( n 1 , n 2 ) = (2 , 1) (bottom) and (3 , 1)( top ). RIGHT: Inter-string distance r ∗ (also related to the size of the transverse space T ) as function of beta on a (3 , 1) configuration. It decays as r ∗ ∼ 5 . 4 β -0 . 2 for β →∞ .CC-BY · From the PDF
Figure 6 Profile functions of a (3 , 1) configuration for different values of the parameter β . The different line patterns correspond to the same values of beta in all the figures. For example, in the upper left plot the values of β are from bottom to top β = 11 . 1 , 6 . 7 , 2 . 7 , 1 . 7 , 1 . 3, and 1 . 1.
Figure 6 Profile functions of a (3 , 1) configuration for different values of the parameter β . The different line patterns correspond to the same values of beta in all the figures. For example, in the upper left plot the values of β are from bottom to top β = 11 . 1 , 6 . 7 , 2 . 7 , 1 . 7 , 1 . 3, and 1 . 1.CC-BY · From the PDF
Figure 7 LEFT: Area covered by the different branches of solutions in the large m limit. The limiting curves correspond to the spherical compactification and the ( m/ 2 , m/ 2) solution. The vertical line represents the cut through the parameter space that we do to obtain the curves on the right. In the plot we have denoted by γ m the upper bound for the gravitational coupling (4.6). RIGHT: The form of the internal geometry, L ( r ), in the limit of large flux, m = 50. The dotted line represents the spherical configuration close to the (49 , 1) case. We also plot the (38 , 12), (29 , 21), (26 , 24) and (25 , 25) cases. We see how the solutions interpolate from the perfectly spherical solution to the tubular configuration of 2 critical strings of half the flux separated by a straight segment. The distance between the strings increases substantially as one approaches the even split, the (25 , 25) case. All these curves are computed for β = 1 . 2.
Figure 7 LEFT: Area covered by the different branches of solutions in the large m limit. The limiting curves correspond to the spherical compactification and the ( m/ 2 , m/ 2) solution. The vertical line represents the cut through the parameter space that we do to obtain the curves on the right. In the plot we have denoted by γ m the upper bound for the gravitational coupling (4.6). RIGHT: The form of the internal geometry, L ( r ), in the limit of large flux, m = 50. The dotted line represents the spherical configuration close to the (49 , 1) case. We also plot the (38 , 12), (29 , 21), (26 , 24) and (25 , 25) cases. We see how the solutions interpolate from the perfectly spherical solution to the tubular configuration of 2 critical strings of half the flux separated by a straight segment. The distance between the strings increases substantially as one approaches the even split, the (25 , 25) case. All these curves are computed for β = 1 . 2.CC-BY · From the PDF
Figure 8 Profile functions of different configurations with a total magnetic flux 2 n = 50 at β = 1 . 818, together with the corresponding large -n approximation (solid line). We show the splittings (25 , 25), (26 , 24) and (29 , 21) with dash-dotted, dashed, and dotted lines respectively.
Figure 8 Profile functions of different configurations with a total magnetic flux 2 n = 50 at β = 1 . 818, together with the corresponding large -n approximation (solid line). We show the splittings (25 , 25), (26 , 24) and (29 , 21) with dash-dotted, dashed, and dotted lines respectively.CC-BY · From the PDF

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Metadata

Authors
Blanco-Pillado, J. J., Reina, B., Sousa, K., & Urrestilla, J.
Venue
Journal of Cosmology and Astroparticle Physics
Publisher
IOP Publishing
Published
2014-06-03
Volume
2014
Issue
06
Pages
001-001
ISSN
1475-7516
DOI
10.1088/1475-7516/2014/06/001
Cited by
8
References
1
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Blanco-Pillado, J. J., Reina, B., Sousa, K., & Urrestilla, J. (2014). Supermassive cosmic string compactifications. Journal of Cosmology and Astroparticle Physics. https://doi.org/10.1088/1475-7516/2014/06/001

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