New perturbative method for analytical solutions in single-field models of inflation

Ureña–López, L. Arturo

doi:10.1103/physrevd.94.063532

Cited by 20 publications

(30 citation statements)

References 51 publications

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“…To briefly illustrate the difference with respect to the dynamical ones, let us consider the well known example in Class Ia which is the quadratic potential V (φ) = (m 2 φ /2)φ 2 (A = 0, B = m φ / √ 2 and α 2 = 0), where m φ is the mass of the scalar field [40]. It can be shown that for this case y 1i = 2 √ 2B/H i = 2m φ /H i , where H i is the initial value of the Hubble parameter (see also Sec.…”

Section: Refmentioning

confidence: 99%

“…[22]. The particular, polar form of the transformation into a dynamical system which we use in this work was first proposed for dark matter models and the inflationary scenario in [39,40], but see also [41,42] for other related works. As mentioned above, we shall show that there is a general parametrization from which almost all the popular quintessence potentials can be derived.…”

Section: Introductionmentioning

confidence: 99%

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New general parametrization of quintessence fields and its observational constraints

2018

Self Cite

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We present a new parameterization of quintessence potentials for dark energy based directly upon the dynamical properties of the equations of motion. Such parameterization arises naturally once the equations of motion are written as a dynamical system in terms of properly defined polar variables. We have identified two different classes of parameters, and we dubbed them as dynamical and passive parameters. The dynamical parameters appear explicitly in the equations of motion, but the passive parameters play just a secondary role in their solutions. The new approach is applied to the so-called thawing potentials and it is argued that only three dynamical parameters are sufficient to capture the evolution of the quintessence fields at late times. This work reconfirms the arbitrariness of the quintessence potentials as the recent observational data fail to constrain the dynamical parameters. 95.36.+x arXiv:1803.09204v2 [gr-qc]

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Section: Refmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New general parametrization of quintessence fields and its observational constraints

2018

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“…The scalar field energy density and pressure are given by the canonical expressions ρ φ = (1/2)φ 2 + V (φ) and p φ = (1/2)φ 2 − V (φ). We define a new set of polar coordinates as in [28,45,46],…”

Section: Background Dynamicsmentioning

confidence: 99%

Cosmological signatures of ultralight dark matter with an axionlike potential

2017

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Nonlinearities in a realistic axion field potential may play an important role in the cosmological dynamics. In this paper we use the Boltzmann code CLASS to solve the background and linear perturbations evolution of an axion field and contrast our results with those of CDM and the free axion case. We conclude that there is a slight delay in the onset of the axion field oscillations when nonlinearities in the axion potential are taken into account. Besides, we identify a tachyonic instability of linear modes resulting in the presence of a bump in the power spectrum at small scales. Some comments are in turn about the true source of the tachyonic instability, how the parameters of the axionlike potential can be constrained by Ly-α observations, and the consequences in the stability of self-gravitating objects made of axions. INTRODUCTIONModern cosmological observations have brought about a large amount of data [1,2], making it possible to constrain, with high accuracy, theoretical models describing the Universe at large scales. The so-called Lambda Cold Dark Matter (ΛCDM) paradigm is very successful at reproducing cosmological observations [1] but it requires a dark matter (DM) component (≈ 26%), effectively described by collisionless particles that interacts mostly gravitationally with other matter components [3][4][5]. However, there are longstanding discussions about how well the ΛCDM model describes the Universe at galactic and sub-galactic scales [6,7]. The solution to these problems may come from the specific properties of the DM, or from an interplay between the DM properties and kinematic effects with baryons, but still the incompleteness of galactic observations may impair our ability to infer the DM distribution properties from them. Given the current status, the further development of theoretical models still is very much desirable if one is to elucidate the properties of this matter component of the Universe.According to recent studies, axion DM has become a compelling candidate to replace CDM [8][9][10], and even some experiments have been already set up to have a direct detection of this elusive particle [11][12][13][14][15][16]. In particular, there are several proposals for detection of ultralight axions (ULA) using laser interferometers [17], analyzing the frequency and dynamics of pulsars [18,19], and also in gravitational wave detectors [20]. Nonetheless, there are still many open questions such as what is the right axion mass limits one can place by using, for instance, galactic kinematics [21][22][23][24][25], and Lyman-α observations [26,27]. At the cosmological level, axion models have been studied considering it as a free scalar field, i.e., as a scalar field endowed with a quadratic potential V (φ) = m 2 φ 2 /2 [28-33]. However, a more realistic form of the axion potential is the trigonometric one,where m φ is the axion mass and f is the decay constant of the axion. The axion potential (1) originally arose in QCD with the aim to solve the strong CP problem [34][35][36][37], and the poten...

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“…(40) can be written in the form of (26) under the simple change of variable ω = 3 n 0 ln (ω). The same transformation can be applied in the master equation, (45), which is transformed into equation (40). Moreover, if we also apply the transformation (78) to (45), then the latter takes the form of the master equation, (26).…”

Section: Equivalent Transformationsmentioning

confidence: 99%

“…In [31][32][33][34][35][36][37], the perturbative reconstruction approach was applied: the inflaton self-interaction potential, V (φ), of the scalar field, φ, was reconstructed by considering a series expansion around a point φ = φ 0 , where the coefficients of the series expansion for the potentials are determined from the observable values of the scalar spectral index and the usual slow-roll parameters; for more details see [38]. Alternative approaches to the reconstruction of the scalar field potential include a stochastic perturbative approach in [39], or another perturbative approach in [40]. Two alternative methods for the reconstruction of the scalar field potential have been proposed in [41] and [42].…”

Section: Introductionmentioning

confidence: 99%

Reconstructions of the dark-energy equation of state and the inflationary potential

Barrow

Paliathanasis

2018

Gen Relativ Gravit

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We use a mathematical approach based on the constraints systems in order to reconstruct the equation of state and the inflationary potential for the inflaton field from the observed spectral indices for the density perturbations n s and the tensor to scalar ratio r . From the astronomical data, we can observe that the measured values of these two indices lie on a two-dimensional surface. We express these indices in terms of the Hubble slow-roll parameters and we assume that n s − 1 = h (r ). For the function h (r ), we consider three cases, where h (r ) is constant, linear and quadratic, respectively. From this, we derive second-order equations whose solutions provide us with the explicit forms for the expansion scale-factor, the scalar-field potential, and the effective equation of state for the scalar field. Finally, we show that for there exist mappings which transform one cosmological solution to another and allow new solutions to be generated from existing ones.

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New perturbative method for analytical solutions in single-field models of inflation

Cited by 20 publications

References 51 publications

New general parametrization of quintessence fields and its observational constraints

New general parametrization of quintessence fields and its observational constraints

Cosmological signatures of ultralight dark matter with an axionlike potential

Reconstructions of the dark-energy equation of state and the inflationary potential

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