## Periodic Reporting for period 1 - BRANECOSMOLOGY (Quantum and String Cosmology with Branes and Fluxes)

Reporting period: 2015-09-01 to 2017-08-31

The standard model of cosmology describes the universe we observe on the largest scales, and it is impressive agreement with a large body of experimental observations. The model holds that the universe is dominated by a positive vacuum energy which is responsible for the exponential spatial expansion. Additionally, the matter content of our universe is dominated by “dark” matter, as well as the regular matter that we are familiar with. Finally, it is widely accepted that a period of slow-roll inflation is responsible for seeding the spatial perturbations that give rise to the temperature fluctuations of the cosmic microwave background (CMB). However, implicit in both the early period of inflation and the late-time vacuum energy, there are open questions in the standard model of cosmology that require a theory of quantum gravity.

It has been the objective of this action to explore constructions within string theory which shed some light onto the open questions involving the nature of the very early universe and also the late-time acceleration. Tracing backwards the exponential expansion during inflation, one is lead to an incredibly high density universe where the theory of general relativity breaks down. The breakdown of general relativity, known as a singularity, signals the need for a theory of quantum gravity. Therefore, the one of the main objectives of this action has been to apply techniques in quantum cosmology and string theory to the study of singularities in cosmology. Furthermore, the period of inflation should be embedded into string theory so as to be consistent with its high energy origin. Finally, if string theory is the correct theory of quantum gravity it should contain vacua consistent with the current vacuum energy. It is an objective to apply the state-of-the-art technology for model building in supergravity to describe positive vacuum energies. By making progress towards filling in these gaps in the standard model of cosmology, we make progress towards some of humankind’s oldest and most fundamental questions: what are the origins and fate of our universe?

It has been the objective of this action to explore constructions within string theory which shed some light onto the open questions involving the nature of the very early universe and also the late-time acceleration. Tracing backwards the exponential expansion during inflation, one is lead to an incredibly high density universe where the theory of general relativity breaks down. The breakdown of general relativity, known as a singularity, signals the need for a theory of quantum gravity. Therefore, the one of the main objectives of this action has been to apply techniques in quantum cosmology and string theory to the study of singularities in cosmology. Furthermore, the period of inflation should be embedded into string theory so as to be consistent with its high energy origin. Finally, if string theory is the correct theory of quantum gravity it should contain vacua consistent with the current vacuum energy. It is an objective to apply the state-of-the-art technology for model building in supergravity to describe positive vacuum energies. By making progress towards filling in these gaps in the standard model of cosmology, we make progress towards some of humankind’s oldest and most fundamental questions: what are the origins and fate of our universe?

The fellow has studied cosmological singularities in Anti-de Sitter (AdS) spacetime using the gauge-gravity duality. This technique relates a gravitational system described by string theory in AdS to a field theory in one less dimension. This is the most promising way to study singularities because the geometric description of spacetime as well as the calculable regime of string theory do not apply where spacetime curvatures become large. Gauge-gravity duality provides a way of mapping the physics of the singularity to a field theory. Thus, we were able to compute correlation functions for operators in the field theory which are dual to correlators in the geometry containing the singularity. We notice signatures in the correlators which most closely probe the singularity that are related to the well known behaviour of correlation functions of massless scalars in dS. Thus, this project constitutes progress in that it identifies signatures in a well defined field theory that are dual to cosmological singularities.

The other work in this action that increases the understanding of the early universe in the frame work of quantum gravity is the embedding of a model of large field inflation in string theory. The specific set-up combines a toy-model of inflation in string theory, Unwinding inflation, with the mechanism of brane-flux annihilation in the Klebanov-Strassler (KS) throat to achieve an explicit embedding of a novel inflationary mechanism in a known string geometry. While there remains a broader question of the explicit compactified geometry which contains the KS throat, this model is currently one of the most explicit and well-controlled examples of large field inflation in string theory.

We close by describing the work on the late-time behavior of the universe in string theory. The first hurdle for any string theory model which even vaguely resembles our universe is achieving a separation of scales between the 3 spatial directions we observe, and the 6 dimensions which string theory predicts. Such a separation of scales is notoriously difficult and crucially important to any string phenomenology. The work in this action includes an extension of a no-go theorem by Maldacena and Nunez which delineates some necessary ingredients to achieving such a separation of scales. Additionally, string theory has notoriously struggled to produce vacuums with positive energy density. The source of this difficulty is the inherent supersymmetry which is present in high energy string theory, and is incompatible with dS. Recent breakthroughs have lead to a formulation of non-linearly realized supersymmetry using nilpotent chiral superfields. The fellow has made use of this state-of-the-art technology to compute the most general supergravity action containing one such nilpotent super field coupled to an arbitrary number of chiral and vector superfields. These results are important to cosmology because the non-linearly realized supersymmetry allows one to describe supersymmetry breaking, resulting in a positive vacuum energy.

