scholarly journals Quantum-gravitational effects on gauge-invariant scalar and tensor perturbations during inflation: The slow-roll approximation

2016 ◽  
Vol 94 (12) ◽  
Author(s):  
David Brizuela ◽  
Claus Kiefer ◽  
Manuel Krämer
Keyword(s):  
Gauge Invariant ◽  
Gravitational Effects ◽  
Slow Roll ◽  
Invariant Scalar ◽  
Tensor Perturbations

scholarly journals Inflationary perturbation spectra at next-to-leading slow-roll order in effective field theory of inflation

2019 ◽  
Vol 79 (11) ◽  
Author(s):  
Guang-Hua Ding ◽  
Jin Qiao ◽  
Qiang Wu ◽  
Tao Zhu ◽  
Anzhong Wang
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
High Energy Physics ◽  
Power Spectra ◽  
High Energy ◽  
Effective Field ◽  
Spectral Indices ◽  
Leading Order ◽  
Slow Roll ◽  
Tensor Perturbations

AbstractThe effective field theory (EFT) of inflation provides an essential picture to explore the effects of the unknown high energy physics in the single scalar field inflation models. For a generic EFT of inflation, possible high energy corrections to simple slow-roll inflation can modify both the propagating speed and dispersion relations of the cosmological scalar and tensor perturbations. With the arrival of the era of precision cosmology, it is expected that these high energy corrections become more important and have to be taken into account in the analysis with future precise observational data. In this paper we study the observational predictions of the EFT of inflation by using the third-order uniform asymptotic approximation method. We calculate explicitly the primordial power spectra, spectral indices, running of the spectral indices for both scalar and tensor perturbations, and the ratio between tensor and scalar spectra. These expressions are all written in terms of the Hubble flow parameters and the flow of four new slow-roll parameters and expanded up to the next-to-leading order in the slow-roll expansions so they represent the most accurate results obtained so far in the literature. The flow of the four new slow-roll parameters, which arise from the four new operators introduced in the action of the EFT of inflation, can affect the primordial perturbation spectra at the leading-order and the corresponding spectral indices at the next-to-leading order.

A COVARIANT APPROACH TO THE GENERALIZED MULTI-INFLATON COSMOLOGICAL PERTURBATION

2009 ◽  
Vol 24 (20n21) ◽  
pp. 3893-3916
Author(s):  
JOYDEV LAHIRI ◽  
GAUTAM BHATTACHARYA
Keyword(s):  
Arbitrary Field ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Covariant Approach ◽  
Slow Roll ◽  
Specific Choice ◽  
Basis System ◽  
Friedmann Robertson Walker ◽  
Scalar Part ◽  
Metric Perturbation

Following the formalism developed in Astrophys. J.375, 443 (1991), differential equations for the gauge invariant scalar part of the metric perturbation in the Friedmann–Robertson–Walker background with multiple inflatons with arbitrary field metric are obtained without any specific choice of gauge. Subsequently, an algorithm for the solution of these equations in the slow-roll approximation is given without any prior choice of the basis system in the field manifold. Vector and tensor perturbations are also briefly reviewed.

Helicity decomposition of metric perturbations

2018 ◽  
Author(s):  
Michele Maggiore
Keyword(s):  
Degrees Of Freedom ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Invariant Metric ◽  
Gauge Invariant ◽  
Tensor Perturbations

Decomposition of the perturbations over FRW into scalar, vector and tensor perturbations. Physical and unphysical degrees of freedom. Gauge-invariant metric perturbations, Bardeen variables. Gauge-invariant perturbations of the energy-momentum tensor

scholarly journals THE EFFECTIVE THEORY OF INFLATION IN THE STANDARD MODEL OF THE UNIVERSE AND THE CMB+LSS DATA ANALYSIS

2009 ◽  
Vol 24 (20n21) ◽  
pp. 3669-3864 ◽  
Author(s):  
D. BOYANOVSKY ◽  
C. DESTRI ◽  
H. J. DE VEGA ◽  
N. G. SANCHEZ
Keyword(s):  
Standard Model ◽  
Initial Conditions ◽  
Density Fluctuations ◽  
Effective Theory ◽  
Spontaneous Breaking ◽  
Fourth Degree ◽  
Slow Roll ◽  
The Standard Model ◽  
Tensor Perturbations ◽  
The Universe

Inflation is today a part of the Standard Model of the Universe supported by the cosmic microwave background (CMB) and large scale structure (LSS) datasets. Inflation solves the horizon and flatness problems and naturally generates density fluctuations that seed LSS and CMB anisotropies, and tensor perturbations (primordial gravitational waves). Inflation theory is based on a scalar field φ (the inflaton) whose potential is fairly flat, leading to a slow-roll evolution. This review focuses on the following new aspects of inflation. We present the effective theory of inflation à la Ginsburg and Landau, in which the inflaton potential is a polynomial in the field φ and has the universal form [Formula: see text], where [Formula: see text], M ≪ M Pl is the scale of inflation and N ~ 60 is the number of e-folds since the cosmologically relevant modes exit the horizon till inflation ends. The slow-roll expansion becomes a systematic 1/N expansion and the inflaton couplings become naturally small as powers of the ratio (M/M Pl )2. The spectral index and the ratio of tensor/scalar fluctuations are [Formula: see text], [Formula: see text], while the running index turns out to be [Formula: see text] and therefore can be neglected. The energy scale of inflation M ~ 0.7 × 1016 GeV is completely determined by the amplitude of the scalar adiabatic fluctuations. A complete analytic study plus the Monte Carlo Markov chain (MCMC) analysis of the available CMB+LSS data (including WMAP5) with fourth degree trinomial potentials showed: (a) the spontaneous breaking of the φ → - φ symmetry of the inflaton potential; (b) a lower bound for r in new inflation: r > 0.023 (95% CL) and r > 0.046 (68 CL); (c) the preferred inflation potential is a double-well, even function of the field with a moderate quartic coupling yielding as the most probable values ns ≃ 0.964, r ≃ 0.051. This value for r is within reach of forthcoming CMB observations. The present data in the effective theory of inflation clearly prefer new inflation. Study of higher degree inflaton potentials shows that terms of degree higher than 4 do not affect the fit in a significant way. In addition, a horizon exit happens for [Formula: see text], making higher order terms in the potential w negligible. We summarize the physical effects of generic initial conditions (different from Bunch–Davies) on the scalar and tensor perturbations during slow roll and introduce the transfer function D(k), which encodes the observable initial condition effects on the power spectra. These effects are more prominent in the low CMB multipoles: a change in the initial conditions during slow roll can account for the observed CMB quadrupole suppression. Slow-roll inflation is generically preceded by a short, fast-roll stage. Bunch–Davies initial conditions are the natural initial conditions for the fast-roll perturbations. During fast roll, the potential in the wave equations of curvature and tensor perturbations is purely attractive and leads to a suppression of the curvature and tensor CMB quadrupoles. An MCMC analysis of the WMAP+SDSS data including fast roll shows that the quadrupole mode exits the horizon about 0.2 e-fold before fast roll ends and its amplitude gets suppressed. In addition, fast roll fixes the initial inflation redshift to be z init = 0.9 × 1056 and the total number of e-folds of inflation to be N tot ≃ 64. Fast roll fits the TT, the TE and the EE modes well, reproducing the quadrupole suppression. A thorough study of the quantum loop corrections reveals that they are very small and are controlled by powers of (H/M Pl )2 ~ 10-9, a conclusion that validates the reliability of the effective theory of inflation. The present review shows how powerful the Ginsburg–Landau effective theory of inflation is in predicting observables that are being or will soon be contrasted with observations.

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