Power-law inflation

Lucchin, F.; Matarrese, S.

doi:10.1103/physrevd.32.1316

Cited by 891 publications

(1,011 citation statements)

References 42 publications

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“…In that case, one has to rely on analytical approximations of numerical calculations. However, the following potential [18] V (φ) = M 4 exp − 4 √ π m Pl…”

Section: Plmentioning

confidence: 99%

Inflation after WMAP3: confronting the slow-roll and exact power spectra with CMB data

Martin

Ringeval

2006

J. Cosmol. Astropart. Phys.

239

374

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Abstract.The implications of the WMAP (Wilkinson Microwave Anisotropy Probe) third year data for inflation are investigated using both the slow-roll approximation and an exact numerical integration of the inflationary power spectra including a phenomenological modelling of the reheating era. At slow-roll leading order, the constraints ǫ 1 < 0.022 and −0.07 < ǫ 2 < 0.07 are obtained at 95% CL (Confidence Level) implying a tensor-to-scalar ratio r 10 < 0.21 and a Hubble parameter during inflation H/m Pl < 1.3 × 10 −5 . At next-to-leading order, a tendency for ǫ 3 > 0 is observed. With regards to the exact numerical integration, large field models, V (φ) ∝ φ p , with p > 3.1 are now excluded at 95% CL. Small field models, V (φ) ∝ 1 − (φ/µ) p , are still compatible with the data for all values of p. However, if µ/m Pl < 10 is assumed, then the case p = 2 is slightly disfavoured. In addition, mild constraints on the reheating temperature for an extreme equation of state w reh −1/3 are found, namely T reh > 2 TeV at 95% CL. Hybrid models are disfavoured by the data, the best fit model having ∆χ 2 ≃ +5 with two extra parameters in comparison with large field models. Running mass models remain compatible, but no prior independent constraints can be obtained. Finally, superimposed oscillations of trans-Planckian origin are studied. The vanilla slow-roll model is still the most probable one. However, the overall statistical weight in favour of superimposed oscillations has increased in comparison with the WMAP first year data, the amplitude of the oscillations satisfying 2|x|σ 0 < 0.76 at 95% CL. The best fit model leads to an improvement of ∆χ 2 ≃ −12 for 3 extra parameters. Moreover, compared to other oscillatory patterns, the logarithmic shape is favoured.

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“…In that case, one has to rely on analytical approximations of numerical calculations. However, the following potential [18] V (φ) = M 4 exp − 4 √ π m Pl…”

Section: Plmentioning

confidence: 99%

Inflation after WMAP3: confronting the slow-roll and exact power spectra with CMB data

Martin

Ringeval

2006

J. Cosmol. Astropart. Phys.

239

374

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“…In general Eqs. (2) and (3) are very difficult, if not impossible, to solve unless the potential has a specific form, as in the exponential model [25]. From the cosmological point of view, however, it is the time-dependence of the scale factor that is important and, in principle, the scalar field potential can be determined directly from high redshift observations [26].…”

Section: Algorithms For Solving the Field Equationsmentioning

confidence: 99%

“…Instead of starting with a form for the potential, an alternative approach is to invert the problem by first specifying the dependence of the scale factor on cosmic time and then solve Eqs. (2) and (3) to reconstruct the corresponding potential [25,27]. Other ansatzes have also been considered in the literature [20,28].…”