The other work in this action that increases the understanding of the early universe in the frame work of quantum gravity is the embedding of a model of large field inflation in string theory. The specific set-up combines a toy-model of inflation in string theory, Unwinding inflation, with the mechanism of brane-flux annihilation in the Klebanov-Strassler (KS) throat to achieve an explicit embedding of a novel inflationary mechanism in a known string geometry. While there remains a broader question of the explicit compactified geometry which contains the KS throat, this model is currently one of the most explicit and well-controlled examples of large field inflation in string theory.

We close by describing the work on the late-time behavior of the universe in string theory. The first hurdle for any string theory model which even vaguely resembles our universe is achieving a separation of scales between the 3 spatial directions we observe, and the 6 dimensions which string theory predicts. Such a separation of scales is notoriously difficult and crucially important to any string phenomenology. The work in this action includes an extension of a no-go theorem by Maldacena and Nunez which delineates some necessary ingredients to achieving such a separation of scales. Additionally, string theory has notoriously struggled to produce vacuums with positive energy density. The source of this difficulty is the inherent supersymmetry which is present in high energy string theory, and is incompatible with dS. Recent breakthroughs have lead to a formulation of non-linearly realized supersymmetry using nilpotent chiral superfields. The fellow has made use of this state-of-the-art technology to compute the most general supergravity action containing one such nilpotent super field coupled to an arbitrary number of chiral and vector superfields. These results are important to cosmology because the non-linearly realized supersymmetry allows one to describe supersymmetry breaking, resulting in a positive vacuum energy.

The work on cosmological singularities went beyond the frontiers of other studies in that the singular geometries were constructed via Euclidean instantons such that the boundary theory was a deformation of a known conformal field theory on dS. Notably, the field theory remained everywhere smooth and well defined in contrast to other studies where the boundary was also singular, making interpretation of results more difficult.

The implementation of a model of large field inflation in string theory is important for both cutting-edge philosophical and observational questions involving quantum gravity. First, there is a conjecture that large field excursions may be impossible in quantum gravity. Thus this model could provide an important counter-example to this conjecture. Because of the relative simplicity of the KS geometry and ingredients involved, this model stands out as a prime candidate to achieve the level of computational control needed for a definite counter-example. Furthermore, such a large field excursion would predict a potentially observable signature in the CMB produced by primordial gravitational radiation.

By the extension of the Maldacena-Nunez no-go theorem, the fellow proves that certain ingredients are necessary for a string compactification to have any hope of resembling our universe. This provides and important starting place and list of ingredients for any future model-builders. Furthermore, at the level of 4-dimensional supergravity, the use of new constructions allowed the fellow to write a general class of actions that could be used to model the late-time acceleration of the universe.

The impact of the experimental predictions of this action are important for current and future missions which will observe the CMB. By expanding the realm of theoretical predictions, this action provides potential channels for the interpretation of future experiments. In addition, by furthering our understanding of the initial conditions and final state of our universe, we take steps towards some of the most fundamental questions of our universe, whose intrinsic interest and worth are difficult to overstate.

The implementation of a model of large field inflation in string theory is important for both cutting-edge philosophical and observational questions involving quantum gravity. First, there is a conjecture that large field excursions may be impossible in quantum gravity. Thus this model could provide an important counter-example to this conjecture. Because of the relative simplicity of the KS geometry and ingredients involved, this model stands out as a prime candidate to achieve the level of computational control needed for a definite counter-example. Furthermore, such a large field excursion would predict a potentially observable signature in the CMB produced by primordial gravitational radiation.

By the extension of the Maldacena-Nunez no-go theorem, the fellow proves that certain ingredients are necessary for a string compactification to have any hope of resembling our universe. This provides and important starting place and list of ingredients for any future model-builders. Furthermore, at the level of 4-dimensional supergravity, the use of new constructions allowed the fellow to write a general class of actions that could be used to model the late-time acceleration of the universe.

The impact of the experimental predictions of this action are important for current and future missions which will observe the CMB. By expanding the realm of theoretical predictions, this action provides potential channels for the interpretation of future experiments. In addition, by furthering our understanding of the initial conditions and final state of our universe, we take steps towards some of the most fundamental questions of our universe, whose intrinsic interest and worth are difficult to overstate.