**Vacuum thin shells in EGB brane-world cosmology**

**Marcos Ramirez - IFEG-CONICET, FaMAF,**

Universidad Nacional de Córdoba, Argentina

Universidad Nacional de Córdoba, Argentina

**GR21 - Columbia University, NYC**

Outline

EGB theory

Thin shells in EGB

Vacuum thin shells exist

This particular construction exist

Interpretations?

Final comments

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

Further possibilities

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

We assume:

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

New phenomenology?

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...

Final comments

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

Thank you

A highly speculative transparency

(for a splitting shell in GR, the continuity equation always has a solution)