Holographic Phase Transitions and Gravitational Waves

Abstract

Cosmological thermal first-order phase transitions are assumed to proceed via the nucleation of bubbles and subsequent expansion and collision. The out-of-equilibrium physics involved during the collision of bubbles is expected to emit Gravitational Waves (GW) detectable by future generation interferometers like the Laser Interferometer Space Antenna (LISA). The Standard Model of Particle Physics (SM) as we know it does not exhibit any first order thermal phase transitions, meaning that the detection of such GW emission would imply the direct observation of new physics beyond the SM. For this reason, a good theoretical understanding of the features of the GW spectrum emitted during first order thermal phase transitions, together with an exploration of possible alternative mechanisms to bubble collisions is needed more than ever. An accurate study of such emission implies knowing out-of-equilibrium properties of the underlying Quantum Field Theory, which is known to be challenging even at weak coupling.

In this thesis we will employ the AdS/CFT, which has proven to be very useful in the study of out-of- equilibrium physics at strong coupling, to investigate the properties of first order thermal phase transitions and its application to the emission of GW in the early universe.

We start in by introducing Jecco, a program written in Julia and freely available. It evolves in time Einstein’s Equations in a gravity theory with a simple scalar field that provides with first order thermal phase transitions. The simulations are done in 3+1 dynamical dimensions and, therefore the dual Quantum Field Theory has dynamics in 2+1. Jecco has been crucial for the results shown in chapters 5 and 6.

Chapter 3 studies the space of non-uniform states at finite volume in a theory with a first order thermal phase transition. This family of solutions is expected in generic first order transitions. We studied their thermodynamic properties and dominance in different thermodynamic ensembles. We additionally studied their dynamical (in-)stability and obtained the end state of the time evolutions. We additionally observed that in the infinite volume limit the dominant states tend to the well-known phase separated configurations.

In chapter 4 we went ahead and study the collision dynamics of phase domains. These collisions where first observed in the full-time evolution of the spinodal instability. In this chapter we set as initial data two identical phase domains with some velocity that we varied. For low speeds we observed that the domains enter a quasi-static regime in which they moved almost undeformed. Eventually the collision takes place, and the result is a larger phase domain that relaxes by oscillating. For larger velocities the quasistatic regime disappears and for large enough speeds the collision leads to a fragmentation. The eventual end state of all collisions is a phase separated configuration.

Chapter 5 analyzes bubbles, their expansion and the critical one. We observed that the late time expanding bubble profile is self-similar, and that hydrodynamics is applicable everywhere but at the walls. Furthermore, we observed a possible simple relation for the wall velocity, challenging to compute from first principles and important to estimate the GW emission in collisions. We also obtained the critical bubble for a given nucleation temperature, relevant for the nucleation temperature.

Finally in chapter 6 we argued that for theories with enough bubble nucleation probability suppression, the universe might get into the unstable, spinodal branch before nucleating bubbles. At this point the exponential growth of unstable modes dominates the dynamics. We performed the full-time evolution of the instability and computed the sourced GW spectrum. The resulting spectrum seems qualitatively different to the bubble collision one and opens the exciting possibility of being distinguishable in future interferometers.

En esta tesis doctoral nos centramos en el estudio de la física asociada a las transiciones de fase y la emisión de ondas gravitacionales en el universo primitivo en teorías cuánticas de campos fuertemente acopladas. El estudio se realiza mediante la dualidad AdS/CFT, traduciendo los problemas de teoría cuántica de campos a problemas de gravedad clásica y dinámica de agujeros negros.

Para ello comenzamos introduciendo Jecco: la herramienta de programación desarrollada durante la tesis y que realiza simulaciones de evolución temporal en una teoría de gravedad deformada con un campo escalar que introduce transiciones de fase.

Una vez explicado el algoritmo empleado, comenzamos a estudiar la física asociada a las transiciones de fase. En el capítulo 3 encontramos el espacio de soluciones inhomogéneas presentes en toda transición de fase de primer orden a volumen finito, estableciendo la preferencia termodinámica. En el capítulo 4 estudiamos la dinámica de colisiones de un tipo de solución inhomogénea encontrada previamente, dominios de fase. Mediante simulaciones con diferentes velocidades de colisión encontramos tres regímenes diferentes según incrementamos la velocidad: colisión con estado cuasi-estático previo, colisión y relajación del dominio resultante sin estado cuasi-estático y, finalmente, colisión y desfragmentación del dominio resultante.

El capítulo 5 pone su atención en el estudio de la dinámica de burbujas, de crucial importancia en la emisión de ondas gravitacionales en la colisión de estas. Obtuvimos la burbuja crítica y la velocidad terminal de la burbuja para distintas temperaturas de nucleación. Con este estudio observamos una relación lineal sencilla para la velocidad terminal de gran interés y de difícil obtención mediante otros métodos de cálculo.

Finalmente, el capítulo 6 estudia el escenario en el que la nucleación de burbujas está suprimida y en donde la dinámica sigue otra vía, la de la inestabilidad espinodal. Realizamos la simulación completa de dicha inestabilidad y computamos el espectro de emisión de ondas gravitacionales. Llegamos a la conclusión de que dicho espectro es muy diferente del de la colisión de burbujas, pudiendo identificar correctamente el origen de la posible detección de ondas gravitacionales en los interferómetros de próxima generación.