## Periodic Reporting for period 1 - STRINGFLATION (Inflation in String Theory - Connecting Quantum Gravity with Observations)

**Reporting period:**2015-10-01

**to**2017-03-31

## Summary of the context and overall objectives of the project

The project “STRINGFLATION” aims at predicting the energy scale of cosmological inflation and the strength of the inflationary gravitational wave signal from string theory. Observations of the cosmic microwave background (CMB) temperature fluctuations have drastically changed cosmology into quantitative science. The results provide strong evidence for two phases of accelerated expansion in our Universe. The late-time phase of acceleration, termed dark energy, is consistent with an extremely small positive cosmological constant, while the evidence for a very early phase of acceleration increasingly supports cosmological inflation.

Very recently, the BICEP2 experiment reported the detection of B-mode polarization in the CMB. Pending future corroboration, this may correspond to a detection of primordial gravitational waves with a fractional power of about 10% of the CMB temperature fluctuations. In the context of inflation this implies an inflationary energy scale close to the scale of Grand Unification, and a large field excursion of the inflationary scalar field. Hence, the inflationary scalar potential needs symmetries to protect it from dangerous quantum corrections. These features strongly motivate the study of high-scale inflation in string theory as a candidate theory of quantum gravity.

We will determine the range of predictions for large-field high-scale inflation in string theory driven by the mechanism of axion monodromy, which was co-discovered by the PI. For this purpose, we will establish a catalog of primary sources for large field ranges from axion monodromy in combination with assistance effects from multiple axion fields. We will analyze the generic effects of the interplay between large-field models of inflation in string theory with its necessary prerequisite, moduli stabilization. Finally, we will study the distribution of inflation mechanisms among the many vacua of string theory. In combination, this gives us a first chance to make string theory testable.

Very recently, the BICEP2 experiment reported the detection of B-mode polarization in the CMB. Pending future corroboration, this may correspond to a detection of primordial gravitational waves with a fractional power of about 10% of the CMB temperature fluctuations. In the context of inflation this implies an inflationary energy scale close to the scale of Grand Unification, and a large field excursion of the inflationary scalar field. Hence, the inflationary scalar potential needs symmetries to protect it from dangerous quantum corrections. These features strongly motivate the study of high-scale inflation in string theory as a candidate theory of quantum gravity.

We will determine the range of predictions for large-field high-scale inflation in string theory driven by the mechanism of axion monodromy, which was co-discovered by the PI. For this purpose, we will establish a catalog of primary sources for large field ranges from axion monodromy in combination with assistance effects from multiple axion fields. We will analyze the generic effects of the interplay between large-field models of inflation in string theory with its necessary prerequisite, moduli stabilization. Finally, we will study the distribution of inflation mechanisms among the many vacua of string theory. In combination, this gives us a first chance to make string theory testable.

## Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The project is well on track with significant progress in WPs 2, 3, 7 and 8, while WP 1, 4, 5, 6, 9 will be addressed later-on as planned, such that all objectives are well on track. STRINGFLATION results in a total of 9 peer-reviewed publications results within the first reporting period.

WP 8: With my former students Benedict Broy and David Ciupke, who both finished their PhD very successfully in summer 2016, we made significant progress concerning WP 8:

In one central result, we were able to complete a quite general analysis of models of exponential plateau inflation in bottom-up effective field theory descriptions where this class of inflation models has unified description using scalar fields with a non-canonically normalized kinetic term with a 2nd-order pole as a function of the non-canonical inflation scalar field, which can be dualized into the presence of a scalar field with non-minimal coupling to Einstein gravity. The observable predictions of these plateau models cluster around the simple Starobinsky-type model values even when a quite broad class of corrections to the scalar potential is taken into account. A second central result was a full understanding of the complete set of higher-derivative corrections to supergravity at the level of 4 superspace derivatives (the leading-order effective action consists of terms with 2 superspace derivatives) and their effects on the supergravity dynamics of scalar fields. These corrections were then successfully employed to build the current state-of-the-art model of exponential plateau inflation in type IIB string theory, an improved class of ‘fibre inflation’ models, which constitutes significant progress for WP 8.

As a part of WP 8, we have started an ongoing multi-field generalization of pole inflation models realizing exponential plateau inflation while using basic structural input for the form of the underlying supergravity from string theory.

