Extranatural Inflation Nuno M. C. Santos CFTP - IST Centro de Física Teórica de Partículas Instituto Superior Técnico - Universidade Técnica de Lisboa Center for Theoretical Particle Physics, Technical University of Lisbon PASC Winter School Sesimbra, 21 st December 2007

Dec 21, 2007 Extranatural Inflation 2 Contents  Introduction  Basics of inflation  (Cosine-type) Natural inflation and observations  Pseudo Nambu-Goldstone boson from 5D  Extranatural inflation  5D flat spacetime  Warped background: AdS 5 spacetime  Conclusions ArXiv: [ hep-ph ] In collaboration with R. González Felipe (ISEL and CFTP-IST, Lisbon )

Dec 21, 2007 Extranatural Inflation 3 Basics of Inflation  Inflation has emerged as the most successful model for understanding the physics of the very early universe  In its most general form it consists of a period of accelerated expansion, during which the universe is driven toward flatness and homogeneity  Inflation also provides a mechanism for generating the initial perturbations which led to structure formation in the universe  The key ingredient of this cosmological acceleration is negative pressure, i.e, a fluid with a vacuum-like equation of state,  slowly rolling scalar field  During inflation, quantum fluctuations on small scales are quickly amplified to scales much larger than the horizon size, where they are frozen as perturbations on the background metric  Two types of perturbations: scalar (curvature), which couple to the stress-energy tensor and form the seeds for structure formation, and tensor (gravitational wave), which do not couple to matter

Dec 21, 2007 Extranatural Inflation 4 Basics of Inflation  Models can be constructed by specifying the potential  different choices of the potential predict different spectra for the primordial fluctuations  The basic predictions of slow-roll inflation are very simple: Gaussian, adiabatic scalar and tensor fluctuations will be created with approximately power-law spectra  The scalar spectrum is conventionally parameterized in terms of a spectral index as and the tensor spectrum as  The scalar-to-tensor ratio is another useful parameterization for tensor perturbations Notice that and are not independent. For single-field models one has

Dec 21, 2007 Extranatural Inflation 5 ‘Naturally’ flat potential from Particle Physics  To satisfy the observational constraints (enough e-folds of inflation, explain the CMB anisotropy measurements)  the potential for the inflaton field must be sufficiently flat  Despite the existence of several cosmologically viable inflaton potentials, the construction of a sufficiently flat and stable (against radiative corrections) potential is a difficult task from the particle physics viewpoint  Among the models of inflation which do not suffer from the fine-tuning problem, the so-called natural inflation is a simple and well-motivated framework. Particularly simple are those realizations which involve a pseudo Nambu-Goldstone boson (pNGB) #, with a potential generally of the form # In particle physics models, Nambu-Goldstone bosons arise whenever a global symmetry is spontaneously broken. If there is an additional explicit symmetry breaking, these particles become pseudo- Nambu-Goldstone bosons. spontaneous breaking scale explicit breaking scale Freese, Frieman & Olinto, PRL 1990 … Savage et al, PRD 2006

Dec 21, 2007 Extranatural Inflation 6 Natural inflation and observations From a field theoretical description it is difficult to justify such Planckian value  The right amplitude for the scalar perturbations gives  Sufficiently flat potential  large values of But …

Dec 21, 2007 Extranatural Inflation 7 Pseudo Nambu-Goldstone boson from 5D Falkowski, PRD 2007  Consider a 5D gauge theory with a gauge group G and the fifth dimension compactified in a finite interval, y  [0,L]  Once the 5D gauge symmetry is broken down to a subgroup of G the fifth components of the gauge fields along the broken gauge group generators give rise to scalar excitations with a flat potential at tree level  These scalars can be viewed as 4D pseudo Nambu-Goldstone bosons  The effective one-loop potential for the pseudo Nambu-Goldstone boson can be derived form factors which depend on the specific 5D background (are in principle calculable) and will depend on quantities that can be related to 5D geometrical quantities for gauge (fermion) particles discrete number that depends on the gauge group structure

Dec 21, 2007 Extranatural Inflation 8 Pseudo Nambu-Goldstone boson from 5D Falkowski, PRD 2007  In the cases we will be interested in the form factors are well approximated by  The energy scales are related to 5D geometrical quantities  The warp factor describes the ‘nature’ of the 5D spacetime.  It can be flat or warped Compositeness scale in 4D Effective low energy coupling  AdS 5 spacetime / RSI  flat Minkowski spacetime

Dec 21, 2007 Extranatural Inflation 9 Extranatural inflation In the following we will only consider one zero gauge mode ( ) and identify the corresponding scalar field with the inflaton Performing the integration, one can see that for the potential has the usual cosine form flat warped

Dec 21, 2007 Extranatural Inflation 10 Extranatural inflation in a 5D flat spacetime Arkani-Hamed et al, PRL 2003 Hofmann et al, NPB 2003 … Gauge inflation: the inflaton is the extra component of a gauge field in a 5D theory compactified in a circle A small value of the effective 4D gauge coupling is required

Dec 21, 2007 Extranatural Inflation 11 Extranatural inflation in AdS 5 spacetime  Let us consider the case where the fifth dimension is a slice of AdS5, which corresponds to the so-called Randall-Sundrum I (RSI) model.  In this model the warp factor is given by  The energy scale corresponds to the curvature of AdS 5, which is related to the negative bulk cosmological constant  The two branes localized at y=0 and y=L have opposite tensions Randall & Sundrum, PRL 1999

Dec 21, 2007 Extranatural Inflation 12 Extranatural inflation in AdS 5 spacetime

Dec 21, 2007 Extranatural Inflation 13 Conclusions  It is possible to obtain successful inflation in different 5D backgrounds  f still with Planckian values, but in this framework f is only an effective quantity  It is possible to derive bounds on the 5D quantities. The bounds imposed on the warped 5th dimension are quite restrictive:, an upper bound which is too small to naturally generate a TeV mass scale at the IR brane  The 4D effective coupling is very small in all the cases considered,, seems unavoidable in the natural inflation scenario  The predicted running of the spectral index is negligible, however larger values can be obtained if we consider additional zero modes. A pNGB inflaton potential of the form is an excellent approximation for the case where both a bosonic and a fermionic zero modes contribute to the inflaton potential. If Feng et al, PRD 2003