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, 21st 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: AdS5 spacetime

Conclusions

ArXiv: 0711.0022 [ 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

AdS5 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 2003Hofmann 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 AdS5 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 AdS5, 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 AdS5 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