Departamento de Física

División de Ciencias e Ingenierías del Campus León Universidad de Guanajuato

“SUPERSIMETRIA Y ESCALAMIENTO ANISOTRÓPICO; DOS MANERAS DE GENERALIZAR LA

FÍSICA”

Dr. Octavio Obregón

) .. ..

ds

2 = �dt

2 + dx

2 + dy

2 + dz

2

NO ) x

2 + y

2 + z

2 = cte

( )x2+( )y2+( )z2 = cte

ds

2 = gµ⌫|{z}Interaccion

gravitacional

dx

µdx

⌫ )

8>>>><

>>>>:

µ, ⌫ = 0, . . . , 3x

0 = t

x

1 = x

x

2 = y

x

3 = z

Fuerzas

Fuerza de Coulomb

q1

d �

fotond

Bosones (Aµ)

Fermiones ( )

proton ( p

En General: “Interacciones”

Fuerza eléctrica

q2 q2

F = Kq1q2

(d+�)2

e ) electron

SimetríasNúcleo

=?...

. . . +isospın

F ⇠ BAhora que tal si

pero

=no tan facil

=

pero nuevas partıculas

B

. . . . . .

. . . . . .

Fotino

Selectron

F

F B

Regresamos a

gµ⌫

⇢Interaccion

gravitacional...B si Supersimetrıa . . . F gµ⌫ . . . µ

sistemas gravitatorios gµ⌫

ds2 = �dt2 + a(t)2⇥dr2 + r2d⌦2

⇤

a(t) radio del UNIVERSO

El UNIVERSO

Ademas � (o ⇤)

“EL SUPERUNIVERSO”

⇤⇤

(gµ⌫ , µ) & (�,�)

0

0.2

0.4

0.6

0.8

1

-1 -0.5 0 0.5 1

y

x

λ=3

A BC

E

IIIIIIIV

A

2-2

1.5

y

1-1

0.50

00x

0.5

1z

1

1.5

2

2

JCAP 1012:011,2010

Phys. Rev. D 80, 104020 (2009)

Phys. Rev. D 84, 024015 (2011)

Quantum Cosmology in Hořava-Lifshitz Gravity

O. Obregón

Motivation

- Self-consistent framework for quantum gravity

- Applications

1. Gravity duals (AdS/CFT)

2. Mathematical (Ricci Flows)

- Reproduce the observed gravitation phenomena

¿How close can we get with this idea?

Additional Motivation

Unification

Cosmology and BH

Problem of time

- Power-counting Renormalizable Ingredients

Anisotropic Scaling

Symmetries - DiffF(M)

Projectable metric N = N(t) Detailed Balance

Hořava Gravity (Minimal Version)

The Action:

Gravity with Anisotropic Scaling

Kinetic term Potential term

Quadratic in first time derivatives of gij

Invatiant under DiffF(M)

Of order 2z in spatial derivatives of gij

Invariant under DiffF(M)

Action in 3 dim

Action in 3+1 dim

κ, λ, μ. w and ΛW are coupling constants, and comparing the terms in yellow with GR

Detailed Balance

Misner parametrization

Wheeler-DeWitt Equation

Kantowski-Sachs Quantum Cosmological Model

GR Hořava

SdS (Hořava)

• Singularity t = 0

• ξ > 0, non-singular

• ξ = 0, 𝑡𝑠 =3

2Λ (singularity)

• ξ < 0, 2 singularities

SdS (GR)

• Singularity t = 0

• 𝑚 = 0, 𝑡ℎ =3

Λ (horizon)

• 2 horizons with 0 < Λ𝑚2 <1

9

𝑑𝑠2 = −Λ𝑡2

3+2ξ

𝑡+

3

4Λ𝑡2− 1

−1

𝑑𝑡2 +Λ𝑡2

3+2ξ

𝑡+

3

4Λ𝑡2− 1 𝑑𝑟2 + 𝑡2𝑑Ω2

WKB Approximation

SAdS (Hořava)

• Singularity t = 0

• −8 > 9Λξ2, 2 singularities

• −8 ≤ 9Λξ2 ≤ 0, unphysical

SAdS (GR)

• Singularity t = 0

• 𝑚 > 0, 1 Horizon

• 𝑚 < 0, Unphysical

- Quantum cosmology in Horava-Lifshitz gravity

Phys. Rev. D 86, 063502 (2012)

- A quantum cosmological model in Horava-Lifshitz gravity

AIP Conf. Proc. 1396, pp. 151-155 (2011)

Results available in...