In models of natural inflation, the inflaton is an axion-like particle. Unfortunately, axion potentials in UV-complete theories appear to be too steep to drive inflation. We show that, even for a steep potential, natural inflation can occur if the coupling between axion and gauge fields is taken into account. Due to this coupling, quanta of the gauge field are produced by the rolling of the axion. If the coupling is large enough, such a dissipative effect slows down the axion, leading to inflation even for a steep potential. The spectrum of perturbations is quasi-scale invariant, but in the simplest construction its amplitude is larger than 10 −5 . We discuss a possible way out of this problem.PACS numbers: 98.80.CqAxion-like particles are the simplest spin-zero degrees of freedom with a nontrivial radiatively stable potential. Moreover, they are abundant in string theory. As a consequence, axions provide excellent inflaton candidates in a UV complete theory that includes gravity. Inflation driven by axions was proposed as early as in 1990 as natural inflation [1]. The axion potential is radiatively stable thanks to a (broken) shift symmetry, and has the form V (Φ) = Λ 4 [cos(Φ/f ) + 1], where f is the axion constant. Neglecting all interactions of Φ apart from those in V (Φ) and those with gravity, the condition for inflation is that V (Φ) is flat in units of the Planck scale (i.e.,for a sufficiently wide range of Φ. In the case of the axion, these conditions are equivalent to f ≫ M P . Unfortunately, string theory appears not to allow such large values of f [2]. Moreover, f < ∼ M P appears also as a consequence of the "gravity as the weakest force" conjecture of [3].In this paper, we show that natural inflation can be realized also for a steep potential. Our mechanism relies on the coupling of the inflaton to gauge fields through the operator Φ F µνF µν . As Φ rolls down its potential, it provides a time-dependent background for the gauge field whose vacuum fluctuations are thus amplified into physical excitations. This production of quanta of gauge field occurs at the expenses of the kinetic energy of the inflaton, slowing it down. If the coupling between Φ and F µν is strong enough, such a dissipation effect can allow to obtain a sufficiently long period of inflation even if f ≪ M P . This way, the question of finding natural inflation in string theory is formulated in a new way: is there, among the many axions of string theory [4], one whose coupling to the gauge fields is large enough? We will argue in Appendix B that the answer to this question might be positive.

There is increasing interest in the role played by pseudo Nambu–Goldstone bosons (pNGBs) in the construction of string-inspired models of inflation. In these models the inflaton is expected to be coupled to gauge fields, and will lead to the generation of magnetic fields that can be of cosmological interest. We study the production of such fields mainly focusing on the model of N-flation, where the collective effect of several pNGBs drives inflation. Because the fields produced are maximally helical, inverse cascade processes in the primordial plasma significantly increase their coherence length. We discuss under what conditions inflation driven by pNGBs can account for the cosmological magnetic fields observed. A constraint on the parameters of this class of inflationary scenarios is also derived by requiring that the magnetic field does not backreact on the inflating background.

In [1], we have proposed a model where natural inflation is realized on a steep potential (V (φ) ∼ cos(φ/f ) with f M P ) as a consequence of the interaction of the inflaton with gauge fields through the coupling φ F µνF µν . In the present work we study the nongaussianities and the spectrum of tensor modes generated in this scenario. The nongaussianities turn out to be compatible with current observations and can be large enough to be detectable by Planck. The non-observation of tensor modes imposes new constraints on the parameter space of the system that are about one order of magnitude stronger than those found in [1]. More importantly, in certain regions of the parameter space tensor modes might be detected by upcoming Cosmic Microwave Background experiments even if inflation occurs at energies as low as the TeV scale. In this case the tensor modes would be chiral, and would lead to distinctive parity-violating correlation functions in the CMB.

We show that maximally helical hypermagnetic fields produced during pseudoscalar inflation can generate the observed baryon asymmetry of the universe via the B + L anomaly in the Standard Model. We find that most of the parameter space of pseudoscalar inflation that explains the cosmological data leads to baryon overproduction, hence the models of natural inflation are severely constrained. We also point out a connection between the baryon number and topology of the relic magnetic fields. Both the magnitude and sign of magnetic helicity can be detected in future diffuse gamma ray data. This will be a smoking gun evidence for a link between inflation and the baryon asymmetry of the Universe.PACS numbers: 98.80.Cq, 12.15.-y.

We study the phase structure of N =1 supersymmetric Yang-Mills theory on R 3 × S 1 , with massive gauginos, periodic around the S 1 , with Sp(2N ) (N ≥2), Spin(N ) (N ≥5), G 2 , F 4 , E 6 , E 7 , E 8 gauge groups. As the gaugino mass m is increased, with S 1 size and strong coupling scale fixed, we find a first-order phase transition both for theories with and without a center. This semiclassically calculable transition is driven, as in SU (N ) and G 2 [1,2], by a competition between monopole-instantons and exotic topological "molecules"-"neutral" or "magnetic" bions. We compute the trace of the Polyakov loop and its twopoint correlator near the transition. We find a behavior similar to the one observed near the thermal deconfinement transition in the corresponding pure Yang-Mills (YM) theory in lattice studies (whenever available). Our results lend further support to the conjectured continuity, as a function of m, between the quantum phase transition studied here and the thermal deconfinement transition in YM theory. We also study the θ-angle dependence of the transition, elaborate on the importance of the quantum-corrected moduli-space metric at large N , and offer comments for the future.