Inflation in String Theory - Connecting Quantum Gravity with Observations

Project Information

STRINGFLATION

Grant agreement ID: 647995

DOI

10.3030/647995

Project closed

EC signature date 22 May 2015

Start date 1 October 2015

End date 31 March 2022

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 854 750,00

EU contribution

€ 1 854 750,00

Coordinated by

DEUTSCHES ELEKTRONEN-SYNCHROTRON DESY
Germany

Periodic Reporting for period 5 - STRINGFLATION (Inflation in String Theory - Connecting Quantum Gravity with Observations)

Reporting period: 2021-10-01 to 2022-03-31

Summary of the context and overall objectives of the project

The project “STRINGFLATION” aimed at predicting the energy scale of cosmological inflation & the strength of the inflationary gravitational wave signal from string theory. The results help us to understand the structure of the very early Universe & its fundamental laws of nature a bit better. It thus advances knowledge – the primary purpose of society: The expression of our desire to know the Universe & ourselves in depth & complexity, through the extension of music, artistical expression or basic research, is the fundamental purpose & goal of all human civilization & by extension of every functioning human society – because on these three pillars we can rise above the origins of our species.
The theory of inflation predicts a background of primordial gravitational waves. If these are strong enough to be detectable as polarization patterns in the cosmic microwave background radiation, inflation happens at such a high energy scale that it ‘feels’ quantum gravity.
Therefore, the project goal was to determine the range of predictions for large-field high-scale inflation in string theory (a candidate theory of quantum gravity) driven by the mechanism of axion monodromy (co-discovered by the PI). In combination with a study of the distribution of inflation mechanisms among the many vacua of string theory, this gives us a first chance to make string theory testable.
The project concluded while reaching its goal: We showed, that the mechanism of axion monodromy inflation predicts a fractional strength of primordial gravitational waves above 0.6%. The two further string theory mechanisms for high-scale inflation currently known provide at this point a preliminary prediction for this fraction to be above 0.1%. A failure to detect this fraction above the value of 0.1% with future measurements of the B-mode polarization in the cosmic microwave background radiation caused by gravitational waves from inflation (e.g. by the CMB Stage 4 program or the Japanese LiteBIRD satellite) would put serious observational pressure on string theory, ultimately allowing us to test & potentially disfavor it.

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

All of the project’s objectives have been achieved. STRINGFLATION so far results in a total of 46 publications, more are in progress. Due to the character limit, the work is highlighted via the most relevant publications (all on arXiv), also indicating collaborations:

WP2 & 1:
1610.05320: L. McAllister (Cornell U.), P. Schwaller, G. Servant, J. Stout (Utrecht U.) & PI;
1705.08950: G. D’Amico (CERN), N. Kaloper (UC Davis), A. Padilla (Nottingham U.), D. Stefanyszyn (Groningen U.) & PI;
1707.08678: J. Moritz, A. Retolaza & PI;
1805.00944: J. Moritz & T. van Riet;
1809.06618: J. Moritz, A. Retolaza Π
1812.03999: A. Hebecker & S. Leonhardt (both Heidelberg U.), J. Moritz & PI;
1902.01412: F. Carta, J. Moritz & PI;
2003.04902 & publicly available software code performing the relevant classification: F. Carta, J. Moritz & PI; also important for WP1 & WP5
2110.02963: F. Carta (Durham U., UK), A. Mininno (IFT Madrid), N. Righi (QU) & PI;

WP2 & 4:
1512.03768: A. Hebecker (Heidelberg U.), F. Rompineve (Heidelberg U.) & PI;
1807.06579: M. Dias, J. Frazer, A. Retolaza & PI;

WP3:
1810.05199: M. Dias, J. Frazer & PI;
We leveraged machine learning algorithms to directly learn the stochastic map from microscopic inflation model parameters to CMB observables. This in turn allowed us to show that single-field axion monodromy inflation predicts r > 0.015 irrespective of string theory details.
2002.02952: V. Domcke, V. Guidetti (Bologna U.), Y. Welling & PI;
2007.04322: F. Carta, N. Righi (QU), Y. Welling & PI; relevant for WP5 as well
2101.05861 & 2112.13861: G. D’Amico (Parma U.), N. Kaloper (UC Davis) & PI;
The results allowed us to analytically capture the map of the leading ‘theory error’ onto the CM observables. We used this structure to establish the lower bound r > 0.006 for the general string theory derived effective quantum field theory capturing all extant models of axion monodromy inflation. This is the central result of STRINGFLATION in relation to its primary task.
2103.08662 & publicly available software code – python/tensorflow based software package dNNsolve, a new deep neural network architecture to efficiently solve differential equations: V. Guidetti, F. Muia (DAMTP Cambridge, UK), Y. Welling & PI – building on initial experience in 1810.05199.

