1. Warm inflation in small field models: a stringy realisation Juan Carlos Bueno Sánchez Lancaster University Work in progress with: M. Bastero-Gil (University of Granada), A. Berera (University of Edinburgh) and K. Dimopoulos (Lancaster University)

2. Radiation production after inflation Inflaton may lose energy non-perturbatively (preheating: non-linear effects ) Weak dissipation: Strong dissipation: Inflaton EOM Cold inflation Introduction Inflaton decay Radiation density (production of radiation during inflation) Warm inflation

3. Equilibrium approach Radiation is close to thermal equilibrium Moss and Xiong ‘07 Warm inflation is very difficult Inflaton may lose energy as well High T: Low T: Yokoyama and Linde ‘99 Chaotic and Hybrid models Bastero-Gil and Berera ‘06 Warm inflation supported for ~ 50-60 e-folds X and Y may belong to large rep. of GUT group with Introduction Dissipation mechanism: Allowed decays with

4. Take inverted potential A small field model Take inflation gives way to radiation domination before Weak dissipation Strong dissipation (with ) Dissipation coefficient

5. Warm inflation  Radiation domination Inflation after horizon exit Spectrum curvature perturbations Spectral index Matching the spectrum

6. Warm inflation in string theory ESP Fixed point of symmetries Trapping mechanism (particle production) Moduli trapping Why an enhanced symmetry point?  m P Strong interaction between and Naturalness of the trapping prefers points with higher number of fields Trapping operates at distances Inflaton is a string modulus passing close to an enhanced symmetry point Environmental selection of larger ESPs typically at Planckian distance

7. Warm inflation in string theory ESP Fixed point of symmetries Trapping mechanism (particle production) Moduli trapping Why an enhanced symmetry point? Strong interaction between and Naturalness of the trapping prefers points with higher number of fields Trapping operates at distances Environmental selection of larger ESPs typically at Planckian distance Environmental selection makes easier to fit the spectrum Inflaton is a string modulus passing close to an enhanced symmetry point

8. gives its oscillation density no overshoot Decay of before inflation Decay of during inflation no overshoot Warm inflation in string theory

9. Decay of before inflation and may overshoot the ESP h is larger but far from its maximum value Warm inflation in string theory

10. Decay of before inflation and may overshoot the ESP h is larger but far from its maximum value Warm inflation in string theory

11. Decay of before inflation and may overshoot the ESP h is larger but far from its maximum value Warm inflation in string theory

12. Decay of before inflation and may overshoot the ESP h is larger but far from its maximum value Warm inflation in string theory

13. Conclusions Full analytical description of inflation in the low-temperature regime. Inflation may finish in weak dissipation, retaining a constant radiation density which may reheat the Universe. Inflation may give way to radiation dominated Universe. Spectral index may be fitted to the observational values by tunning H The observed spectrum may be matched for a wide range of curvatures In particular for String theory (modulus + ESP) may fix initial conditions for warm inflation Initial radiation bath from decay products Strong interaction between fields Trapping provides environmental selection mechanism making easier fit spectrum