Decoherence of gauge-invariant metric fluctuations during inflation

Abstract

I study the gauge-invariant fluctuations of the metric during inflation. In the infrared sector the metric fluctuations can be represented by a coarse-grained field. We can write a Schrödinger equation for the coarse-grained metric fluctuations which is related to an effective Hamiltonian for a time dependent parameter of mass harmonic oscillator with a stochastic external force. I study the wave function for a power-law expanding universe. I find that the phase space of the quantum state for super Hubble scalar metric perturbations loses its coherence at the end of inflation. This effect is a consequence of interference between the super Hubble metric perturbations and its canonical conjugate variable, which is produced by the interaction of the coarse-grained scalar metric fluctuation with the environment.PACS numbers: 98.80.Cq, 04.62.+vThe inflationary model [1] solves several difficulties which arise from the standard cosmological model, such as the horizon, flatness and monopole problems, and it provides a mechanism for the creation of primordial density of fluctuations, nedeed to explain the structure formation [2]. The most widely accepted approach assumes that the inflationary phase is driving by a quantum scalar field ϕ associated to a scalar potential V (ϕ). Within this perspective, the stochastic inflation proposes to describe the dynamics of this quantum field on the basis of two pieces: the homogeneous and inhomogeneous components. Usually the homogeneous one is interpreted as a classical field φ c (t) that arises from the vacuum expectation value of the quantum field. The inhomogeneous component φ( x, t) are the quantum fluctuations. The field that take into account only the modes with wavelengths larger than the now observable universe is called coarse-grained field and its dynamics is described by a second order stochastic equation [3].Stochastic inflation has played an important role in inflationary cosmology in the last two decades. This approach gives the possibility to make a description of the matter field fluctuations in the infrared (IR) sector by means of the coarse-grained matter field [2,4]. Since these perturbations are classical on super Hubble scales, in this sector one can make a standard stochastic treatment for the coarse-grained matter field. The IR sector is very important because the spatially inhomogeneities in super Hubble inflationary scales would explain the present day observed matter structure in the universe. Matter field fluctuations are responsible for metric fluctuations around the background Friedmann-RobertsonWalker (FRW) metric. When these metric fluctuations do not depend on the gauge, the perturbed globally flat isotropic and homogeneous universe is described by [5] where a is the scale factor of the universe and (ψ, χ) are the perturbations of the metric. In the particular case where the tensor T αβ is diagonal, one obtains: χ = ψ [6]. I consider a semiclassical expansion for the scalar field ϕ( x, t) = φ c (t) + φ( x, t) [3], with expectation values 0|ϕ|0 = φ c...

Observational constraints on quantum decoherence during inflation

“…Clearly, the structures observed today are classical objects and the question of how the quantum-toclassical transition occurred in a cosmological context remains unanswered and has been the subject of many investigations . It is widely believed that decoherence [37][38][39] could have played an important role in that process [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. On more general grounds, cosmological fluctuations have to couple (at least gravitationally) to the other degrees of freedom present in the Universe.…”

Non Gaussianities from quantum decoherence during inflation

“…It is usually believed to be especially relevant for microphysical systems. More recently however, it has also been shown to be of interest in cosmology [5][6][7][8][9][10][11][12][13][14][15][16][17]. The reason is that, according to the theory of cosmic inflation [18][19][20], all structures originate from quantum fluctuations in the early universe [21,22].…”

Quantum Imprints on CMBR

“…For a more extensive study of this phenomenon, one may refer to [70][71][72][73][74][75][76][77]. It is widely believed that decoherence [74,107,108] could have played an important role in the process of classicalization of inflationary perturbations [46,[79][80][81]87,[109][110][111][112][113][114][115][116][117][118][119][120][121][122]. As was discussed in [119], cosmological fluctuations couple (at least gravitationally) to the other degrees of freedom present in the universe, treated as an open quantum system.…”