Adiabatic regularization of the power spectrum in nonminimally coupled general single-field inflation

Alinea, Allan L.; Kubota, Takeshi

doi:10.1103/physrevd.97.063513

Cited by 10 publications

(7 citation statements)

References 73 publications

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“…This case is schematically illustrated in figure 3, and corresponds to the situation discussed in refs. [22,25] when the Hubble parameter at a later time during inflation is smaller than the one at horizoncrossing, H(τ )/H(τ * ) ≪ 1. However, for the models β > −2, i.e., H(τ )/H(τ * ) > 1, which refs.…”

Section: Jcap11(2018)006mentioning

confidence: 99%

Adiabatic regularization of power spectrum and stress tensor of relic gravitational wave without low-frequency distortion

Zhang

Wang

2018

J. Cosmol. Astropart. Phys.

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Adiabatic regularization is a method to remove UV divergences in quantum fields in curved spacetime. For relic gravitational wave generated during inflation, regularization on all k-modes of the power spectrum to 2nd adiabatic order, and of the energy density and pressure to 4th order, respectively, causes low-frequency distortions. To avoid these, we regularize only the short modes inside the horizon during inflation (corresponding to the present frequencies f 10 9 Hz), and keep the long modes intact. Doing this does not violate the energy conservation since the k-modes of RGW are independent of each other during inflation. The resulting spectra are UV convergent and simultaneously free of low-frequency distortion, and these properties remain in the present spectra after evolution, in contrast to regularization at the present time which has some distortion or irregularities. The spectra generally exhibit quick oscillations in frequency domain, even if the initial spectra during inflation have no oscillations. This pattern is due to the interference between the positive and negative frequency modes developed during cosmic expansion, and may be probed by future RGW detections.

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Section: Jcap11(2018)006mentioning

confidence: 99%

Adiabatic regularization of power spectrum and stress tensor of relic gravitational wave without low-frequency distortion

Zhang

Wang

2018

J. Cosmol. Astropart. Phys.

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“…Then we take a three-dimensional spherical section of this system and let a 'civilisation' start 1 Readers interested in the so-called Fermi-paradox and colonisation, their analysis and/or proposed solutions within the framework of an effectively static section(s) of the Universe and percolation/cellular automata, may refer to [12][13][14][15][16] and the references therein. 2 For cosmological perturbations in the early Universe and its relation to the horizon, readers may refer to [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Percolation of ‘civilisation’ in a homogeneous isotropic universe

Alinea,

Jadrin

2023

Eur. J. Phys.

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In this work, we consider the spread of a `civilisation' in an idealised homogeneous isotropic universe where all the planets of interest are habitable. Following a framework that goes beyond the usual idea of percolation in common undergraduate computational physics textbooks, we investigate the behaviour of the number of colonised planets with time, and the total colonisation time for three types of universes. These include static, dark energy-dominated, and matter-dominated universes. For all these types of universes, we find a remarkable fit with the Logistic Growth Function for the number of colonised planets with time. This is in spite of the fact that for the matter- and dark-energy dominated universes, the space itself is expanding. For the total colonisation time, T, the case for a dark energy-dominated universe is marked with divergence beyond the linear regime characterised by small values of the Hubble parameter, H. Not all planets in a spherical section of this universe can be `colonised' due to the presence of a shrinking Hubble sphere. In other words, the recession speeds of other planets go beyond the speed of light making them impossible to reach. On the other hand, for a matter-dominated universe, while there is an apparent horizon, the Hubble sphere is growing instead of shrinking. This leads to a finite total colonisation time that depends on the Hubble parameter characterising the universe; in particular, we find T ~ H for small H and T ~ H^2 for large H.

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“…[16][17][18] . Using this knowledge may allow one to perform calculations in the more general model with ease and simplicity as in the derivation of non-gaussianity [19,20], adiabatic regularisation of power spectrum [21,22], or the mere calculation of power spectrum. Furthermore, knowledge of invariance or transformation properties of primordial cosmological perturbations may facilitate in relating one model of inflation to another.…”

Section: Introductionmentioning

confidence: 99%

Transformation of Primordial Cosmological Perturbations Under the General Extended Disformal Transformation

Alinea,

Kubota

2020

Preprint

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Primordial cosmological perturbations are the seeds that were cultivated by inflation and the succeeding dynamical processes, eventually leading to the current Universe. In this work, we investigate the behaviour of the gauge-invariant scalar and tensor perturbations under the general extended disformal transformation, namely, g µν → A(X, Y, Z)g µν + Φ µ Φ ν , where X ≡ − 1 2 φ ;µ φ ;µ , Y ≡ φ ;µ X ;µ , Z ≡ X ;µ X ;µ and Φ µ ≡ Cφ ;µ + DX ;µ , with C and D being a general functional of (φ, X, Y, Z). We find that the tensor perturbation is invariant under this transformation. On the other hand, the scalar curvature perturbation receives a correction due the conformal term only; it is independent of the disformal term at least up to linear order. Within the framework of the full Horndeski theory, the correction terms turn out to depend linearly on the gauge-invariant comoving density perturbation and the first time-derivative thereof. In the superhorizon limit, all these correction terms vanish, leaving only the original scalar curvature perturbation. In other words, it is invariant under the general extended disformal transformation in the superhorizon limit, in the context of full Horndeski theory. Our work encompasses a chain of research studies on the transformation or invariance of the primordial cosmological perturbations, generalising their results under our general extended disformal transformation. Apart from the cosmological perturbations, this work and the transformation considered herein, give us strong impetus to go beyond the current horizon of scalar-tensor theories.

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Adiabatic regularization of the power spectrum in nonminimally coupled general single-field inflation

Cited by 10 publications

References 73 publications

Adiabatic regularization of power spectrum and stress tensor of relic gravitational wave without low-frequency distortion

Adiabatic regularization of power spectrum and stress tensor of relic gravitational wave without low-frequency distortion

Percolation of ‘civilisation’ in a homogeneous isotropic universe

Transformation of Primordial Cosmological Perturbations Under the General Extended Disformal Transformation

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