15 research outputs found
Clarifying Slow Roll Inflation and the Quantum Corrections to the Observable Power Spectra
Slow-roll inflation can be studied as an effective field theory. The form of
the inflaton potential consistent with the data is V(phi) = N M^4
w(phi/[sqrt{N} M_{Pl}]) where phi is the inflaton field, M is the inflation
energy scale, and N ~ 50 the number of efolds. The dimensionless function
w(chi) and field chi are O(1). This form of the potential encodes the slow-roll
expansion as an expansion in 1/N.A The Hubble parameter, inflaton mass and
non-linear couplings are of the see-saw form in terms of M/M_{Pl}. The quartic
coupling is lambda~1/N (M/M_{Pl})^4. The smallness of the non-linear couplings
is not a result of fine tuning but a natural consequence of the validity of the
effective field theory and slow roll approximation. Quantum corrections to slow
roll inflation are computed and turn to be an expansion in powers (H/M_{Pl})^2.
The corrections to the inflaton effective potential and its equation of motion
are computed, as well as the quantum corrections to the observable power
spectra. The near scale invariance of the fluctuations introduces a strong
infrared behavior naturally regularized by Delta=(n_s -1)/2+r/8. We consider
scalar curvature and tensor perturbations as well as light scalars and Dirac
fermions coupled to the inflaton.The subhorizon part is completely specified by
the trace anomaly of the fields with different spins and is solely determined
by the space-time geometry. This inflationary effective potential is strikingly
different from the usual Minkowski space-time result.Quantum corrections to the
power spectra are expressed in terms of the CMB observables. Trace anomalies
(especially the graviton part) dominate these quantum corrections in a definite
direction: they enhance the scalar curvature fluctuations and reduce the tensor
fluctuations.Comment: 20 pages, 1 figure, Opening Lecture at JGRG15 Tokyo, Japan, November
2005. Lecture at Miami05, Key Biscayne, Florida, December 200
Constraints on dark matter particles from theory, galaxy observations and N-body simulations
Mass bounds on dark matter (DM) candidates are obtained for particles
decoupling in or out of equilibrium with {\bf arbitrary} isotropic and
homogeneous distribution functions. A coarse grained Liouville invariant
primordial phase space density is introduced. Combining its
value with recent photometric and kinematic data on dwarf spheroidal satellite
galaxies in the Milky Way (dShps), the DM density today and -body
simulations, yields upper and lower bounds on the mass, primordial phase space
densities and velocity dispersion of the DM candidates. The mass of the DM
particles is bound in the few keV range. If chemical freeze out occurs before
thermal decoupling, light bosonic particles can Bose-condense. Such
Bose-Einstein {\it condensate} is studied as a dark matter candidate. Depending
on the relation between the critical()and decoupling()temperatures, a
BEC light relic could act as CDM but the decoupling scale must be {\it higher}
than the electroweak scale. The condensate tightens the upper bound on the
particle's mass. Non-equilibrium scenarios that describe particle production
and partial thermalization, sterile neutrinos produced out of equilibrium and
other DM models are analyzed in detail obtaining bounds on their mass,
primordial phase space density and velocity dispersion. Light thermal relics
with and sterile neutrinos lead to a
primordial phase space density compatible with {\bf cored} dShps and disfavor
cusped satellites. Light Bose condensed DM candidates yield phase space
densities consistent with {\bf cores} and if also with cusps.
Phase space density bounds from N-body simulations suggest a potential tension
for WIMPS with .Comment: 27 pages 8 figures. Version to appear in Phys. Rev.
Quantum corrections to the inflaton potential and the power spectra from superhorizon modes and trace anomalies
We obtain the effective inflaton potential during slow roll inflation by
including the one loop quantum corrections to the energy momentum tensor from
scalar curvature and tensor perturbations as well as quantum fluctuations from
light scalars and light Dirac fermions generically coupled to the inflaton.
