Loop Quantum Cosmology: holonomy corrections to inflationary models

Artymowski, Michał; Lalak, Zygmunt; Szulc, Łukasz

doi:10.1088/1475-7516/2009/01/004

Cited by 35 publications

(37 citation statements)

References 30 publications

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“…Singularity resolution is confirmed for a large set of initial conditions, in confirmation with the generic result on resolution of singularities in Bianchi-I spacetime in LQC [56]. In contrast to the isotropic inflationary models in LQC where there is a single bounce of the isotropic scale factor [57][58][59][60][61][62][63][64] always occurring at the maximum allowed value of the energy density ρ max = 0.41 ρ Pl , the resolution of singularity in Bianchi-I spacetime occurs via non-singular bounces of the three directional scale factors (a 1 , a 2 , a 3 ) occurring at a range of values of energy density and anisotropic shear scalar σ 2 , bounded by ρ max (same as in the isotropic model) and σ 2 max = 11.57/l 2 Pl . In the isotropic LQC, ρ = ρ max at the bounce constrains the value of the inflaton velocity at the bounce for a given initial value of the inflaton field.…”

Section: Introductionsupporting

confidence: 75%

A quantum gravitational inflationary scenario in Bianchi-I spacetime

Gupt¹,

Singh²

2013

Class. Quantum Grav.

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We investigate the φ 2 inflationary model in the Bianchi-I spacetime using the effective spacetime description of loop quantum cosmology to understand the issues of the resolution of initial singularity, isotropization, effect of anisotropies on the amount of inflation, and the phase space attractors in the presence of non-perturbative quantum gravitational modifications. A comparative analysis with the classical theory by including more general initial conditions than the ones previously considered in the latter is also performed. We show that, in general, the classical singularity is replaced by a bounce of the mean scale factor in loop quantum cosmology. Due to the underlying quantum geometric effects, the energy density of the inflaton and the anisotropic shear remain bounded throughout the non-singular evolution. Starting from arbitrary anisotropic initial conditions, a loop quantum universe isotropizes either before or soon after the onset of slow-roll inflation. We find a double attractor behavior in the phase space dynamics of loop quantum cosmology, similar to the one in classical theory, but with some additional subtle features. Quantum modifications to the dynamical equations are such that, unlike the classical theory, the amount of inflation does not monotonically depend on the initial anisotropy in loop quantum cosmology. Our results suggest that a viable non-singular inflationary model can be constructed from highly anisotropic initial conditions in the Planck regime.

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Section: Introductionsupporting

confidence: 75%

A quantum gravitational inflationary scenario in Bianchi-I spacetime

Gupt¹,

Singh²

2013

Class. Quantum Grav.

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“…[21,22]. Finally, we should obtain the spectrum of the tensor perturbations in the form shown in Fig.…”

Section: Suppressing Low Cmb Multipoles With a Bounce+inflation Scenariomentioning

confidence: 99%

Gravitational waves from the big bounce

Mielczarek

2008

J. Cosmol. Astropart. Phys.

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In this paper we investigate gravitational waves production during the Big Bounce phase inspired by the Loop Quantum Cosmology. We consider the influence of the holonomy corrections to the equation for tensor modes. We show that they act like additional effective graviton mass, suppressing gravitational waves creation. However, this effects can be treated perturbatively. We investigate the simplified model without these corrections and find its exact analytical solution. For this model we calculate a spectrum of the gravitational waves from the Big Bounce phase. The obtained spectrum decreases to zero for the low energy modes. Based on this observation we indicate that this effect can lead to the low CMB multipoles suppression and gives a potential way to test Loop Quantum Cosmology models. We also consider a scenario with a post-bounce inflationary phase. The obtained power spectrum gives qualitative explanation of the CMB spectra, including low multipoles suppression. This result is a challenge to construct a consistent bounce+inflation model in the Loop Quantum Cosmology.

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“…[24]. There is also an alternative approach to incorporate loop quantum corrections to cosmological perturbations developed in Refs.…”

Section: Introductionmentioning

confidence: 99%

Inflationary power spectra with quantum holonomy corrections

Mielczarek¹

2014

J. Cosmol. Astropart. Phys.

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Abstract. In this paper we study slow-roll inflation with holonomy corrections from loop quantum cosmology. Both tensor and scalar power spectra of primordial perturbations are computed up to the first order in slow-roll parameters and V /ρ c , where V is a potential of the scalar field and ρ c is a critical energy density (expected to be of the order of the Planck energy density). Possible normalizations of modes at short scales are discussed. In case the normalization is performed with use of the Wronskian condition applied to adiabatic vacuum, the tensor and scalar spectral indices are not quantum corrected in the leading order. However, by choosing an alternative method of normalization one can obtain quantum corrections in the leading order. Furthermore, we show that the holonomy-corrected equation of motion for tensor modes can be derived from an effective background metric. This allows us to prove that the Wronskian normalization condition for the tensor modes preserves the classical form.

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Loop Quantum Cosmology: holonomy corrections to inflationary models

Cited by 35 publications

References 30 publications

A quantum gravitational inflationary scenario in Bianchi-I spacetime

A quantum gravitational inflationary scenario in Bianchi-I spacetime

Gravitational waves from the big bounce

Inflationary power spectra with quantum holonomy corrections

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