Preinflationary and inflationary fast-roll eras and their signatures in the low CMB multipoles

Journal Article · Mon Mar 15 04:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.063520· OSTI ID:21409384

Destri, C ^[1]; Vega, H J. de ^[2]; Sanchez, N G ^[3]

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1. Dipartimento di Fisica G. Occhialini, Universita Milano-Bicocca and INFN, sezione di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano (Italy)
2. LPTHE, Universite Pierre et Marie Curie (Paris VI) et Denis Diderot (Paris VII), Laboratoire Associe au CNRS UMR 7589, Tour 24, 5eme. etage, Boite 126, 4, Place Jussieu, 75252 Paris, Cedex 05 (France)
3. Observatoire de Paris, LERMA, Laboratoire Associe au CNRS UMR 8112 and 61, Avenue de l'Observatoire, 75014 Paris (France)

We study the entire coupled evolution of the inflaton {phi}(t) and the scale factor a(t) for general initial conditions {phi}(t{sub 0}) and d{phi}(t{sub 0})/dt at a given initial time t{sub 0}. The generic early Universe evolution has three stages: decelerated fast roll followed by inflationary fast roll and then inflationary slow roll (an attractor always reached for generic initial conditions). This evolution is valid for all regular inflaton potentials v({phi}). In addition, we find a special (extreme) slow-roll solution starting at t=-{infinity} in which the fast-roll stages are absent. At some time t=t{sub *}, the evolution backwards in time from t{sub 0} reaches generically a mathematical singularity where a(t) vanishes and the Hubble parameter becomes singular. We determine the general behavior near the singularity. The classical homogeneous inflaton description turns to be valid for t-t{sub *}>10t{sub Planck} well before the beginning of inflation, quantum loop effects are negligible there. The singularity is never reached in the validity region of the classical treatment and therefore it is not a real physical phenomenon here. Fast-roll and slow-roll regimes are analyzed in detail including the equation of state evolution, both analytically and numerically. The characteristic time scale of the fast-roll era turns to be t{sub 1}=(1/m){radical}(V(0)/[3M{sup 4}]){approx}10{sup 4}t{sub Planck}, where V is the double-well inflaton potential, m is the inflaton mass, and M the energy scale of inflation. The whole evolution of the fluctuations along the decelerated and inflationary fast-roll and slow-roll eras is computed. The Bunch-Davies initial conditions are generalized for the present case in which the potential felt by the fluctuations can never be neglected. The fluctuations feel a singular attractive potential near the t=t{sub *} singularity (as in the case of a particle in a central singular potential) with exactly the critical strength (-1/4) allowing the fall to the center. Precisely, the fluctuations exhibit logarithmic behavior describing the fall to t=t{sub *}. The power spectrum gets dynamically modified by the effect of the fast-roll eras and the choice of Bunch-Davies initial conditions at a finite time through the transfer function D(k) of initial conditions. The power spectrum vanishes at k=0.D(k) presents a first peak for k{approx}2/{eta}{sub 0} ({eta}{sub 0} being the conformal initial time), then oscillates with decreasing amplitude and vanishes asymptotically for k{yields}{infinity}. The transfer function D(k) affects the low cosmic microwave background multipoles C{sub l}: the change {Delta}C{sub l}/C{sub l} for 1{<=}l{<=}5 is computed as a function of the starting instant of the fluctuations t{sub 0}. Cosmic microwave background quadrupole observations indicate large suppressions, which are well reproduced for the range t{sub 0}-t{sub *} > or approx. 0.05/m{approx_equal}10 100t{sub Planck}.

• OSTI ID: 21409384
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 6 Vol. 81; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
79 ASTRONOMY AND ASTROPHYSICS
AMPLITUDES
ATTRACTORS
COSMOLOGICAL MODELS
ELECTROMAGNETIC RADIATION
EQUATIONS
EQUATIONS OF STATE
FLUCTUATIONS
FUNCTIONS
HUBBLE EFFECT
INFLATIONARY UNIVERSE
MASS
MATHEMATICAL MODELS
MATHEMATICAL SOLUTIONS
MICROWAVE RADIATION
MULTIPOLES
RADIATIONS
RELICT RADIATION
SINGULARITY
SPECTRA
TRANSFER FUNCTIONS
UNIVERSE
VARIATIONS