During slow roll inflation there is a clean and unambiguous separation between
superhorizon and subhorizon contributions to the energy momentum tensor. The
superhorizon part is determined by the curvature perturbations and scalar field
fluctuations: both feature infrared enhancements as the inverse of a
combination of slow roll parameters which measure the departure from scale
invariance in each case.Fermions and gravitons do not exhibit infrared
divergences. The subhorizon part is completely specified by the trace anomaly
of the fields with different spins and is solely determined by the space-time
geometry. The one-loop quantum corrections to the amplitude of curvature and
tensor perturbations are obtained to leading order in slow-roll and in the
(H/M_PL)^2 expansion. This study provides a complete assessment of the
backreaction problem up to one loop including bosonic and fermionic degrees of
freedom. The result validates the effective field theory description of
inflation and confirms the robustness of the inflationary paradigm to quantum
fluctuations. Quantum corrections to the power spectra are expressed in terms
of the CMB observables:n_s, r and dn_s/dln k. Trace anomalies (especially the
graviton part) dominate these quantum corrections in a definite direction: they
enhance the scalar curvature fluctuations and reduce the tensor fluctuations.Comment: 18 pages, no figure
Particle decay during inflation: self-decay of inflaton quantum fluctuations during slow roll
Particle decay during inflation is studied by implementing a dynamical
renormalization group resummation combined with a small Delta expansion. Delta
measures the deviation from the scale invariant power spectrum and regulates
the infrared. In slow roll inflation, Delta is a simple function of the slow
roll parameters epsilon_V, eta_V.We find that quantum fluctuations can
self-decay as a consequence of the inflationary expansion through processes
which are forbidden in Minkowski space-time. We compute the self-decay of the
inflaton quantum fluctuations during slow roll inflation.For wavelengths deep
inside the Hubble radius the decay is enhanced by the emission of ultrasoft
collinear quanta, i.e. bremsstrahlung radiation of superhorizon quanta which
becomes the leading decay channel for physical wavelengths
H<<k_{ph}(eta)<<H/(eta_V-eps_V). The decay of short wavelength fluctuations
hastens as the physical wave vector approaches the horizon. Superhorizon
fluctuations decay with a power law eta^Gamma in conformal time where in terms
of the amplitude of curvature perturbations Delta^2_R, the scalar spectral
index n_s, the tensor to scalar ratio r and slow roll parameters: Gamma \simeq
[32 xi^2_V Delta^2_R]/ /(n_s-1+r/4)^2.The behavior of the growing mode
eta^{eta_V-epsilon_V+Gamma}/eta features an anomalous scaling dimension Gamma.
We discuss the implications of these results for scalar and tensor
perturbations and for non-gaussianities in the power spectrum. The recent WMAP
data suggests Gamma >3.6 10^{-9}.Comment: 27 pages, LaTex, 5 .eps figures, to appear in Phys. Rev.
CMB quadrupole suppression: II. The early fast roll stage
Within the effective field theory of inflation, an initialization of the
classical dynamics of the inflaton with approximate equipartition between the
kinetic and potential energy of the inflaton leads to a brief fast roll stage
that precedes the slow roll regime. The fast roll stage leads to an attractive
potential in the wave equations for the mode functions of curvature and tensor
perturbations. The evolution of the inflationary perturbations is equivalent to
the scattering by this potential and a useful dictionary between the scattering
data and observables is established.Implementing methods from scattering theory
we prove that this attractive potential leads to a suppression of the
quadrupole moment for CMB and B-mode angular power spectra. The scale of the
potential is determined by the Hubble parameter during slow roll. Within the
effective field theory of inflation at the grand unification (GUT) energy scale
we find that if inflation lasts a total number of efolds N_{tot} ~ 59, there is
a 10-20% suppression of the CMB quadrupole and about 2-4% suppression of the
tensor quadrupole. The suppression of higher multipoles is smaller, falling off
as 1/l^2. The suppression is much smaller for N_{tot} > 59, therefore if the
observable suppression originates in the fast roll stage, there is the upper
bound N_{tot} ~ 59.Comment: Some comments and references adde
Inflation and nonequilibrium renormalization group
We study de spectrum of primordial fluctuations and the scale dependence of
the inflaton spectral index due to self-interactions of the field. We compute
the spectrum of fluctuations by applying nonequilibrium renormalization group
techniques.Comment: 6 pages, 1 figure, submitted to J. Phys.