Section: Algorithms For Solving the Field Equationsmentioning

confidence: 99%

Ermakov-Pinney equation in scalar field cosmologies

2002

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It is shown that the dynamics of cosmologies sourced by a mixture of perfect fluids and self-interacting scalar fields are described by the non-linear, Ermakov-Pinney equation. The general solution of this equation can be expressed in terms of particular solutions to a related, linear differential equation. This characteristic is employed to derive exact cosmologies in the inflationary and quintessential scenarios. The relevance of the Ermakov-Pinney equation to the braneworld scenario is discussed. reviews, see, e.g., [3]). The simplest mechanism for inflation utilises the potential energy associated with the self-interaction of a scalar inflaton field to drive the accelerated expansion. High redshift observations of type Ia supernovae suggest that the universe is experiencing another phase of accelerated expansion at the present epoch [4]. This, combined with the CMB data, presents a picture of the universe dominated by a dark energy component [5,6]. One possible source of this dark energy is a scalar quintessence field that interacts with baryonic and non-baryonic matter in such a way that its potential energy is currently dominating the cosmic dynamics [7]. The observations favour a model of structure formation where 70% of the energy density of the universe is presently in the form of quintessence [6]. The remaining fraction of the energy density is comprised of visible and cold dark matter which collectively act as a pressureless perfect fluid.The ekpyrotic scenario has recently been proposed as an alternative to the standard inflationary cosmology [8]. In this scenario the big bang is interpreted as the collision of two domain walls or branes travelling through a fifth dimension. Before the collision, the effective dynamics on the four dimensional branes is described by Einstein's gravity minimally coupled to a self-interacting scalar field. The field parametrizes the separation between the branes and at early times slowly rolls down a negative potential. This results in an accelerated collapse of the universe and since the field is minimally coupled, its energy density is related to the Hubble parameter by the standard Friedmann equation. Thus, self-interacting scalar fields play a central role in modern cosmology and in view of the above developments, it is important to investigate cosmologies that contain both a scalar field and a perfect fluid.In this paper, we develop an analytical approach to models of this type by expressing the cosmological field equations in terms of an Ermakov system [9,10,11]. In general, an Ermakov system is a pair of coupled, second-order, non-linear ordinary differential equations (ODEs) [11] and such systems often arise in studies of nonlinear optics [12], nonlinear elasticity [13], molecular structures [14] and quantum cosmology [15]. (For further references, see, e.g., Refs. [16]). In the one-dimensional case, the two equations decouple and the system reduces to a single equation known as the Ermakov-Pinney equation [9,17]. This is given by 1

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“…Perturbed Power Law (PPL) [12,13] is an extension to Power Law (PL) inflationary model [10,[14][15][16] by considering higher order corrections to Hubble parameter. These corrections to Hubble parameter leads to an effective mass for the inflaton field, which in turn affects the density power spectra P ( k).…”

Section: Background Of Perturbed Power Law (Ppl) Model Of Inflationmentioning

confidence: 99%

Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements

Mukherjee

Das

Joy³

et al. 2015

J. Cosmol. Astropart. Phys.

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Cosmic Microwave Background (CMB) is an important probe for understanding the inflationary era of the Universe. We consider the Perturbed Power Law (PPL) model of inflation which is a soft deviation from Power Law (PL) inflationary model. This model captures the effect of higher order derivative of Hubble parameter during inflation, which in turn leads to a non-zero effective mass m eff for the inflaton field. The higher order derivatives of Hubble parameter at leading order sources constant difference in the spectral index for scalar and tensor perturbation going beyond PL model of inflation. PPL model have two observable independent parameters, namely spectral index for tensor perturbation ν t and change in spectral index for scalar perturbation ν st to explain the observed features in the scalar and tensor power spectrum of perturbation. From the recent measurements of CMB power spectra by WMAP, Planck and BICEP-2 for temperature and polarization, we estimate the feasibility of PPL model with standard ΛCDM model. Although BICEP-2 claimed a detection of r = 0.2, estimates of dust contamination provided by Planck have left open the possibility that only upper bound on r will be expected in a joint analysis. As a result we consider different upper bounds on the value of r and show that PPL model can explain a lower value of tensor to scalar ratio (r < 0.1 or r < 0.01) for a scalar spectral index of n s = 0.96 by having a non-zero value of effective mass of the inflaton field m 2 eff H 2 . The analysis with WP+ Planck likelihood shows a non-zero detection of m 2 eff H 2 with 5.7 σ and 8.1 σ respectively for r < 0.1 and r < 0.01. Whereas, with BICEP-2 likelihood m 2 eff H 2 = −0.0237 ± 0.0135 which is consistent with zero.

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Power-law inflation

Cited by 891 publications

References 42 publications

Inflation after WMAP3: confronting the slow-roll and exact power spectra with CMB data

Inflation after WMAP3: confronting the slow-roll and exact power spectra with CMB data

Ermakov-Pinney equation in scalar field cosmologies

Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements

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