WP 7: We extended the analysis of accidentally occurring small-field inflation regions in a high-dimensional scalar potential modelled by a Gaussian random function, as a lowest-order approximation to the moduli supergravity effective action arising from string compactification, this being the main task of WP 7. One major result consists in calculating an estimate for the combined probability of accidental small-field inflation in a Gaussian random potential followed by a graceful exit into a local minimum with small positive cosmological constant as a candidate for our current-day universe. This established that, despite the potentially large number of fields participating, cosmologically viable accidental small-field inflation is exponentially rare compared to any other mechanism driving inflation in string theory, which incorporates more symmetry structure in the scalar potential than given by Gaussian random potential. In a second main result, Mafalda Dias and Jonathan Frazer showed that, despite the rarity of such accidental small-field inflation models, the presence of many fields drives the appearance of a universal and simple form of the observable curvature perturbation 2-point function power spectrum. Finally, this enabled a new and efficient framework to numerically calculate the full curvature perturbation 3-point function (the ‘non-Gaussianity’) in such models with a large number of scalar fields. In the future, this should allow us to look for possible universal feature of the multi-field non-Gaussianity arising from stringy Gaussian random potential accidental small-field inflation setups. For this purpose, we hired Mafalda Dias for the period of 09/2016 – 12/2016 as this allowed us to employ her specific skills in numerical analysis of both the dynamics and the observable 2-point and 3-point function (‘non-Gaussianity’) of the power spectrum of curvature perturbations of inflation models with multiple scalar fields with an arbitrary potential. These were crucial in obtaining the two multi-fiel

WP 8: With my former students Benedict Broy and David Ciupke, who both finished their PhD very successfully in summer 2016, we made significant progress concerning WP 8:

In one central result, we were able to complete a quite general analysis of models of exponential plateau inflation in bottom-up effective field theory descriptions where this class of inflation models has unified description using scalar fields with a non-canonically normalized kinetic term with a 2nd-order pole as a function of the non-canonical inflation scalar field, which can be dualized into the presence of a scalar field with non-minimal coupling to Einstein gravity. The observable predictions of these plateau models cluster around the simple Starobinsky-type model values even when a quite broad class of corrections to the scalar potential is taken into account. A second central result was a full understanding of the complete set of higher-derivative corrections to supergravity at the level of 4 superspace derivatives (the leading-order effective action consists of terms with 2 superspace derivatives) and their effects on the supergravity dynamics of scalar fields. These corrections were then successfully employed to build the current state-of-the-art model of exponential plateau inflation in type IIB string theory, an improved class of ‘fibre inflation’ models, which constitutes significant progress for WP 8.

As a part of WP 8, we have started an ongoing multi-field generalization of pole inflation models realizing exponential plateau inflation while using basic structural input for the form of the underlying supergravity from string theory.

WP 7: We extended the analysis of accidentally occurring small-field inflation regions in a high-dimensional scalar potential modelled by a Gaussian random function, as a lowest-order approximation to the moduli supergravity effective action arising from string compactification, this being the main task of WP 7. One major result consists in calculating an estimate for the combined probability of accidental small-field inflation in a Gaussian random potential followed by a graceful exit into a local minimum with small positive cosmological constant as a candidate for our current-day universe. This established that, despite the potentially large number of fields participating, cosmologically viable accidental small-field inflation is exponentially rare compared to any other mechanism driving inflation in string theory, which incorporates more symmetry structure in the scalar potential than given by Gaussian random potential. In a second main result, Mafalda Dias and Jonathan Frazer showed that, despite the rarity of such accidental small-field inflation models, the presence of many fields drives the appearance of a universal and simple form of the observable curvature perturbation 2-point function power spectrum. Finally, this enabled a new and efficient framework to numerically calculate the full curvature perturbation 3-point function (the ‘non-Gaussianity’) in such models with a large number of scalar fields. In the future, this should allow us to look for possible universal feature of the multi-field non-Gaussianity arising from stringy Gaussian random potential accidental small-field inflation setups. For this purpose, we hired Mafalda Dias for the period of 09/2016 – 12/2016 as this allowed us to employ her specific skills in numerical analysis of both the dynamics and the observable 2-point and 3-point function (‘non-Gaussianity’) of the power spectrum of curvature perturbations of inflation models with multiple scalar fields with an arbitrary potential. These were crucial in obtaining the two multi-fiel

## Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The human condition has expressed itself since time immemorial by a fundamental desire to understand and to know itself, its place within the cosmos, and its origins and future. This desire to understand in the broadest sense drove the three pillars of human civilization – music, the arts, and science (subsuming here mathematics, natural sciences, and humanities on equal footing) – it is through this threefold endeavor that we can rise above the origins of our species. Hence, the expression of our desire to know through the extension of music, artistical expression or basic research is the fundamental purpose and goal of all human civilization and by extension of every functioning human society. Therefore, the progress in understanding of the origin and laws of nature governing the earliest ages of the Universe, and by extension our own ultimate origin, which this project has so far achieved and is further aiming for, constitutes crucial progress for all of society in its primary purpose of sustaining our journey towards understanding the human condition.