The Lyth Bound and the End of Inflation
We derive an extended version of the well-known Lyth Bound on the total
variation of the inflaton field, incorporating higher order corrections in slow
roll. We connect the field variation to both the spectral index of
scalar perturbations and the amplitude of tensor modes. We then investigate the
implications of this bound for ``small field'' potentials, where the field
rolls off a local maximum of the potential. The total field variation during
inflation is {\em generically} of order , even for potentials with
a suppressed tensor/scalar ratio. Much of the total field excursion arises in
the last e-fold of inflation and in single field models this problem can only
be avoided via fine-tuning or the imposition of a symmetry. Finally, we discuss
the implications of this result for inflationary model building in string
theory and supergravity.Comment: 10 pages, RevTeX, 2 figures (V3: version accepted for publication by
JCAP
Clarifying Inflation Models: Slow-roll as an expansion in 1/N_{efolds}
14 pages, no figures, version to appear in Phys Rev DSlow-roll inflation is studied as an effective field theory.We find as consistent form of the inflaton potential V(phi)=N M^4 w(phi/[sqrt{N}M_P]) where phi is the inflaton field, M the inflation energy scale, M_P the Planck mass, and N~50 the number of efolds since the relevant modes exited the horizon till the end of inflation. The dimensionless function w(chi) and field chi are O(1). The WMAP value for the amplitude of scalar adiabatic fluctuations |\Delta_{k ad}^(S)| fixes the inflation scale M ~ 0.77 10^16 GeV precisely at the GUT scale. This general form of the potential makes manifest that the slow roll expansion is an expansion in 1/N. Powers of 1/N count the orders in the slow roll expansion.This form of the inflaton potential suggests that the super symmetry breaking scale is at the inflation and GUT scales.A Ginzburg-Landau realization of this inflaton potential reveals that Hubble, inflaton mass and non-linear couplings are of the see-saw form in terms of the small ratio M/M_P. For example, the quartic coupling lambda ~ 1/N (M/M_P)^4.The smallness of the non-linear couplings is not a result of fine tuning but a natural consequence of the validity of the effective field theory. We clarify the Lyth bound which relates the tensor/scalar ratio and the value of phi/M_P.Effective field theory is valid for V(phi
Quantum corrections to slow roll inflation and new scaling of superhorizon fluctuations
21 pages, 1 figurePrecise cosmological data from WMAP and forthcoming CMB experiments motivate the study of the quantum corrections to the slowroll inflationary parameters.We find the quantum (loop) corrections to the equations of motion of the classical inflaton, its quantum fluctuations and the Friedmann equation in general single field slow roll inflation.We implement a renormalized effective field theory EFT approach based on an expansion in (H/M_{Pl})^2 and slow roll parameters epsilon_V,eta_V,sigma_V, xi_V.We find that the leading order quantum corrections to the inflaton effective potential and its equation of motion are determined by the power spectrum of scalar fluctuations. Its near scale invariance introduces a strong infrared behavior naturally regularized by the slow roll parameter Delta = eta_V-epsilon_V=(n_s-1)/2+r/8.To leading order in the EFT and slow roll expansions we find V_{eff}(Phi_0)=V_R(Phi_0)[1+(Delta^2_T/32)(n_s-1+3r/8) /(n_s-1+r/4)+higher orders]where n_s and r=Delta^2_T/Delta^2_R are the CMB observables that depend implicitly on Phi_0, and V_R(Phi_0) is the renormalized classical inflaton potential.This effective potential during slow roll inflation is strikingly different from the Minkowski space-time result.Superhorizon scalar field fluctuations grow for late times eta -> 0^- as |\eta|^{-1+Delta-d_} where d_ is a novel quantum correction to the scaling exponent related to the self decay of superhorizon inflaton fluctuations eta is the conformal time. We generalize this to the case of the inflaton interacting with a light scalar field. These quantum corrections arising from interactions will compete with higher order slow-roll corrections and must be taken into account for the precision determination of inflationary parameters
The Effective Theory of Inflation in the Standard Model of the Universe and the CMB+LSS data analysis
Review article, 134 pages, 41 figuresInternational audienceInflation is part of the Standard Model of the Universe supported by CMB and large scale structure LSS datasets. This review presents new developments of inflation in three main chapters. (I): The effective theory of inflation a la Ginsburg-Landau (GL): the inflaton potential is a polynomial with universal form making explicit the inflation energy scale M, the Planck mass and the inflation e-folds number N ~ 60. The slow-roll expansion becomes a systematic 1/N expansion and the inflaton couplings are naturally small as powers of (M/M_{Pl})^2. The spectral index (n_s - 1) and the ratio of tensor/scalar fluctuations r are O(1/N), the running index is O(1/N^2). M ~ 0.7 10^{16} GeV is completely determined by the scalar adiabatic fluctuations amplitude. (II): A Monte Carlo Markov Chains (MCMC) analysis of the CMB+LSS data (including WMAP5) with our analytic theoretical results yields: a lower bound for r (new inflation): r > 0.023 (95%CL), r > 0.046 (68%CL); the preferred inflation potential is a double well, even function of the field yielding as most probable values n_s ~ 0.964, r ~ 0.051. This value for r is within reach of forthcoming CMB observations. Slow-roll inflation is generically preceded by a short fast-roll stage which leads to a suppression of the CMB quadrupoles. MCMC analysis of the WMAP+SDSS data shows that fast-roll fits the TT, TE and EE modes well reproducing the quadrupole suppression and fixes the total number of efolds of inflation to be N_{total} ~ 64. (III) Quantum loop corrections are very small and controlled by powers of (H /M_{Pl})^2 ~ 10^{-9} which validates the effective theory of inflation. We show how powerful is the GL theory of inflation in predicting observables