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Vacuum thin shells in EGB brane-world cosmology
Transcript of Vacuum thin shells in EGB brane-world cosmology
Marcos Ramirez - IFEG-CONICET, FaMAF,
Universidad Nacional de Córdoba, Argentina
GR21 - Columbia University, NYC
Thin shells in EGB
Vacuum thin shells exist
This particular construction exist
Lovelock gravity in a nutshell
Thin shells in EGB gravity
In a spacetime of 5 or 6 dimensions
A higher-dimensional generalization of GR
There is a junction condition for a source concentrated on a hypersurface (Davis, PRD 2003 - Gravanis-Willison, PLB 2003 )
A simple and usual setting
A 5-dimensional spacetime foliated by 3-dimensional constant curvature manifolds
These equations can have a non-trivial solution even if S=0
A vacuum thin shell
There is a Birkhoff theorem (Zegers, JMP 2005), so every vacuum region has a metric
This is Einstein-Gauss-Bonnet (EGB) theory of gravity
Xi is +1 or -1. The first option is called the "stringy branch", while the second one is the "gr branch"
Garraffo et. al. (JMP 2007) studied the dynamics of vacuum thin shells in isotropic spacetimes
And a non-vacuum thin shell
A brane-world in a Z2-symmetric bulk has the equation of motion
In GR, these kind of constructions are possible:
From a shell made of two non-interacting components a splitting thin shell construction can be made
If the orientations of the bulk are standard, then the shell matches two different branches
A "false vacuum" bubble
In a brane-world context (with Z2 symmetry), this separation can be interpreted as a part of the matter-energy content of the universe leaving the brane
In a EGB brane-world setting, this other construction is possible
The central mass parameter is obtained from imposing the continuity of the normal vector at the separation point
Considering the accelerations at the separation point, a condition for the existence of this construction is obtained (it could be interpreted as a stability condition)
Ramirez, CQG 2015
The mass parameter of the "stringy" branch is also obtained by imposing continuity of the normal vector
The continuity condition is a transcendental equation for mu', so a general stability (or feasibility) condition can not be written
And this equation has solutions only if the initial bulk spacetime satisfies:
Where the effective potential is written in terms of the functions
The gr-branch has the Schwarzschild-Tangherlini solution as a limit, the stringy one has no small alpha limit
Both branches are asymptotically dS or AdS (so for a given Lambda and alpha there are two different effective cosmological constants)
If Lambda=0, the gr-branch is asymptotically flat, but the stringy branch is not
The "false vacuum bubbles" can not be stably static nor oscillatory
Also, the masses of the bulk regions can not be equal
Two gr-branches can only be glued if alpha<0 and the bulk regions must have the wormhole orientation
The dynamics is described by:
With some fine tuning of the involving constants, standard cosmology can be recovered in the large "a" limit
Both the 4-d gravitational coupling constant and cosmological constant appear as functions of the parameters of this construction (hence the fine tuning)
For small "a", equations are completely different than the standard picture (but there is a big bang)
This construction is possible for small "a" in a not-so-radiation-dominated
brane-world, and the parameters can be chosen so that the effective Friedmann equation tends to the standard one at large scale parameter
After the splitting of the vacuum shells, both the effective cosmological constant and gravitational coupling constant change
Anyway, this can not happen if we are near the "standard model regime", it can only take place at early times
And apparently, the vacuum shells always end up colliding with the central shell in relatively "short" period of time
After the splitting, the vacuum shells quickly recombine, what shell-crossing condition should we use?
Can varying Lambda and varying G models be reproduced?
Reverse the branches?
Anyway, we know that the non-gr branches have some issues...
We showed that we can smoothly glue vacuum thin shells to non-vacuum thin shells at certain points of the latter's evolution
This exotic solutions might also signal something pathological regarding thin shells in Lovelock theory
Similar solutions in GR are possible, but they always involve separating matter-energy fields. Their strangeness can be understood as a consequence of the neglected matter-energy degrees of freedom. This is not the case
Also, a formal proof that thin shells in Lovelock are well-defined (whether they make sense as weak solutions) is still lacking
A highly speculative transparency
(for a splitting shell in GR, the continuity equation always has a solution)