WP5:
1910.09568: F. Carta, S. Giacomelli (Oxford U.), H. Hayashi (Tokai U.) & R. Savelli (INFN & Rome U.);
2002.07816: F. Carta & A. Mininno (IFT Madrid);
2008.01027: M. Akhond (Swansea U.), F. Carta, S. Dwivedi (SCU, Chengdu), H. Hayashi (Tokai U., Hiratsuka) & S.-S. Kim (Chengdu U. of Sci. Tech.); highly relevant for aspects of WP5, WP1 & WP2
2104.13847: G. Ballesteros (IFT Madrid), A. Ringwald (DESY), C. Tamarit (TUM, Germany) & Y. Welling;
2110.02964: M. Cicoli (Bologna U.), V. Guidetti, N. Righi (QU) & PI;

WP6:
1901.03657: A. Achucarro (Leiden U.), E. J. Copeland (Nottingham U.), O. Iarygina (Leiden U.), G. A. Palma (Chile U.), D.-G. Wang (Leiden U.) & Y. Welling;
1907.02020: A. Achucarro (Leiden U.) & Y. Welling;
1907.02951: Y. Welling;
1908.06956: A. Achucarro (Leiden U.), G. A. Palma (Chile U.), D.-G. Wang (Leiden U.) & Y. Welling;
2101.07272 & publicly available software code + database performing the computation of the database of all genus-0 GV invariants of all CICYs with less than 10 volume moduli: F. Carta (Durham U., UK), A. Mininno (IFT Madrid), N. Righi (QU) & PI; also relevant for WP3
2204.13124: N. Kaloper (UC Davis) & PI;

WP7:
1604.05970: M. Dias, J. Frazer & M. C. D. Marsh (Cambridge U.);
1606.07768: F. Pedro (IFT & UAM Madrid) & PI;
1609.00379: M. Dias, J. Frazer, D. J. Mulryne (Queen Mary U.) & D. Seery (Sussex U.);
1611.07059: F. Pedro (IFT & UAM Madrid) & PI;
1706.03774: M. Dias, J. Frazer & M. C. D. Marsh (Cambridge U.);
1710.08913: S. Hotinli (Imperial Coll.), J. Frazer, A. H. Jaffe (Imperial Coll.), J. Meyers (CITA) & L. C. Price (Carnegie Mellon)

WP8:
1604.05326: B. Broy, D. Croone (Groningen U.) & D. Roest (Groningen U.);
1605.00651: D. Ciupke;
1609.03570: B. Broy;
1707.05830: R. Kallosh (Stanford), A. Linde (Stanford), D. Roest (Groningen U.), Y. Yamada (Stanford) & PI;
1805.02659: M. Dias, J. Frazer, A. Retolaza, M. Scalisi & PI.

WP9 is currently being addressed in collaboration with a new DESY postdoc, J. Leedom. This collaboration is nearing completion with a publication planned for June 2022.

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)

Discovery of new axionic states of string theory compactifications unknown prior to 2018 – so called ‚thraxions‘;
Use of neural networks to predict a lower bound on the future detectable gravitational wave signal from inflation for axion monodromy inflation in string theory;
Constructing a full effective field theory for monodromy inflation with several axions, we give the first general prediction for the minimal gravitational wave signal for axion inflation in string theory; future failure to detect a signal of such strength can rule out string axion inflation & put pressure on string theory itself; – this answers the main goal of the project;
Development of a new neural network structure capable of efficiently learning to numerically solve a wide range of differential equations, with public software code dNNsolve;
Discovery of a few rather universal axion states in string theory which can provide fuzzy dark matter solving several problems with conventional cold dark matter models.

Graphic description of the project's main theme