Extranatural Inflation Nuno M. C. Santos CFTP - IST Centro de Física Teórica de Partículas...
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Transcript of Extranatural Inflation Nuno M. C. Santos CFTP - IST Centro de Física Teórica de Partículas...
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